Jointly Organised by - KIIT

Jointly Organised by

Prof. Hrushikesha MohantyVice-Chancellor,

KIIT-Deemed to be University

Message

Dr. Shashank ChaturvediDirector

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Prof. Jnyana Ranjan MohantyRegistrar,


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It gives me immense pleasure to convey you that two days Plasma Scholars

Colloquium (PSC 2020) is organized by our Department of Physics, School of

Applied Sciences, KIIT Deemed to be University, Bhubaneswar, and the Plasma

Science Society of India (PSSI) from October 8-9, 2020 on Virtual platform.

In the 21st Century, one of the most important applications of the technology is

based on Plasma Science in all the sector of like industries, agriculture, energy as

well as health. This PSC 2020, especially in this COVID 19 pandemic situation

where the whole world is struggling to get the new normal life. Young

Students/Researchers Colloquium will be very much beneficial for the students

working in the field of Plasma.

I am confident the deliberations and discussion will open a new path to take

forward the Plasma research in the next level

I wish Colloquium (PSC 2020) is a grand success.

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Dr. Puspalata PattojoshiDean SAS,


(Dr. Paritosh Chaudhuri)General Secretary

Plasma Science Society of India (PSSI)

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SAS, KIIT-Deemed to be University

Dr. S. K. S. ParasharConvener

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8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020)

October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

1

CONTENTSCode Title Page

No.Basic Plasma Experiments and Simulations

OL1-1 Cross-field charge particle transport inside a void created by an obstacleinserted in a magnetized plasma column, Satadal Das, IPR

8

OL1-2 Probing Ne ECR plasma to study the gas mixing and anomalous effect,Puneeta Tripathi, IUAC, New Delhi

9

OL1-3: Electrical conductivity of a plasma confined in a dipole magnetic field:systematic experiments and theory, A. Nanda, IIT Kanpur

10

OL1-4: Floating potential fluctuations in atmospheric pressure micro-plasma jets, D.Behmani, IIT Kanpur

11

OL1-5: Comparative study of plasma antenna and monopole metal antenna,Manisha Jha, IPR

12

OL1-6: Magnetic field effects on 13.56 MHz capacitive coupledradio-frequency sheaths, S. Binwal, Jamia Millia Islamia, Delhi

13

OL1-7: Does the fate of 2D incompressible high Reynolds number turbulencedepend on initial conditions? : A revisit! Shishir Biswas, IPR

14

OL1-8: Study on ion re-circulation and potential well structure in an inertialelectrostatic confinement fusion device using 2D-3V PIC simulation,D. Bhattacharjee, CPP-IPR

15

OL1-9: Molecular dynamics simulation of collisional cooling of He and its binarymixtures with Ne, Ar, Kr and Xe for creating strongly coupled cryo plasmas,S. S. Mishra, IIT Kanpur

16

OL1-10: Effects of flow Velocity and Density of Dust Layers on theKelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma: MolecularDynamic Study, Bivash Dolai, Guru Ghasidas Vishwavidyalaya,Bilaspur

17



2

OL1-11: Simulation Study of Planar Anode Micro Hollow Cathode Discharge UsingDielectric Layer, Khushboo Meena, CEERI, Pilani

18

Fusion Science and TechnologyOL2-1: Impact of Energetic Particles in the First-Wall Erosion in Fusion Power

Reactors, P. N. Maya, IPR20

OL2-2: Disruptions study in Aditya-U Tokamak, Suman Dolui, IPR 21

OL2-3: Simulation of runaway electron generation in fusion grade tokamak andsuppression by impurity injection, Ansh Patel, PDPU, Gandhinagar

22

OL2-4: Simultaneous measurement of thermal conductivity and thermal diffusivityof ceramic pebble bed using transient hot-wire technique,Harsh Patel, IPR

24

OL2-5: A DDPM-DEM-CFD flow characteristic analysis of pebble bed for fusionblanket, Chirag Sedani, IPR

25

OL2-6: Initial results of Laser Heated Emissive Probes operated in cold condition inAditya-U Tokamak, A. Karnik, VIT Chennai

28

OL2-7: Evidence Of Non-local Transport in ADITYA-U Tokamak,T. Macwan, IPR

29

OL2-8: Parametric Study of SMBI CD Nozzle for ADITYA-U Tokamak,K. Singh, IPR

30

OL2-9: Study of Sawtooth Induced Heat Pulse Propagation in the ADITYATokamak, S. Patel, PDPU, Gandhinagar

31

OL2-10: Calculation of Toroidal and Poloidal Rotation in Aditya-U Tokamak,A. Kumar, IPR

32

Basic Plasma TheoryOL3-1: Electron-Acoustic Solitary waves in Fermi Plasma with Two-Temperature

Electrons, Ankita Dey, Lady Brabourne College, University ofCalcutta

34

OL3-2: Quantum Electro-static Shock Fronts in Two Component Plasma withNon-thermal Distributive Ion, Subhangi Chakraborty, JIS University,Kolkata

35

OL3-3: Thermal Instability of Two-Component Plasma with Radiative Heat-LossFunctions Frictional Effect of Neutrals and Hall Current, SachinKaothekar, Mahakal Institute of Technology & Management, Ujjain

36



3

OL3-4: Target Shape Effects on the Energy of Ions Accelerated in RadiationPressure Dominant (RPD) Regime, S. Jain, University of Kota, Kota

37

OL3-5: Study of slow mode solitons in a negative ion plasma with superthermalelectrons, X. Mushinzimana, University of Rwanda

38

OL3-6: Effect of the non-thermal electrons on ion-acoustic cnoidal wave inun-magnetized plasmas, P. C. Singhadiya, Seth RLS Govt. College,Rajasthan.

39

OL3-7: Formation of shock fronts in inner magnetospheric plasma,J. Sarkar, Jadavpur University

40

OL3-8: Slow and fast modulation instability and envelope soliton of ion acousticwaves in fully relativistic plasma having nonthermal electrons, IndraniPal, Jadavpur University

41

OL3-9: To Study the Growth Rates of Waves between Piezoelectric and FerroelectricSemiconductor Using QHD Model In Quantum Plasma,Manisha Raghuvanshi, Govt. M.V.M college Shivaji nagar, Bhopal

42

OL3-10 Diagnostics of Ar-CO2 mixture plasma using CR model,N. Shukla, IIT Roorkee

44

OL3-11 Large amplitude ion-acoustic compressive solitons in plasmas withpositrons and superthermal electronsS. K. Jain1, P. C. Singhadiya and J. K. Chawla1Govt. College, Dholpur, Rajasthan, India-328001

45

Dusty Plasma, Laser Plasma, Plasma ApplicationsOL4-1: Study of Arc Fluctuations of a DC Transferred Arc Plasma,

S. P. Sethi, CSIR-IMMT, Bhubaneswar47

OL4-2: Inductive Energy Storage System with Plasma opening Switch: A review,Kanchi Sunil, BARC, Mumbai

48

OL4-3: Role of plasma sheath in the energy management during plasma surfacemodification of polymer, Bivek Pradhan Sikim Manipal University

49

OL4-4: Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) plasmaregion, Siba Prasad Acharya, SINP, Kolkata

50

OL4-5: Effect of negative charge dust on ion-acoustic dressed solitons inun-magnetized plasmas, J K Chawla, Govt. College Tonk, Rajasthan

51

OL4-6: Effect of collision on dust–ion acoustic shock wave in dusty plasma withnegative ions, Jyotirmoy Goswami, Jadavpur University.

52



4

OL4-7: Equilibrium configuration of self gravitating dusty plasmas, M. Shukla,Jawaharlal Nehru College, Pasighat.

53

OL4-8: Strong and collimated terahertz radiation by photo mixing of Hermite CoshGaussian lasers in collisional plasma, Sheetal Chaudhary, CCSU, Meerat

54

OL4-9: Effect of laser pulse profile on controlling the growth ofRayleighTaylor instability in radiation pressure dominant regimeKrishna Kumar Soni, University of Kota, Kota

55

OL4-10: Laser-driven radially polarized terahertz radiation generation in hot Plasma,Manendra, CCSU, Meerat

56

FULL PAPERPSC-1 Simulation of runaway electron generation in fusion grade tokamak

and suppression by impurity injectionAnsh Patel1, Santosh P. Pandya21School of Liberal Studies, PanditDeendayal Petroleum University,Gandhinagar, India2Institute for Plasma Research, Bhat, Gandhinagar, India.

58

PSC-2 Effects of flow Velocity and Density of Dust Layers on theKelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma:Molecular Dynamic StudyBivash Dolai and R. P. PrajapatiDepartment of Pure and Applied Physics, Guru GhasidasVishwavidyalaya, Bilaspur-495009 (C.G.), India

63

PSC-3 Study on ion re-circulation and potential well structure in an inertialelectrostatic confinement fusion device using PIC simulationD. Bhattacharjee1, S. Adhikari2 and S. R. Mohanty1, 31Center of Plasma Physics-Institute for Plasma Research, Sonapur,Kamrup(m), Assam, 782402, India2Department of Physics, University of Oslo, PO Box 1048 Blindern,NO-0316 Oslo, Norway3Homi Bhabha National Institute, Anushaktinagar, Mumbai,Maharashtra, 400094, India

70

PSC-4 Slow and fast modulation instability and envelope soliton of ionacoustic waves in fully relativistic plasma having nonthermalelectronsIndrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,21 Department of Physics, Jadavpur University, Kolkata-700032, India2East Kolkata Centre for Science Education and ResearchP-1, B.P.Township, Kolkata-700 094, India

75



5

PSC-5 Effect of negative charge dust on ion-acoustic dressed solitons inunmagnetized plasmasJ. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2Department of Physics, Govt. College Tonk, Rajasthan, India-3040011Seth RLS Govt. College, Kaladera, Rajasthan, India-3038012Govt. College, Dholpur, Rajasthan, India-328001

80

PSC-6 Inductive Energy Storage System with Plasma Opening Switch: AreviewKanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,21Homi Bhabha National Institute, Mumbai-400094,2Pulsed Power & Electro-Magnetics Division, Bhabha AtomicResearch Centre Facility, Atchutapuram, Visakhapatnam, AndhraPradesh, India-531011

85

PSC-7 Simulation Study of Planar Anode Micro Hollow Cathode DischargeUsing Dielectric LayerKhushboo Meena1, R P Lamba11CSIR-Central Electronics Engineering Research Institute(CSIR-CEERI), Pilani-333031, Rajasthan, India.

91

PSC-8 Effect of laser pulse profile on controlling the growth ofRayleigh-Taylor instability in radiation pressure dominant regimeKrishna Kumar Soni, Shalu Jain, N.K. Jaiman, and K.P.MaheshwariDepartment of Pure & Applied Physics, University of Kota,Kota-324005 (Rajasthan)

96

PSC-9 Effect of the nonthermal electrons on ion-acoustic cnoidal wave inunmagnetized plasmasP. C. Singhadiya1, J. K. Chawla2, S. K. Jain1Seth RLS Govt. College, Kaladera, Rajasthan, India-3038012Department of Physics, Govt. College Tonk, Rajasthan, India-304001Govt. College, Dholpur, Rajasthan, India-328001

101

PSC-10 Target Shape Effects on the Energy of Ions Accelerated in theRadiation Pressure Dominated (RPD) RegimeS. Jain, K. K. Soni, N. K. Jaiman, K. P. MaheshwariDepartment of Pure & Applied Physics, University of Kota,Kota-324005 (Rajasthan)

106

PSC-11 Effect of magnetic field on the sheath width of a 13.56 MHz radiofrequency capacitive argon dischargeS Binwal1, S K Karkari2, L Nair11Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi,110025, India2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar,Gujarat, 382428, India

111



6

PSC-12 Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO)plasma regionS. P. Acharya1, a, A. Mukherjee2, b, and M. S. Janaki1, c1Saha Institute of Nuclear Physics, Kolkata, India2National University of Science and Technology, “MISiS”, Moscow,Russia

116

PSC-13 Large amplitude ion-acoustic solitons in plasmas with positrons andtwo superthermal electronsS. K. Jain1, P. C. Singhadiya2 and J. K. Chawla1Govt. College, Dholpur, Rajasthan, India-3280012Seth RLS Govt. College, Kaladera, Rajasthan, India-303801Department of Physics, Govt. College Tonk, Rajasthan, India-304001

122



7

Basic PlasmaExperiments

&Simulations



8

OL1-1

Cross-field charge particle transport inside a void created by anobstacle inserted in a magnetized plasma column

Satadal Das1, S.K.Karkari21 Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, India, HBNI2 Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, India, HBNI

e-mail: [email protected]

Voids are created inside plasma when a macroscopic object blocks the transmission of chargeparticles from a high density region to a low density region or during a situation where primarysource of ionization is annulled by an obstacle. The phenomena leads to a creation of local spacecharge, which intern can affect the ion dynamics in the region around the obstacle. Such effectsare commonly seen in the case of dusty plasma and around cosmic objects such as commentarytail or an artificial satellite revolving in geo-stationary orbits around the earth. The voidformation is common in laboratory plasmas; for example a shadow gets created behind anelectrostatic probe or a limiter in a magnetized plasma. The formation of particle free regions in rfdischarges under microgravity conditions is also a well-known phenomenon. It was commonlyaccepted that the ion drag force is responsible for the formation of particle free region in thecentral part of discharge. The ion drag force is driven by an outflow of positive ions from anionizing region towards the surrounding particle free diffused region. If the plasma is stronglymagnetized, the electric potential created by the void can strongly affect the dynamics of chargeparticles around the obstacle.

In this talk, a study on radial potential and density variation inside a void created in a partiallymagnetized plasma column shall be presented. The void is created by partially blocking theanode of a hot cathode filament discharge produced in argon. It will be shown that the filling rateof charge particles inside the ionization free region increases with application of magnetic field.With increasing the axial magnetic field strength, the collision probability between chargedparticles and neutrals increases, which leads to higher drag force. The increase in drag forcetowards the center leads to faster filling of charged particles inside void. A simple force balanceequation in combination with short-circuiting effect is adequate to describe the void formationmatching precisely with our experimental data.

References[1] Khrapak, S. A., Ivlev, A. V., Morfill, G. E., & Thomas, H. M. (2002). Ion drag force incomplex plasmas. Physical review E, 66(4), 046414.[2] Zafiu, C., Melzer, A., & Piel, A. (2002). Ion drag and thermophoretic forces acting on freefalling charged particles in an rf-driven complex plasma. Physics of plasmas, 9(11), 4794-4803.[3] Akdim, M. R., & Goedheer, W. J. (2001). Modeling of voids in colloidal plasmas. PhysicalReview E, 65(1), 015401.[4] Simon, A. (1955). Ambipolar diffusion in a magnetic field. Physical Review, 98(2), 317.[5] Das, Satadal, and Shantanu K. Karkari. "Positive ion impediment across magnetic field in apartially magnetized plasma column." Plasma Sources Science and Technology (2019).[6] Lieberman, M. A., & Lichtenberg, A. J. (2005). Principles of plasma discharges and materialsprocessing. John Wiley & Sons.



9

OL1-2

Probing Ne ECR plasma to study the gas mixing and anomalous effect

Puneeta Tripathi*, Sushant Kumar Singh, Pravin KumarInter-University Accelerator Centre, New Delhi, India-110067

*E-mail: [email protected]

The Electron Cyclotron Resonance (ECR) ion source [1] is well known for producingmultiply charged ions with relatively high intensity especially for particle accelerators.The first ECR ion source built by the inventor, (Late) Richard Geller, was reported inearly 1970’s. Since then, there have been substantial improvements in its performancedue to new emerging technologies. The 4th generation superconducting ECR ion sourcesshow beam intensities in the order of emA, which are remarkable, and have opened upnew channels of their applications. Apart from design technologies, the gas mixingexperiments [2, 3] also help to build high intensity of highly charged ions in ECRplasmas. In continuation of earlier efforts for understanding the gas mixing andsubsequent anomalous effect with Xe and Kr plasma, we recently performed anexperiment with pure and mixed (with oxygen and helium gases at various levels) NeECR plasma using LEIBF [4] at IUAC, New Delhi, India. The new results are quiteinteresting and shed more light on the understanding of these two important plasmaprocesses. The charge state distribution of pure, oxygen and helium mixed Ne ECRplasma will be discussed to address the important findings of gas mixing effect andisotope anomaly.

References:[1] R. Geller, Electron Cyclotron Resonance Ion Sources and ECR Plasmas, IOP, Bristol

(1996)[2] A G Drentje, Nucl. Instr. and Meth. in Phys. Res. B, 9 (1985) 526[3] A. G. Drentje, A. Kitagawa, and M. Muramatsu, Rev. Sci. Instrum. 81 (2010) 02B502[4] P. Kumar, G. Rodrigues, U.K. Rao, C.P. Safvan, D. Kanjilal, A. Roy, Pramana-Ind. J.

Phys. 59 (2002)805



10

OL1-3

Electrical conductivity of a plasma confined in a dipole magnetic field:systematic experiments and theory

A. Nanda and S. BhattacharjeeDepartment of Physics, Indian Institute of Technology Kanpur, India


The plasma confined by a dipole magnetic field emerges as the host to a multitude of fascinatingphysics phenomena, due to its unique confinement scheme while relies on plasmacompressibility. For understanding of the underlying transport mechanisms in dipole plasmas,investigation on one of the fundamental properties such as electrical conductivity is inevitable.There have been some reports of earlier works primarily on theoretical progress in conductivity;and their applications to both laboratory and space plasma [1,2]. However, unlike a true dipolefield, most of the works consider the magnetic field along a particular direction only [3,4]. Oneof these pioneering works in the ionospheric plasma assumes a plasma sheet surrounding theearth, by taking the angle of dip into account, and neglecting normal components of theassociated electric field [4]. However, despite such advancements, the magnetic geometry andthe physics of the real problem do not seem to have been addressed in totality. Therefore,electrical conductivity in a bidirectional (r,) magnetic dipole field still remains unexplored, byincluding possible couplings between the all the magnetic and the electric field components.

The present study relies on the measurements from a compact dipole plasma device [5,6] havingplasma size ≫ size of the magnet, and thus the conventional approximations of plasma sheet andunidirectional magnetic field may not hold in the voluminous plasma. To address the problem, amathematical model is formulated using the momentum equation, by considering the net velocitydue to all possible particle drifts. The statistical nature of plasma is preserved by modifying thecollision parameter by averaging it over the experimentally measured electron energydistribution function [7]. The Ohm’s law is derived, from which the conductivity dyad is obtained.The dyad constitutes of one Pedersen, two Hall and three longitudinal terms in contrast to theprevious works having single terms for each type of conductivity. A unique finding which hasnot been reported earlier is the explicit magnetic field dependence (both individual and coupledcomponent wise) in the longitudinal terms of the conductivity.

In the colloquium, results of the above-mentioned investigation will be presented. The reasonbehind the existence of multiple Hall and longitudinal terms, and the explicit field dependenceobserved in the longitudinal terms will be discussed.

References[1] V. Rohansky, Rev. Plasma Phys., 24, 1-52 (2008).[2] R. A. Trueman et al., Front. Phys.: Space Phys., 1, 31 (2013).[3] P. Porazik et al., Phys. Plasmas, 24, 052121 (2017).[4] K. I. Maeda, Journal of Atmospheric and Terrestrial Physics, 39, 1041 (1977).[5] A. R. Baitha et al., Plasma Res. Express, 1, 045005 (2019).[6] A. R. Baitha et al., AIP Advances, 10, 045328 (2019).[7] G. G. Lister et al., J. Appl. Phys., 79, 12 (1996).



11

OL1-4

Floating potential fluctuations in atmospheric pressuremicro-plasma jets

D. Behmani, K. Barman, and S. BhattacharjeeDepartment of Physics, Indian Institute of Technology, Kanpur, Uttar Pradesh: 208016


Potential fluctuations play an important role in the transport of charged particles, and are knownto give rise to instabilities in the plasma. Characterization of fluctuations in atmosphericmicro-plasma jets is crucial due to its broad applications in biomedicine [1], surface treatment oftissues, cancer cells, and wounds [2], and surface alteration of polymers [3]. Fluctuations andnon-uniformities in the potential (or the electrical field) can disrupt thetransport and heating of particles penetrating the target surface, which is further knownto control the activation energy and adhesive properties of the surface. Therefore, fluctuations ofthe above-mentioned parameters in the plasma jet must be analysed for the reliability of theapplications.

The objective of the current work is to analyse potential fluctuations in atmospheric pressuremicro-plasma jets. The plasma is generated inside a glass capillary tube by applying high voltageand charge particles emerge from the capillary in the atmospheric air as a fine plasma jet of ~10mm in length and ~0.8 mm in diameter. A two-pin probe with a diameter of 0.18 mm and a lengthof 2 mm each is used to measure the floating potential at two neighbouring points (separated by0.267 mm) inside the jet.

Conventional techniques such as Fast Fourier transform (FFT) and synchro squeezedtime-frequency analysis (TFA) are used to analyse the fluctuations [4]. It is found that most of thefluctuations are of low frequency and lie in the range 0 – 20 kHz. The dependence of fluctuationson the operating parameters such as applied voltage, gas flow-rates, and working gas mixtureratio (helium and argon) has been studied. It has been observed that at a constant flow rate (1l/min), the fluctuation increases with increase in the applied voltage (from 7 kV to 11 kV), thenachieves a maximum value at 11 kV, owing to the high discharge current at that particular voltageand then decreases. At a fixed applied voltage of 14 kV, when the gas flow rate is increased, theplasma jet becomes turbulent at a flowrate of 3 l/min and the turbulent regime has a significantlyhigher level of fluctuations. In the case of a gaseous mixture of He and Ar, various generalproperties of argon gas, e.g. poor thermal conductivity and lower ionization potential relative tohelium gas, make the argon jet extremely unstable than the helium jet. Time-frequency analysisalso helps to understand the fluctuating behavior of the micro-plasma jet, where the temporalbehavior of the frequencies can be observed. The present research is helpful in choosing suitableoperating parameters and gas as per the requirements of the application.

References[1] Sousa J S, Niemi K, Cox L, Algwari Q T, Gans T and O'connell D J. Appl. Phys. 109 123302

(2011).[2] Tian W, Lietz A M, and Kushner M J Plasma Sources Sci. Technol. 25 055020 (2016).[3] Penkov O V, Khadem M, Lim W S and Kim D E J. Coat. Technol. Res. 12 225-235 (2015).[4] Tu X, Yan J, Yu L, Cen K and Cheron B Appl. Phys. Lett. 91 13 (2007).



12

OL1-5

Comparative study of plasma antenna and monopole metal antenna

Manisha Jha1, Nisha Panghal, Dr. Rajesh Kumar1Institute for Plasma Research, Gujarat


Plasma antenna is a column of ionized gas which can be used to receive and transmitelectromagnetic waves for communication, stealth and radar purpose. The change in the plasmadensity can help to reconfigure the antenna electrically rather than mechanically. This property ofplasma antenna makes it more attractive than a conventional metal antenna. In this paper, amonopole plasma antenna is designed in CST for communication in VLF range. Further acomparative study between the monopole metal and plasma antenna is done in terms of returnloss, VSWR, gain, Bandwidth which shows that the metal can be replaced by plasma column inantennas.

References[1]Rajneesh Kumar,Study of RF Produced Plasma Columns thesis by, Gujarat University, andAhmedabad[2]Theodore Anderson, Plasma Antennas



13

OL1-6

Magnetic field effects on 13.56 MHz capacitive coupledradio-frequency sheaths

S Binwal1, S K Karkari2, L Nair11Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi, 110025, India

2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar, Gujarat, 382428, India


Radio-frequency discharges produced by capacitive driven parallel plate electrodes are widelypopular in semi-conductor industries for the processing of silicon substrates. The ion energy andion flux are the two important parameters in the discharge which governs the physical andchemical processes happening at the substrate. The ions are mainly accelerated inside the sheathswhere almost the entire rf voltage is concentrated. The sheath region depends on the plasmaparameters namely the electron density, electron temperature and the potential drop across thesheaths. External means of controlling the plasma parameters is necessary by means of which theplasma processes at the substrates can be tailored. This may be achieved by introducing anexternal magnetic field, which can enhance the discharge efficiency by influencing the collisionrate [1]. Not only will the magnetic field confine the charge particles inside the bulk plasma, itwill also affect the sheath impedance which controls the rf current flowing through the discharge.Simulation studies have recently demonstrated the effect of magnetic field on the electrontemperature and the sheath width in capacitive discharges. However the experimentalmeasurements could not be performed due to the sheath dimensions being extremely small.

In this paper we discuss about a non-invasive method for determining the sheath width ina 13.56 MHz rf discharge in the presence of an external magnetic field. Further, the effectof magnetic field, discharge current and pressure on the capacitive sheaths is investigated. Theexperimental results report almost 55.5 % reduction in the sheath width for the argon dischargeoperating at 1.0 Pa background pressure and 7.0 mT of applied magnetic field compared with theunmagnetized case. The results suggest that the magnetic field can be used as a controlling knobto tune the sheath width and hence the ion bombarding energy in a single frequency capacitivedischarge. This can enable the user to optimize the processing window in a desirable manner.

References[1] Passive inference of collision frequency in magnetized capacitive argon discharge. Physics

of Plasmas 25.3 (2018)



14

OL1-7

Does the fate of 2D incompressible high Reynolds number turbulencedepend on initial conditions? : A revisit!

Shishir Biswas1, Rajaraman Ganesh11Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, HBNI, India.


In two dimensional (2D) incompressible, nearly inviscid fluid turbulence, inverse cascade ofvorticity is enforced as total energy and total circulation are nearly conserved, along with severalweakly conserved higher order Casimirs [1]. In the past, several competing “extremization” ideashave been looked into, to “predict” the final or late-time fate of this inverse cascade process, suchas, a fluid entropy extremization model [1] and a fluid enstrophy extremization model [2,3]. Inthe past, these models have also been looked into using numerical simulations.In this work, using a newly developed, 2D high precision, very large scale GPU solver which canhandle �th�� grid sizes easily, we revisit the above discussed idea: does one always obtain thesame final state of vorticity at large scales or are there pockets of initial conditions which wouldlead to very different late time large scale vorticity profiles? We consider initial conditions withvarious values of initial total positive circulation Ct

+= ωt+� x,y,t = t dx dy and initial total

negative circulation as Ct−= ωt

−� x,y,t = t dx dy control parameters [1], where ωz� = ∇�� × v�� isfluid vorticity and investigate numerically, the fate of long time states. Several interestingobservations obtained will be presented.

References[1] Studies in Statistical Mechanics of Magnetised Plasmas: A Thesis [1998]: Rajaraman

Ganesh [IPR].[2] Montgomery D, Matthaeus WH, Stribling WT, Martinez D, Oughton S. Relaxation in two

dimensions and the ‘‘sinh‐Poisson’’equation. Physics of Fluids A: Fluid Dynamics. 1992Jan; 4(1):3-6.

[3] Matthaeus WH, Stribling WT, Martinez D, Oughton S, Montgomery D. Selective decay andcoherent vortices in two-dimensional incompressible turbulence. Physical review letters.1991 May 27; 66(21):2731.



15

OL1-8

Study on ion re-circulation and potential well structure in an inertialelectrostatic confinement fusion device using 2D-3V PIC simulation

D. Bhattacharjee1, S. Adhikari2, N. Buzarbaruah1 & S. R. Mohanty1, 31Center of Plasma Physics-Institute for Plasma Research, Sonapur, Kamrup(M),

Assam, 780402, India.2Department of Physics, University of Oslo, PO Box 1048 Blindern, Oslo, Norway.

3Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, 400094, India.


Kinetic simulations are performed using PIC (Particle-in-Cell) method to study the ionbehavior inside a table-top neutron source, Inertial Electrostatic Confinement Fusion(IECF) device. In this device, lighter ions are accelerated, re-circulated and concentratedat the center by using an electrostatic field. These ions are capable of producing fusion atthe central region of the cathode during high voltage operations [1, 2]. An open sourcePIC code, XOOPIC [3] is used to simulate the ion dynamics for different experimentalconditions. The potential structure from the simulation indicates the formation ofmultiple potential well inside the cathode depending upon the applied cathode voltage(ranging from -1kV to -5kV) and the number of cathode grid wires. The ion density at thecore region of this device has been observed to be of the order of 1016 m-3, which closelyresembles the exact experimentally obtained results. The ion energy distribution function(IEDF) has been measured from the phase space at different locations to identify thepatterns of ion dynamics for different grid assembly and experimental conditions. Finally,the simulated results are compared with the experimental results, measured usingdifferent Langmuir probes.

References

[1] R. Hirsch, J. Appl. Phys., 38, 4522 (1967).[2] N. Buzarbaruah, S.R. Mohanty and E. Hotta, Nucl. Instrum. Methods Phys. Res. Sec. A, 911,

66 (2018).[3] J.P. Verboncoeur, A.B. Langdon and N.T. Gladd, "An Object-Oriented Electromagnetic PIC

Code", Comp. Phys. Comm., 87, 199 (1995).



16

OL1-9

Molecular dynamics simulation of collisional cooling of He and itsbinary mixtures with Ne, Ar, Kr and Xe for creating strongly coupled

cryoplasmas

S. S. Mishra and S. BhattacharjeeDepartment of Physics, IIT Kanpur, India


Cryoplasmas are microplasmas created at extremely low temperatures (below room temperatureto 4K) and usually at atmospheric pressure. They are expected to provide a firm base tounderstand the physics of strongly coupled plasma systems, where the coupling parameter(gamma) (the ratio of mean Coulomb interaction energy of the particles to their mean kineticenergy) would be greater than or equal to 1. The relatively simpler production mechanism andlarge plasma lifetimes as compared to conventional laser-based techniques, makes themattractive. In these weakly ionized plasmas, the neutral gas acts as a controlling agent formanipulating the plasma parameters (electron/ion temperature and density), which in turn, allowsto control the gamma values of the plasma. To this effect, the gas temperature dependence ofplasma parameters in Helium cryoplasma has been investigated earlier [1]. However, the exactinfluence of neutral gas interactions at low temperatures on the plasma properties, remains anopen question.In order to answer this question, two studies are vital: (i) proper knowledge of the correct

interaction potential acting between the gaseous atoms, and (ii) the efficiency of collisionalcooling of gaseous atoms and eventually the cooling of plasma species through the interactionswith the neutral atoms in such low temperatures (~10K). Conventionally, the Lennard-Jones (LJ)potential is employed to model the gases, however, at low temperatures often discrepancies ariseas the gas properties significantly deviate from their ideal behavior. Therefore, the applicabilityof the LJ potential must be scrutinized in the aforementioned temperature range.In order to investigate the cooling process of He gas and the effect of gas mixing of He with

other noble gases such as Ne, Ar, Kr and Xe, on the process, a molecular dynamics simulation hasbeen set up using LAMMPS [2]. To replicate the cooling mechanism used in cryoplasmaexperiments, the working gas, which is initially at 300K, is put in contact with the cold metallicwalls, maintained at 10K. This will help in elucidating the collisional cooling process involved.Initially, the interactions among the gases are to be guided by LJ potential. To model theinteractions of unlike gas atoms, two types of mixing rules are employed: Lorentz–Berthelot andFender–Halsey [3].In the colloquium, the cooling rate of pure He system and the mixtures will be presented. The

effect of mass and interaction strength of secondary gas on the cooling rate of He are to bediscussed. The performance of the LJ potential, and both the mixing rules, will be ascertained bycomparing the transport properties with the available experimental results [4].

References[1] Y. Noma et al., J. Appl. Phys., 109, 053303 (2011).[2] S. Plimpton, J. Comp. Phys 117, 1(1995).[3] A. Frijns et. al., Micromachines, 11, 319 (2020).[4] A. Rahaman, Phys. Rev. A., 2, 136 (1964).



17

OL1-10

Effects of flow Velocity and Density of Dust Layers on theKelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma:

Molecular Dynamic Study

Bivash Dolai and R. P. PrajapatiDepartment of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya,

Bilaspur-495009 (C.G.), India


The effect of different velocities and density of flowing dusty plasma layers are investigated onhydrodynamic Kelvin-Helmholtz (K-H) instability. The dust particles are too massive ascompared to the electrons and ions. Therefore, the electron and ion fluids are taken to be lightBoltzmann fluid and they only contributes as the neutralizing background to the charged dustgrains. The dust particles are interacting through the Yukawa potential. Thus, the system can betermed as Yukawa one component fluid. The problem has been simulated using the MDsimulation technique through open source LAMMPS code.

We consider the two layers of such Yukawa one component fluids with same anddifferent dust density, and different velocity profiles. The effect of different flow velocities, flowdirection and different density are studied on the K-H instability. We have calculated the growthrate of the K-H instability for such configurations. For excitation of K-H instability, themagnitude of the equilibrium velocity of fluid must be greater than the dust thermal velocity. It isfound that the dust flow velocity and density gradient enhance the growth rate of the K-Hinstability.

References[1] J. Ashwin and R. Ganesh, Phys. Rev. Lett. 104, 215003 (2010).[2] S. K. Tiwari, A. Das, D. Angom, B. G. Patel and P. Kaw, Phys. Plasmas 19, 073703 (2012).[3] V. S. Dharodi, S. K. Tiwari, and A. Das, Phys. Plasmas 21, 073705 (2014).



18

OL1-11

Simulation Study of Planar Anode Micro Hollow Cathode DischargeUsing Dielectric Layer

Khushboo Meena1, R P Lamba11CSIR-Central Electronics Engineering Research Institute (CSIR-CEERI),

Pilani-333031, Rajasthan, India.

email: [email protected]

Microdischarges are very popular for a long time and they have many advantages due to theirsmall size [1]. Micro Hollow Cathode Discharge(MHCD) is one of the micro discharge which isformed in the cylindrical shaped hollow cathode and responsible for the generation of highelectron density discharge, but it has a very short period of a lifetime due to the sputtering effecton the cathode walls and moving of the discharge from glow to arc region [2]. There is anothertype of discharge called Dielectric Barrier Discharge(DBD)which is also known as silentdischarge as well as Ozone production discharge. In this discharge single or double dielectricbarrier layers are used between electrodes so, it has the advantage of low electrode erosion.So for benefitting the effect of both the discharges DBD and MHCD in a single model wecombined both the discharge for the generation of high electron density without moving fromglow to arc discharge and for increasing the life span of the discharge by overcoming thesputtering effect a hollow cathode structure.In this paper, a 2D-axis symmetric model is designed and simulated using the Plasma Module ofCOMSOL 5.4 Software [3]. This model includes the MHCD as well as DBD discharge. In thismodel, a dielectric layer of 40µm is placed on the inside wall of the anode. In this model, a planaranode is used which is covering one side of the hollow cathode. The diameter of the hollowcathode is 500µm and a height of 500µm is used. Argon gas is used for the discharge atatmospheric pressure. Pulsed voltage is applied to have the 1000ns period cycle. In this model forthe ignition of the discharge takes place at the minimum distance between anode and cathode.After that discharge gets sustained in the hollow cathode cavity and attains the stable abnormalglow discharge having high electron density in the order of 1018 m-3.

References[1] A.D. White, “New hollow cathode glow discharge”, J. Appl. Phys. 30 711–719(1959).[2] C. Meyer, Daniel Demecz, E. L. Gurevich, U. Marggraf, G. Jestel, J. Franzke, J.

Anal. At. Spectrom., 27, 677, (2012).[3] COMSOL Multiphysics Documentation, 2019, [online] Available:

http://www.comsol.co.in.



19

Fusion Science&

Technology



20

OL2-1

Impact of Energetic Particles in the First-Wall Erosion in FusionPower Reactors

P. N. Maya and S.P. Deshpande1Institute for Plasma Research, Bhat, Gandhinagar, 382428, Gujarat, India


Plasma-wall interactions in a fusion power reactor are significantly more complex than thepresent-day tokamaks due to the presence of highly energetic fusion products (14 MeV neutrons,3.5 MeV alpha-particles), externally injected impurities along with charge-exchange neutrals.The non-linear interaction of these particles along with the hydrogen isotope plasma with theplasma-facing components can alter the fundamental processes of erosion, redeposition andconsequently the impurity generation and transport in a tokamak. The energetic ion distributionon the first-wall is rather asymmetric and this results in additional erosion and redeposition zoneson the first-wall. In this article we discuss the erosion of the first-wall material due to fast-alphaparticles and charge-exchange H-isotope neutrals on the first-wall of fusion power reactors. Foralpha particles, we will show the influence of different poloidal distributions of fast-ions in theerosion. We also discuss the effect of different first-wall materials in the impurity generationsuch as carbon, tungsten, lithium etc. An extrapolation of these results for different geometry andaspect ratio of the tokamak will be presented.



21

OL2-2

Disruptions study in Aditya-U Tokamak

Suman Dolui1,2, Kaushlender Singh1,2, Tanmay Macwan1,2, Harshita Raj1,2, SumanAich1, Rohit Kumar1, K A Jadeja1, K M Patel1, V K Panchal1,S.Purohit, M.B

Chowdhuri, R L Tanna1, J. Ghosh1,2 and ADITYA-U Team1

1 Institute for Plasma Research, Bhat, Gandhinagar, India, 3824282Homi Bhabha National Institute, Mumbai, India, 400094


Disruptions in tokamak, is a sudden loss of magnetic confinement of plasma. A huge amount ofplasma current abruptly terminate in a few ms. As a consequence, plasma facing components and thevessel are encountered by huge amount of heat loads and electromagnetic force. Hence, due todisruption there is a chance of severe damage to the system. Avoidance of disruption [1] and real timemitigation is a very important field of work in tokamak. There are many possible causes for disruption.Disruption is a multidimensional catastrophic phenomena. Many number of disrupted plasmadischarges have been studied in Aditya-U tokamak. Behavior of plasma parameters during disruptionhas been noticed carefully. It has been noticed that how some parameters like ‘rise rate of current’ inramp-up phase , edge-q value[2] play a role in plasma disruptions and how they are incorporated withother parameters like amount of impurity , vertical magnetic field , error filed , plasma density andtemperature. Overall it is being tried to create a plasma parameter space where the plasma productionmay be operated safely. Underlying physics of such phenomena also has been explored.

References

[1] ‘Novel approaches for mitigating runaway electrons and plasma disruptions inADITYA tokamak’, R.L. Tanna et al 2015 Nucl. Fusion 55 063010.[2] Characterization of the plasma current quench during disruptions in ADITYATokamak’, Shishir Purohit et al 2020 Nucl. Fusion



22

OL2-3

Simulation of runaway electron generation in fusion grade tokamakand suppression by impurity injection

Ansh Patel1, Santosh P. Pandya21School of Liberal Studies, Pandit Deendayal Petroleum University, Gandhinagar, India

2Institute for Plasma Research, Bhat, Gandhinagar, India.


During disruptions in fusion-grade tokamaks like ITER, large electric fields are inducedfollowing the thermal quench period which can generate a substantial amount of RunawayElectrons (RE) that can carry up to 10 MA current with energies as high as several tens of MeV[1-3]. These runaway electrons can cause significant damage to the Plasma Facing Componentsdue to their localized energy deposition. To mitigate these effects, impurity injections of high-Zatoms have been proposed [1-3]. In our talk, we use a self-consistent 0D tokamak disruptionmodel as implemented in PREDICT code [6] which has been upgraded to take into account theeffect of impurity injections on RE dynamics as suggested in [4-5]. Dominant RE generationmechanisms such as the secondary avalanche mechanism as well as primary RE-generationmechanisms namely Dreicer, hot-tail, tritium decay and Compton scattering (from γ-rays emittedfrom activated walls) have been taken into account. These different RE-generation mechanismsprovides seed RE-electrons of different amount and corresponding maximum amplitude ofRE-current (Left plot below). In these simulations, the effect of impurities is taken into accountconsidering collisions of REs with free and bound electrons as well as scattering from full andpartially-shielded nuclear charge. These corrections were also implemented in the relativistic testparticle model to simulate RE-dynamics in momentum space. We show that the presence ofimpurities has a non-uniform effect on the Runaway Electron Distribution function (Right plotbelow). Low energy RE (a few MeV) lose their energy due to collisional dissipation while thehigh energy RE are scattered in momentum space and dissipate their energy due to highersynchrotron backreaction due to its dependence on total energy and pitch-angle. We show thatthe combined effect of pitch-angle scattering induced by the collisions with impurity ions andsynchrotron emission loss results in the faster dissipation of RE-energy distribution function [7].The variation of different RE generation mechanisms during different phases of the disruption,mainly before and after impurity injections is reported.

References:

Impurity injection at t=30 msAr = 1e+20 m-3

AverageRE-energy

Dissipation ofRE-energydistributionfunction

HighenergyRE

Low energyRE



23

[1] M. Lehnen, et.al., Journal of Nuclear Materials, 463, pp39-48, (2015)[2] E. M. Hollmann, et. al., Physics of Plasmas, 22, 021802, (2015)[3] M. Lehnen, et.al., ITER Disruption mitigation workshop, Report:ITR-18-002, (2018)[4] J. R. Martín-Solís, et.al., Physics of Plasmas, 22, 092512, (2015)[5] J. R. Martín-Solís, et.al., Nucl. Fusion , 57, 066025 (2017)[6] Santosh P. Pandya, PhD thesis, AIXM0036, Aix-Marseille University, France, (2019)[7] Ansh Patel, et.al., PTS-2020, MF-02, Abstract#45, (2020)



24

OL2-4

Simultaneous measurement of thermal conductivity and thermaldiffusivity of ceramic pebble bed using transient hot-wire technique

Harsh Patel1, 2,*, Maulik Panchal1, Abhishek Saraswat1, Paritosh Chaudhuri1, 21Institute for Plasma Research, Bhat, Gandhinagar – 382428, India

2Homi Bhabha National Institute, Anushaktinagar, Mumbai – 400094, India

*E-mail address: [email protected]

Lithium-based ceramics in the form of pebble beds have been considered as tritiumbreeder material in the breeder blanket of the fusion reactor. It is very essential to studythermal characteristics of these ceramic pebble beds subjected to fusion relevantconditions. Thermal conductivity (�), thermal diffusivity (�) and specific heat (��) of apacked bed are some of the important parameters for the design of breeder blanketmodule. In the present study, the transient hot-wire technique based experimental setuphas been designed and fabricated to measure � , � and �� of Indian made lithiummetatitanate (Li2TiO3) pebble bed. Thermal properties of Li2TiO3 pebble bed (1 ± 0.15mm pebble diameter and �63% packing fraction) are measured within the temperaturerange of 45°C to 800°C in stagnant helium gas environment. In addition to this, the effectof gas pressure variation for the range of 0.105 MPa to 0.4 MPa has also been studied.Empirical equations are suggested for � and � of Li2TiO3 pebble bed as a function oftemperature at different pressure in helium environment.

References

[1] S. Pupeschi, R. Knitter, and M. Kamlah, “Effective thermal conductivity of advancedceramic breeder pebble beds,” Fusion Eng. Des., vol. 116, pp. 73–80, 2017.

[2] M. Panchal, C. Kang, A. Ying, and P. Chaudhuri, “Experimental measurement andnumerical modeling of the effective thermal conductivity of lithium meta-titanate pebblebed,” Fusion Eng. Des., vol. 127, no. October 2017, pp. 34–39, 2018, doi:10.1016/j.fusengdes.2017.12.003.

[3] M. Panchal, A. Saraswat, S. Verma, and P. Chaudhuri, “Measurement of effective thermalconductivity of lithium metatitanate pebble bed by transient hot-wire technique,” FusionEng. Des., vol. 158, no. April, p. 111718, 2020, doi: 10.1016/j.fusengdes.2020.111718.



25

OL2-5

A DDPM-DEM-CFD flow characteristic analysis of pebble bed for fusionblanket

Chirag Sedania,b*, Paritosh Chaudhuria,ba Institute For Plasma Research, Bhat, Gandhinagar, Gujarat, 382428, India.b Homi Bhabha National Institute, Anushaktinagar, Mumbai, 400094, India.

*Corresponding E-mail id: [email protected]

In a solid breeder blanket the functional material, lithium ceramics are kept in the form ofpebble bed. Helium is used as purge gas which flows through the pebble bed. The flowcharacteristics are important in consideration of design and run the breeding blanketefficiently which depends on the arrangement of the pebble bed. In the present study, acomputational model of unitary pebble bed was conducted using DDPM-DEM-CFD tostudy the purge gas flow characteristics of the gas in the pebble bed. The parameterswhich affect the flow characteristics are porosity, pressure distribution, and pressure dropand wall effect. The velocity distribution near the wall region was observed to have manyfluctuations. The results show that the DDPM-DEM-CFD simulation model has an errorwith about 6% for estimating pressure drop when compared with the empirical equation(Ergun Equation). Also, an Artificial Neural Network (ANN) is used to predict thepressure drop. ANN is a machine learning technique which predicts the outcome basedon the training given using the data set. Here, the data set is generated using the Ergunequation and then it is trained for the prediction. The results of the simulation are foundto be in good agreement with the Ergun equation and ANN prediction.

References:

[1] P.J. Gierszewski, J.D. Sullivan, Ceramic sphere-pac breeder design for fusionblankets, Fusion Engineering Design 17 (1991) 95-104.

[2] A. Ying, A. Akiba, L.V. Boccaccini, S. Casadio, G. Dellórco, M. Enoeda, K. Hayashi,J.B. Hegeman, R. Knitter, J. van der Laan , J.D. Lulewicz, Z.Y. Wen, Status andperspective of the R&D on ceramic materials for testing in ITER, Journal NuclearMaterials 367-370 (2007) 1281-1286.

[3] A. Abou-Sena, f. Arbeiter, L.V. Boccaccini, J. Rey, G. Schlindwein, Experimentalstudy and analysis of the purge gas pressure drop ccross the pebble bed for the fusionHCPB blanket, Fusion Engineering and Design, 88 (2013) 243-247.

[4] F. Augier, f.Idoux, J.Y. Delenne, Numerical Simulations of transfer and transportproperties inside packed beds of spherical particles, Chem. Eng. Sci. 65 (2010)1055-1064.



26

[5] T. Eppinger, K. Seidler, M. Kraume, DEM-CFD simulations of fixed bed reactorswith small tube diameter ratios, Chem. Eng. J. 166 (2011) 324-331.

[6] G.D. Wehinger, T. Eppinger, M. Kraume, detailed numerical simulations of catalyticfixed-bed reactors: heterogeneous dry reforming of methane, Chem. Eng. Sci. 122 (2015)197-209.

[7] Y. Seki, K. Ezato, K. Yokoyama, et al., A Study on Flow Field of Purge Gas forTritium Transfer Though Breeder Pebble Bed in Fusion Blanket, NTHAS8,Beppu, Japan,2012, pp. 9–12, December.

[8] A. Ali, A. Frederik, V.B. Lorenzo, et al., Experimental study and analysis of thepurgegas pressure drop across the pebble beds for the fusion HCPB blanket, Fusion Eng. Des.88 (4) (2013) 243–247.

[9] Youhua Chen, Lei Chen, Songlin Liu, Guangnan Luo, Flow characteristic analysis ofpurge gas in unitary pebble bed by CFD simulation coupled with DEM geometry modelfor fusion blanket, Fusion Engineering and Design, 114 (2017) 84-90.

[10] https://www.itascacg.com

[11] https://www.ansys.com/products/fluids/ansys-fluent

[12] https://www.ansys.com/en-in

[13] P. A. Cundall and O. D. L. Strack. "A Discrete Numerical Model for GranularAssemblies". Geotechnique. 29. 47–65. 1979.

[14] H. Hertz. “Über die Berührung fester elastischer Körper”. Journal für die reine undangewandte Mathematik. 92. 156-171. 1881.

[15] Reimann, J., Vicente, J., Ferrero, C. Rack, A., Gan, Y. (2020) 3d tomographyanalysis of the packing structure of spherical particles in slender prismatic containers.International Journal of Materials Research. 111(1): 65-77.

[16] Reimann, J., Vicente, J., Brun, E., Ferrero, C., Gan, Y., Rack, A. (2017) X-raytomography investigations of mono-sized sphere packing structures in cylindricalcontainers. Powder Technology, 318: 471-483.

[17] Moscardini, M., Gan, Y., Pupeschi, S., Kamlah, M. (2018) Discrete element methodfor effective thermal conductivity of packed pebbles accounting for the Smoluchowskieffect. Fusion Engineering and Design, 127: 192-201.

[18] H. Calis, J. Nijenhuis, B. Paikert, F. Dutzenberg, C. van Den Bleek, CFD modelingand experimental validation of pressure drop and flow profile in a novel structuredcatalytic reactor packing, Chem. Eng. Sci. 56 (2001) 1713-1720.

[19] R.K. Reddy, J.B. Joshi, CFD modeling of pressure drop and drag coefficient in fixedand expanded beds, Chem. Eng. Res. Des. 86 (2008) 444-453.



27

[20] A. G. Dixon, M. Nijemeisland, E.H. Stitt, Packed tubular reactor modeling andcatalyst design using computational fluid dynamics, Advance in Chemical Engineering31 (2006) 307-389.[21] Gupta AK, Guntuku SC, Desu RK, Balu A (2015) Optimisation of turningparameters by integrating genetic algorithm with support vector regression and artificialneural networks. Int J Adv Manuf Technol 77(1–4):331–339.

[22] Prasad KS, Desu RK, Lade J, Singh SK, Gupta AK (2013) Finite element modelingand prediction of thickness strains of deep drawing using ANN and LS-Dyna for ASS304.AIP Conf Proc 1567(1):402–405.

[23] Gupta AK (2010) Predictive modelling of turning operations using response surfacemethodology, artificial neural networks and support vector regression. Int J Prod Res48(3):763–778.

[24] Desu, R. K., Peeketi, A. R., & Annabattula, R. K. (2019). Artificial neuralnetwork-based prediction of effective thermal conductivity of a granular bed in a gaseousenvironment. Computational Particle Mechanics, 6(3), 503-514.

[25] S. Ergun, Fluid flow through packed bed columns, J. Mater. Sci. Chem. Eng. 48(1952) 89-94.



28

OL2-6

Initial results of Laser Heated Emissive Probes operated in coldcondition in Aditya-U Tokamak

A. Kanik1, A. Sarma1,2, J. Ghosh3, R. L. Tanna3, M. Shah3, T. Macwan3,4, S. Aich3,S. Patel3,5, K. Singh3,4, S. Duloi3,4, R. Kumar3, K. Jadeja3, K. Patel3 and

ADITYA-U team1Vellore Institute of Technology (Chennai)

2North East Centre for Training and Research (Shillong)3Institute for Plasma Research (Gandhinagar)

4Homi Bhabha National Institute5Birla Institute of Technology and Science (Jaipur)


Measurement of a plasma potential spatial, azimuthal and radial profiles is a challenging tasksince ages and not many diagnostics can perform the task with accuracy. Langmuir probes havebeen used for indirect measurements of the plasma potential and other plasma parameters inalmost every plasma devices. Despite of the fact of existence of many theories and experimentaltechniques, the percentage of error in observations is significant that becomes more intense withhigh magnetic fields. Emissive probe are efficient tools and excellent substitutes to Langmuirprobes for direct measurement of plasma potential and it’s fluctuations with comparably moreaccuracy and have been an active diagnostics in many devices. Despite of the fact of the existenceof many theories and experimental techniques, the percentage of error in observations issignificant. In this paper, we report the measurement of floating potential and its fluctuations inedge region of ADITYA-U tokamak. An assembly for measurement of potential in the edgeregion of ADITYA-U tokamak plasma was designed, fabricated and installed for the first time. Anovel experimental arrangement for the said measurements has been developed and installed onthe ADITYA-U tokamak making use of an actuator which enables measurements up to 50 mminside the limiter.

References[1] Vara Parasad Kella et al, Review of Scientific Instruments, 87, 043508 (2016)[2] J P Sheehan and N Hershkowitz, Plasma Sources Sci. Technol., 20 063001 (2011)



29

OL2-7

Evidence Of Non-local Transport in ADITYA-U Tokamak

T. Macwan1,2, H. Raj1,2, S. Dolui1,2, K. Singh1,2, S. Patel1,3, P Gautam1, N. Yadava1,4,J Ghosh1,2, R L Tanna1,2, K A Jadeja1, K M Patel1, R. Kumar1, S. Aich1, V K

Panchal1, U. Nagora1,2, J. Raval1, D. Kumawat1, M B Chowdhuri1, R Manchanda1,P. K. Chattopadhyay1,2, A Sen1,2, R Pal1,5 and ADITYA-U Team1

1Institute for Plasma Research, Gandhinagar 382 4282Homi Bhabha National Institute, Mumbai, 400 085

3Pandit Deendayal Petroleum University, Gandhinagar 382 0074 The National Institute of Engineering, Mysuru 570 008

5 Saha Institute for Nuclear Physics, Kolkata 700 064


One of the main challenges for the successful operation of future devices like ITER is thepredictive capability of various transport models. The energy and particle transport in a tokamakis dominated by microscopic instabilities, which are assumed to be local. The locality here refersto the local gradients in density and temperature which gives rise to fluctuating fields, which areresponsible for the diffusive transport across the magnetic field lines. However, recentexperiments have revealed a non-locality in the heat and momentum transport [2]. Particularly, aphenomena known as ‘cold pulse propagation’ is considered a prime example of non-localtransport. It is marked by an increase in the core temperature when the edge plasma is cooled, ona time scale faster than the diffusive time scales. It is triggered by injecting a trace amount ofimpurities in the plasma edge or with supersonic molecular beam injection (SMBI). InADITYA-U tokamak, the cold pulse propagation is triggered by multiple puffs of H2 gas, whichare usually used for plasma fuelling. Here, the dynamics of cold pulse in ADITYA-U is studiedwith the variation of the gas puff amount.

References[1] W. Horton, Rev. Mod. Phys., 71, 735 (1999)[2] K. Ida, Nucl Fusion, 55, 19 (2015)



30

OL2-8

Parametric Study of SMBI CD Nozzle for ADITYA-U Tokamak

Kaushlender Singh1,2, Suman Dolui1,2, Tanmay Macwan1,2, B Arambhadiya1, K AJadeja1, K M Patel1, Siju George1,Sharvil Patel1,3 , Harshita Raj1,2, Ankit Kumar1,2,Suman Aich1, Rohit Kumar1, Y Pravastu1, D C Raval1, V K Panchal1, R L Tanna1, J

Ghosh1,2 and ADITYA-U Team1

1 Institute for Plasma Research, Bhat, Gandhinagar, India, 3824282Homi Bhabha National Institute, Mumbai, India, 400094

3 Pandit DeenDayal Petroleum University, Gandhinagar, India, 382007


Converging diverging (CD) nozzle is one of the most important and fundamentalinventions in the course of science. Several engineering and scientific advancementsutilize the concept of compressible flows through CD nozzle [1]. Among its importantuses, CD nozzles are also being used for Supersonic Molecular Beam Injection (SMBI)as a fueling technique for tokamaks [2]. While designing the SMBI system, we need tostudy various properties related to the geometrical design of the nozzle. Many importantoperational parameters such as Mach disk location [3], cluster formation [4], number ofinjected molecules, and variation of Mach number depend on the design of the CD nozzle[1] [5]. These can be optimized by simulation and analytic study of the CD nozzle’sgeometry [1]. In this paper details of the recent upgrades in the installed SMBI systemand parametric study of SMBI CD nozzle for ADITYA-U tokamak will be presented.

References[1] Jagmit Singh, Luis E. Zerpa, Benjamin Partington and Jose Gamboa, Heliyon 5 e01273(2019)[2] Wang En-yao et al Sci. Technol. 3 673 (2001).[3] Wen S. Young, The Physics of Fluids 18, 1421 (1975).[4] O.F. Hagena and W. Obert, J. Chem. Phys. 56 (1972) 1793.[5] He, X., Feng, X., Zhong, M. et al. J. Mod. Transport. 22, 118–121 (2014).



31

OL2-9

Study of Sawtooth Induced Heat Pulse Propagationin the ADITYA Tokamak

S. Patel1, J. Ghosh2,3, M. B. Chowdhury2, K. B. K. Mayya1, T. Macwan2,3,R. Manchanda2, S. Aich2, S. Dolui2,3, K. Singh2,3, R. Kumar2, R. L. Tanna2,T. K. A. Jadeja2, K. Patel2, J. Raval2, V. Kumar2, S. Joisa2, P. K. Atrey2,

U. C. V. S. Rao2, P. Vasu2, S. B. Bhatt2, Y. C. Saxena2, and ADITYA Team2

1Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 3820072Institute for Plasma Research, Gandhinagar, Gujarat 382428

3HBNI, Anushaktinagar, Mumbai, Maharashtra 400094


Sawtooth instability is the commonly observed phenomena in all class of tokamak and have beenwidely used to understand and test the theoretical models for the transport of heat in tokamakdevice [1,2]. Sawtooth remains one of the active areas of research in thermonuclear fusionphysics, considering removal of helium ash and impurity control in the plasma core [3]. InADITYA tokamak, in many plasma discharges, sawtooth are observed for nearly entire durationproviding original source of heat perturbation. In these plasma discharges, corresponding tosawtooth crash, inverted sawtooth are observed in �� spectral line emission emitting from theedge region of plasma. The time-lag analysis of soft X-ray and �� signal shows that sawtoothpulse propagates from core to edge region within 200 ��ec. To explain such fast propagation ofsawtooth induced heat pulse, higher values of thermal diffusivity, about ten times that of thermaldiffusivity estimated from power balance is required. To understand this phenomenon, presentstudy investigates the effect of sawtooth crash in fast propagation of heat pulse in plasmadischarges of ADITYA tokamak.

References[1] E. D. Fredrickson, M. E. Austin, R. Groebner et al., Phys. Plasmas, 7, No. 12, (2000).[2] M W Kissick et al Nucl. Fusion, 38, 821, (1998)[3] ITER Physics Expert Group on Disruptions, Plasma Control, and MHD et al Nucl.

Fusion, 39, 2577 (1999).



32

OL2-10

Calculation Of Toroidal and Poloidal Rotation in Aditya-U Tokamak

Ankit Kumar1,2, G Shukla3, K Shah3 , Tanmay Macwan1,2 , Kaushlender Singh1,2 ,Suman Dolui1,2 , M.B.Chawdhuri1, R Manchanda1, R.L.Tanna1, J.Ghosh1,2 ,

Aditya Team1

1Institute for Plasma Research, Bhat, Gandhinagar 382 428, India2HBNI, Training School complex, Anushakti Nagar, Mumbai 400 085, India

3Department of Science, Pandit Deendayal Petroleum University, Gandhinagar 382 421, India


Toroidal and poloidal rotation in a tokamak plasma is believed to play a significant role inreducing the turbulence in the edge region and thus improving the energy and particleconfinement time [1,2]. Inside a tokamak, there are mainly two magnetic fields, toroidal field BT

and poloidal field Bp. The presence of electric field along with the magnetic field gives rise to anE×B drift. The Er -component of electric field along with BT give rise to an E×B drift in the

poloidal direction which is termed as the poloidal rotation. Further, the E×B drift that arises in thetoroidal direction due to Er & BP is known as the toroidal rotation. We have studied theserotations for Aditya-U tokamak and calculated the values for toroidal and poloidal rotation alongthe radial direction of the torus. Due to larger values of Er in the edge region as compared to thecore region, the plasma rotation in the edge is found to be significantly larger than the core. Wealso studied the variation of the diamagnetic drift produced as the result of pressure gradientinside the tokamak.

References[1] Burrell, K.H. Phys. Plasmas 1997, 4, 1499–1518.[2] H. Biglari, P. H. Diamond, and P. W. Terry Physics of Fluids B: Plasma Physics 2, 1 (1990)[3] Pravesh Dhyani 2014 Nucl. Fusion 54 083023



33

Basic Plasma

Theory



34

OL3-1

Electron-Acoustic Solitary waves in Fermi Plasma withTwo-Temperature Electrons

Ankita Dey1, S. Pramanick2, S. Chakraborty3, M. Sarkar3, S. Chandra41Lady Brabourne College, Kolkata, West Bengal, India

2Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India3Jadavpur University, Kolkata, West Bengal, India

4Physics Department Government General Degree College at Kushmandi,Dakshin Dinajpur, India


Electron Acoustic waves in Fermi Plasma with two temperature electrons have variousapplications in space and laboratory-made plasmas. In some dense plasma systems like the insideof compact stars, Fermi plasma is important. We have studied Fermi plasma system with threecomponents, two temperature electrons, and ions. The hot electrons are mobile and producerestoring force to the system while cold electrons are immobile and produce inertia to the system.We have studied the dispersion behavior of electron acoustic waves in Fermi plasma with twotemperature electrons and investigated its dependence with various plasma parameters. we haveinvestigated Korteweg-de Vries Burger’s equation for the solitary profile of Fermi plasmas withtwo temperature electrons and investigated its dependence with various plasma parameters.

References[1] Chandra, S.; Paul, S.N.; Ghosh, B.; “Electron-acoustic solitary waves in arelativisticallydegenerate quantum plasma with two-temperature electrons”, Astrophys SpaceSci,343:213–219, (2013)[2] Ali, S., Shukla, P.K.: Phys. Plasmas 13, 022313 (2006)[3] Bains, A.S., Tribeche, M., Gill, T.S.: Phys. Lett. A 375, 2059 (2011)



35

OL3-2

Quantum Electro-static Shock Fronts in Two Component Plasma withNon-thermal Distributive Ion

Subhangi Chakraborty1, Jyotirmoy Goswami1,2*1 JIS University, 81, Nilgunj Rd, Jagarata Pally, Deshpriya Nagar, Agarpara,

Kolkata, West Bengal 7001092 188, Raja Subodh Chandra Mallick Rd, Jadavpur, Kolkata, West Bengal 700032


The theoretical investigation of shocks a dense quantum plasma containing electrons atfinite temperature and non-thermal distributive ions has been administrated. The shockstructures of small nonlinearity are studied by using the quality reductive perturbationmethod. we have got considered collisions to be absent, and the shocks arise out ofviscous force. The KdV–Burger equation has been derived and analyzed numerically.The results are important in explaining the various phenomena of the laser-plasmainteraction of dense plasma.



36

OL3-3

Thermal Instability of Two-Component Plasma with RadiativeHeat-Loss Functions Frictional Effect of Neutrals and Hall Current

Sachin Kaothekar11Department of Physics, Mahakal Institute of Technology & Management,

Ujjain-456664, M.P., India.

e-mail: [email protected], [email protected]

The effect of neutral frictions, Hall current and radiative heat-loss function on the thermalinstability of viscous two-component plasma has been investigated incorporating the effects offinite electrical resistivity and thermal conductivity. A general dispersion relation is obtainedusing the normal mode analysis method with the help of relevant linearized perturbationequations of the problem and a modified thermal condition of instability is obtained. We find thatthe thermal instability condition is modified due the presence of radiative heat-loss function,thermal conductivity and neutral particle. The Hall current parameter affects only thelongitudinal mode of propagation. For the case of longitudinal propagation we find that thecondition of thermal instability is independent of the finite electron inertia, Hall current,magnetic field strength, finite electrical resistivity and viscosity of two-components, but dependson the radiative heat-loss function, thermal conductivity and neutral particle. From the curves wefind that the temperature dependent heat-loss function, thermal conductivity and viscosity oftwo-components shows stabilizing effect, while density dependent heat-loss function and finiteelectrical resistivity shows destabilizing effect. The effect of neutral collision frequency isdestabilizing in longitudinal mode. These results are helpful in understanding the structureformation in HI region.

References[1] G. B. Field,. Astrophys. J. 142, 531-567, (1965).[2] S. Kaothekar, J. Porous Media, 21, 679-699, (2018).[3] P. Kempski, and E. Quataert, Mon. Not. Royal Astron. Soc., 493, 1801-1817, (2020).



37

OL3-4

Target Shape Effects on the Energy of Ions Accelerated in RadiationPressure Dominant (RPD) Regime

S. Jain, K. K. Soni, N. K. Jaiman, K. P. MaheshwariDepartment of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)


The study of the interaction of an ultra-intense laser pulse with a thin dense plasma foil is offundamental importance for different research fields such as efficient ion acceleration, highfrequency intense radiation sources, medical applications, investigation of high energy collectivephenomena in relativistic astrophysics [1]. We consider the interaction of an ultrashort,ultra-intense laser with ultrathin plasma layer leading in the generation of ion beam [2]. In thisreference, we evaluate the energy and luminosity of the ion beam and their dependence on thelaser and target parameters. Numerical results are presented for the Gaussian shaped foil targetand Flat target. The effect of plasma foil thickness on the accelerated ion energy and theluminosity has also been studied.

References[1] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys.

Uspekhi, 56, 429-464 (2013).[2] T. Zh. Esirpekov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phy. Rev. Lett.,

92, 175003 (2004).



38

OL3-5

Study of slow mode solitons in a negative ion plasma withsuperthermal electrons

X. Mushinzimana1, F. Nsengiyumva2, L. L. Yadav31Department of Physics, University of Rwanda- College of Science and Technology,

P. O. B. 3900 Kigali, Rwanda2Department of Civil Engineering, Institut d'Enseignement Superieur de Ruhengeri,

P. O. B. 155 Musanze, Rwanda3Department of Mathematics, Science and Physical Education, University of Rwanda-College of

Education, P.O. B. 55 Rwamagana, Rwanda


Slow mode nonlinear structures are investigated in a negative ion plasma comprising heavypositive ions, light negative ions and kappa distributed electrons.After finding the linear dispersion relation, the reductive perturbation method is used to derivethe Korteweg de Vries equation and to find the solitary wave solution. The effects of the positiveand negative ion temperatures as well as the spectral index on the soliton amplitude and widthare studied in detail. These effects are also studied using the arbitrary large amplitude Sagdeevpseudopotential method. With this method, it is shown that as the ion temperatures increase, thesoliton existence domain narrows.

References[1] T. S. Gill, P. Bala, H. Kaur, N. S. Saini, S. Bansal and J. Kaur, The European Physical JournalD, 31, 91-100 (2004).[2] K. Jilani, A. M. Mirza and T. A. Khan, Astrophys Space Sci, 344, 135-143 (2013).[3] X. Mushinzimana and F. Nsengiyumva, AIP Advances, 10, 065305 (2020).



39

OL3-6

Effect of the nonthermal electrons on ion-acoustic cnoidal wave inunmagnetized plasmas

P. C. Singhadiya1, J. K. Chawla2 and S. K. Jain1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801

2Department of Physics, Govt. College Tonk, Rajasthan, India-304001Govt. College, Dholpur, Rajasthan, India-328001


Using reductive perturbation method, Korteweg de Vries (KdV) and modified KdV(mKdV) equation is derived for a unmagnetized plasma having warm ions andnonthermal electrons. The cnoidal wave solution of the KdV and mKdV equation isdiscussed in detail. The effect of nonthermal electron on the characteristics of the cnoidalwave and soliton are also discussed. It is found that nonthermal electron has asignificant effect on the amplitude and width of the cnoidal waves, while it also affectsthe width and amplitude of the soliton in plasmas. The numerical results are plottedwithin the plasma parameters for laboratory and space plasmas for illustration.

References[1] H. Schamel, Plasma Phys. 14, 905 (1972).[2] Yashvir, T. N. Bhatnagar and S. R. Sharma, Plasma Phys. Controlled Fusion 26, 1303(1984).[3] L. L. Yadav, R. S. Tiwari, K. P. Maheshawari and S. R. Sharma, Phys. Rev. E 52,304

(1995).[4] R. S. Tiwari, S. L. Jain and J. K. Chawla, Phys. Plasmas 14, 022106 (2007).[5] R. Sabry, W. M. Moslem and P. K. Shukla, Plasma Phys. 16, 032302 (2009).[6] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Plasma Phys. 17,042301

(2010).[7] O. R. Rufai, Plasma Phys. 22, 052309 (2015).[8] J. K. Chawla, P. C. Singhadiya and R, S. K. Tiwari, Pramana J. Phys., 94, 13 (2020).



40

OL3-7

Formation of shock fronts in inner magnetospheric plasma

J. Sarkar1, S. Chandra2, J. Goswami1, B. Ghosh11Department of Physics, Jadavpur University, Kolkata - 700 032, India

2Department of Physics, Government General Degree College at Kushmandi, DakshinDinajpur-733121, India


Nonlinear analysis for the finite amplitude electron-acoustic-wave is considered in a magnetizedviscous plasma. The quantum hydrodynamic model (QHD) is used to describe the thickly andthinly populated electron species with the Kappa distributive ion. Viscous effects have beenconsidered for the thickly populated electron. By employing the standard reductive perturbationtechnique (RPT), the KdV-Burger equation has been derived, which exhibits shock waves.KdV-B equation transforms into the KdV equation when there is no viscous term. The form ofthe effective magnetic field is the Earth-like magnetospheric magnetic field. The shock fronts andthe solitary structures have been studied with a variety of different plasma parameters. Theresults are essential in explaining the various phenomena in the inner magnetosphere.



41

OL3-8

Slow and fast modulation instability and envelope soliton of ionacoustic waves in fully relativistic plasma having

nonthermal electrons

Indrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,21 Department of Physics, Jadavpur University, Kolkata-700032, India.

2 East Kolkata Centre for Science Education and ResearchP-1, B.P.Township, Kolkata-700 094, India.

e-mail: [email protected];[email protected]

Modulation instability and envelope soliton of slow and fast ion acoustic waves have beentheoretically studied in unmagnetized fully relativistic plasma consisting of cold positive ionshaving constant stream velocity and nonthermal electrons using Fried and Ichikawa method. Theexpression of nonlinear Schrodinger equation in fully relativistic plasma has been derived forslow- and fast- mode of the wave and the conditions for the existence of modulation instabilitiesare obtained. From the nonlinear Schrodinger equation, the solution for envelope solitons forslow- and fast- modes of the wave are also obtained. The profiles of bright- and dark-envelopesolitons are drawn and discussed taking different values of ion-stream velocity and nonthermalelectrons. It is observed that relativistic ion stream velocity and nonthermal electrons havesignificant roles on slow and fast modulation instability and envelope solitons in relativisticplasma. The results are new and would be applicable in astrophysical plasma.

References

[1] B D Fried and Y H Ichikawa, Journal of Physical Society of Japan, 34, 1073 (1973).[2] S N Paul and A Roychowdhury, Chaos Fractals and Solitons, 91, 406 (2016).[3] S N Paul, A Roychowdhury and Indrani Paul, Plasma Physics Reports, 45, 1011 (2019).



42

OL3-9

To Study the Growth Rates of Waves between Piezoelectric andFerroelectric Semiconductor Using QHDModel In Quantum Plasma

Manisha Raghuvanshi1, Sanjay Dixit2Department of physics, Govt. M.V.M college shivaji nagar, Bhopal,

Barkatullah University Bhopal MP

e-mail: * [email protected]; ** [email protected]

Using QHD model, the parametric instability of piezoelectric and ferroelectric materials ofsemiconductor quantum plasma has been studied. We present a analytical investigation oncompare the piezoelectric and ferroelectric properties of materials in semiconductor plasma .It isfound that what’s effects in low and high temperature, dielectric constant, growth rate andfrequency of the materials. Detailed analysis of the dielectric, ferroelectric and piezoelectricproperties of BaTiO3 and InSb. In this article explained the various types of application inpiezoelectric and ferroelectric materials in quantum plasma. The results obtained in this work arediscussed and compare the properties of similar and distinct materials of the semiconductorquantum plasma.Key words: parametric instability, piezoelectric and ferroelectric materials, QHD model.

References

1. Haas, F. "A magnetohydrodynamic model for quantum plasmas."Physics ofPlasmas,12.6(2005)

0621172. Manfredi, Giovanni. "How to model quantum plasmas." Fields Inst. Commun 46(2005)263-287.3. Mattias Marklund and Padma K. Shukla “Nonlinear collective effects inphoton–photonAnd Photon plasma interactions” Department of Physics, UmeaUniversity SE–901 87 Umea,Sweden, (2006). Phys.784. Cai-Xia, He, and Xue Ju-Kui. "Parametric instabilities in quantum plasmas with Electronexchange—correlation effects." Chinese Physics B 22.2 (2013): 025202.5. Chen, Francis F. "Plasma Applications." Introduction to Plasma Physics and ControlledFusion. Springer International Publishing, 2016. 355-411.6. Ghosh, S., and S. Dixit. "Modulational instability of a laser beam in a piezoelectric Materialwith strain dependent dielectric constant." Physics Letters A 118.7 (1986), 354-356.7. Guha, S., P. K. Sen, and S. Ghosh. "Parametric instability of acoustic waves inTransversely magnetised piezoelectric semiconductors." physica status solidi (a) 52.2 (1979):407-414.8. Haas, F., et al. "Quantum ion-acoustic waves." physics of plasmas 10.10 (2003).



43

9. Kaw, Predhiman K. "Parametric excitaiton of ultrasonic waves inpiezoelectric"Semiconductor Journal of Applied Physics 44.4 (1973): 1497-1498.10. Khan, S. A., S. Mahmood, and H. Saleem. "Linear and nonlinear ion-acoustic waves invery dense magnetized plasmas." Physics of Plasmas 15.8 (2008): 082303.11. Markowich, P. A., and C. A. Ringhofer. “C. Schmeiser, “Semiconductor Equations” 199012. Salimullah, M., T. Ferdousi, and F. Majid. "Stimulated Brillouin scattering ofElectromagnetic waves in magnetized semiconductor plasmas." Physical Review B 50.19(1994): 14104.13. Sharma, R. R., and V. K. Tripathi. "Stimulated Brillouin scattering of laser radiation in apiezoelectric semiconductor." Physical Review B 20.2 (1979): 748.14. Shukla, P. K. "A new dust mode in quantum plasmas." Physics Letters A 352.3 (2006):242-243.15. Singh, T., and M. Salimullah. "Nonlinear interaction of a Gaussian EM beam With anelectrostatic upper hybrid wave: Stimulated Raman scattering." Il Nuovo Cimento D 9.8 (1987):987-998.16. Uzma, Ch, et al. "Stimulated Brillouin scattering of laser radiation in a Piezoelectricsemiconductor: Quantum effect." Journal of Applied Physics 105.1(2009): 013307.



44

OL3-10

Diagnostics of Ar-CO2 mixture plasma using CR model

N. Shukla1, R.K. Gangwar2, and R. Srivastava11Department of Physics, Indian Institute of Roorkee, Roorkee-247667 India2Department of Physics, Indian Institute of Tirupati, Tirupati-517506 India


We develop a reliable collisional radiative (CR) model for the Ar-CO2 mixture plasma. Thismodel utilizes the complete set of electron impact excitation cross-sections of various finestructure levels of Ar by relativistic distorted wave (RDW) theory calculated by our group [1].This model incorporated several important processes such as excitation and de-excitation of Ardue to its collision with electrons in the plasma, radiative absorption and decay, ionization as wellas recombination. The model uses the OES measurements of recently reported low-pressure DCgenerated Ar-CO2 plasma by Rodriguez et al. [2]. The plasma parameters viz. electron density (ne)and electron temperature (Te) are obtained as a function of different pressures (0.2, 0.3, and 0.6mbars) and discharge powers at 25 and 50% concentrations of CO2 in Ar. These results aredetermined using measured intensities of seven intense emission lines out of 3p54p (2p) → 3p54s(1s) fine-structure transitions. It is observed that both the electron density and electrontemperature increase with the increase of 2CO concentration, which is in confirmation withexperimental predictions.

References[1] R. K. Gangwar et al. J. Appl. Phys. 111 053307(2012).[2] J. Rodriguez et al. Phys. Plasmas 25, 053512 (2018).



45

OL3-11

Large amplitude ion-acoustic compressive solitons in plasmas withpositrons and superthermal electrons

S. K. Jain1, P. C. Singhadiya2 and J. K. Chawla1Govt. College, Dholpur, Rajasthan, India-328001

2Seth RLS Govt. College, Kaladera, Rajasthan, India-303801Department of Physics, Govt. College Tonk, Rajasthan, India-304001


The large amplitude ion-acoustic solitons in plasma consisting of ions, positrons alongwith cold and hot superthermal electrons have been studied. An energy integral equationfor the system has been derived with the help of SPM(Pseudo potential method). It isfound that compressive solitons exist in the plasma system for the selected set of plasmaparameters. The effect of the spectral indexes of hot electrons (kh), spectral indexes ofcold electrons (kc), temperature ratio of two species of electron ),( 1 positronconcentration ),( ionic temperature ratio ),( positron temperature ratio )( and Machnumber (M) on the characteristics of the large amplitude ion-acoustic solitons arediscussed in detail. The amplitude of the solitons increases with an increase in positronconcentration ),( ionic temperature ratio ),( positron temperature ratio )( and Machnumber (M), however any decrease in spectral indexes (kh, kc) increases the amplitude ofthe solitons.The present study of the paper may be helpful in space and astrophysical plasma systemwhere positrons and superthermal eelectrons coexist.

References[1] F. B. Rizzato, Plasma Phys. Control. Fusion 40, 289 (1988).[2] F. C. Michel, Rev. Mod. Phys. 54, 1 (1982).[3] S. I. Popel, S. V. Vladimirov, P. K. Shukla, Phys. Plasmas 2, 716 (1995).[4] R. Bharuthram and P. K. Shukla, Phys. Fluids 29, 3214 (1996).[5] E. F. El-Shamy, Phys. Plasmas 21, 082110 (2014).[6] N. S. Saini, B. S. Chahal, A. S. Bains and C. Bedi, Phys. Plasmas 21, 022114 (2014).[7] K. Kumar and M. K. Mishra, AIP Advances 7, 115114 (2017).[8] P. C. Singhadiya, J. K. Chawla, and S. K. Jain, Pramana J. Phys., 94, 90 (2020).



46

Dusty Plasma,Laser Plasma,

PlasmaApplications



47

OL4-1

Study of Arc Fluctuations of a DC Transferred Arc Plasma

S P Sethi1, D P Das2, S K Behera21CSIR-Institute of Minerals and Materials Technology, Bhubaneswar 751013,

India2CSIR-Institute of Minerals and Materials Technology, Bhubaneswar 751013,

India


Arc fluctuations, a vital issue in an DC Transferred Arc Plasma, DC transferred arc plasma is asophisticated technique, widely used in pyro-metallurgy process, extraction of minerals from itsores, fine powder smelting. But to maintain a stable arcing is a crucial challenge for obtaininghigher productivity and safe operation. Stability and instability of arc can be derived from arcfluctuation characteristics for a given current, gas flowrate, cathode electrode positions. Theacquired arc fluctuation characteristics in terms of volts helps in identifying the stability andinstability characteristics. The presented work justifies the parameters that contribute to the arcfluctuations in a smelting performance, and what precautions and techniques need to be initiatedduring the progress of smelting process, so that extraction process can be carried out byincreasing the overall productivity of the process.



48

OL4-2

Inductive Energy Storage System with Plasmaopening Switch: A review

Kanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,21Homi Bhabha National Institute Mumbai-400094,

2Pulsed Power & Electro-Magnetics Division, Bhabha Atomic Research Centre Facility,Atchutapuram, Visakhapatnam, Andhra Pradesh, India-531011,


Pulse compression technique is used to generate high powers in the range of Terawatt withsecondary energy storage device as inductive energy store (IES) with plasma opening switch(POS) having charging time is in the range of microseconds and output pulse duration innanoseconds. The inductive energy store is more advantage compared to most widely usedcapacitive energy storage devices with respect to energy density which is 10 -100 times high [1].The parameters that define the performance of IES system are peak output voltage, peak outputcurrent, rise times and pulse widths of current and voltage. Employing of POS results inmultiplication of voltage and power with good energy coupling between the source and load. Theuse of POS improves the load current rise times as well [1]. The IES with POS technology is usedin different applications include generation of particle beams, radiation sources, fusion researchand defense applications. Some of the facilities of plasma opening switch for mega-ampere areGIT-16 [2], MAGPIE [3], COBRA [4], DECADE [5], ACE-4 [6]. The experimental results ofthese facilities gives details of current conduction phase and opening phase of micro second POS.This paper provides details of different facilities of POS technology and simulation of idealmodel of inductive energy system with different functions of variation of POS switch resistanceconnected to resistive load.

References[1] R. A. Meger., et. al., Appl. Phys. Lett., 42, 943 (1983).[2] S. P. Bugaev., et.al., Russian Physics Journal, 40, 1154-1161(1997).[3] Hall, G. N., et al., Review of Scientific Instruments, 85, 943-945 (2014).[4] Shelkovenko, Tatiana A., et al., IEEE transactions on plasma science, 34, 2336-2341 (2006).[5] P. Sincerny et al., Tenth IEEE International Pulsed Power Conference, 3-6 July 1995,

Albuquerque, NM, USA, 405-416(1995).[6] R. Crumley, D. Husovsky and J. Thompson, 12th IEEE International Pulsed Power

Conference, 27-30 June 1999, Monterey, CA, USA, 1118-1121(1999).



49

OL4-3

Role of plasma sheath in the energy management during plasmasurface modification of polymer

Bivek Pradhan and Utpal DekaDepartment of Physics,

Sikkim Manipal Institute of Technology, Sikkim Manipal UniversityMajitar, Rangpo, Sikkim-737136


The ubiquitous use plasma for surface treatment of polymers for variousapplications like automobile, biomedical, textile, etc is a well-establishedtechnique. The optimization of the plasma parameters for maximum efficiencyafter plasma treatment is of utmost importance. In this work we have presentedthe role of plasma sheath in managing the energy deposition on the surface ofPTFE (poly(tetra-fluoro-ethylene) polymer. The amount of energy required forbreaking of the polymer bonds in presence of secondary electron emission hasbeen theoretically estimated. A multicomponent O2-N2 plasma is considered. Thesheath potential in presence of secondary electron emission from the polymersurface has been evaluated as a function of varying density ratio of oxygen tonitrogen and also for different temperature ratio of electron to ion for cold and hotplasma is evaluated. The potential structure for different ratios remains similarand almost same but the magnitude of the potential changes for cold and hotplasma. The heat transmission coefficient through the sheath in presence ofsecondary emission from the polymer is evaluated. It is seen that the heattransmission coefficient varies linearly with w.r.t. electron to ion temperatureratio for the hot plasma and it is more in hot plasma than that of cold plasma. Thetime required for the bond breaking of C-C with bond energy of 348kJ/mol or5.78eV for PTFE polymer is estimated and shown that it will take more time tobreak in case of cold plasma compared to that of hot plasma.



50

OL4-4

Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO)plasma region

Siba Prasad Acharya1, a, Abhik Mukherjee2, b, and M. S. Janaki1, c1Saha Institute of Nuclear Physics, Kolkata, India

2National University of Science and Technology, “MISiS”, Moscow, Russia

e-mail: a [email protected], b [email protected], c [email protected]

We consider the system consisting of the plasma environment in the Low Earth Orbital(LEO) region in presence of charged space debris objects. This system is modelled forthe first time as a weakly coupled dusty plasma; where the charged space debris objectsare treated as weakly coupled dust particles with two dimensional space and timedependences. The dynamics of the ion acoustic waves in the system is found to begoverned by a forced Kadomtsev-Petviashvili (KP) type model equation, where theforcing term depends on the distribution of debris objects. Exact accelerated planarsolitary wave solutions are obtained from the forced KP equation upon transferring theframe of reference, and applying a specific non holonomic constraint condition. For adifferent constraint condition, the forced KP equation also admits lump wave solutions.The dynamics of exact accelerated lump wave solutions, which are happened to bepinned, is also explored. Approximate dust ion acoustic wave solutions with timedependent amplitudes and velocities for different types of localized space debrisfunctions are analyzed. Our work provides a much clearer insight of the debris dynamicsin the plasma medium in the LEO region, revealing some novel results that areimmensely helpful for various space missions. Different perspectives for practicalapplications of our theoretical results are discussed in detail.

References[1] A. Sen, S. Tiwari, S. Mishra, and P. Kaw, Advances in Space Research, Vol. 56,

429-435 (2015).[2] A. R. Seadawy, and K. El-Rashidy, Results in Physics, Vol. 8, 1216-1222 (2018).[3] M. Lin, and W. Duan, Chaos, Solitons and Fractals, Vol. 23, 929-937 (2005).[4] M. S. Janaki, B. K. Som, B. Dasgupta, and M. R. Gupta, Journal of the Physical

Society of Japan, Vol. 60, 2977-2984 (1995).[5] S. Reyad, M. M. Selim, A. EL-Depsy, and S. K. El-Labany, Physics of Plasmas, Vol.

25, 083701 (2018).[6] X. Yong, W. X. Ma, Y. Huang, and Y. Liu, Computers and Mathematics with

Applications, Vol. 75, 3414-3419 (2018).[7] J. Yu, F. Wang, W. Ma, Y. Sun, and C. M. Khaliue, Nonlinear Dynamics, Vol. 95,

1687-1692 (2019).



51

OL4-5

Effect of negative charge dust on ion-acoustic dressed solitons inunmagnetized plasmas

J. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2Department of Physics, Govt. College Tonk, Rajasthan, India-3040011Seth RLS Govt. College, Kaladera, Rajasthan, India-303801

2Govt. College, Dholpur, Rajasthan, India-328001


Propagation of an ion-acoustic soliton in a plasma consisting of negative charge dust isconsidered the reductive perturbation method (RPM). The well known RPM has beenused to derive the KdV equation. This exact solution reduce to the dressed solitonsolution when mach number is expanded in terms of soliton velocity. Variation ofamplitude and width for the KdV soliton, core structure, dressed soliton and exact solitonare graphically represented to different values of negative ions and mach number.The present study of this paper may be helpful in space and astrophysical plasma systemwhere negative charge dust ions are present.

References[1] Y. H. Ichikawa, T. Mitsu-Hashi and K. Konno, J. Phys. Soc. Jpn., 41, 1382 (1976).[2] N. Sugimoto and T. Kakutani, J. Phys. Soc. Jpn., 43, 1469 (1977).[3] R. S. Tiwari, A. Kaushik, M. K. Mishra, Physics Letters A, 365, 335 (2007).[4] R. S. Tiwari, Physics Letters A, 372, 3461 (2008).[5] Yashvir, R. S. Tiwari and S. R. Sharma, Canadian Journal of Physics, 66, 824 (1988).[6] R. S. Tiwari and M. K. Mishra, Physics of Plasmas, 13, 062112 (2006).[7] P. Chatterjee, K. Roy, G. Mondal, S. V. Muniandy, S. L. Yap and C. S. Wong,Physics of

Plasmas, 16, 122112 (2009).[8] P. Chatterjee, K. Roy, S. V. Muniandy and C. S. Wong , Physics of Plasmas, 16,112106

(2009).[9] K. Roy and P. Chatterjee, Indian Journal of Physics, 85, 1653 (2011).



52

OL4-6

Effect of collision on dust–ion acoustic shock wave in dusty plasma withnegative ions

Jyotirmoy Goswami1*, Jit Sarkar1, Swarniv Chandra1,2 and Basudev Ghosh11 Department of Physics, Jadavpur University, Kolkata – 700 032, India

2 Department of Physics, Government College Kushmandi, W.B. – 733121, India


In this paper we have investigated the properties of dust–ion acoustic (DIA) shock wave in adusty plasma containing two types of ions. We have used the reductive perturbation technique(RPT) to derive the Korteweg–de Vries–Burgers (KdVB) equation for dust acoustic shock wavesin a homogeneous, unmagnetized and collisional plasma containing Boltzmann distributedelectrons, singly charged positive ions, singly charged negative ions and dust particles in thebackground. The KdVB equation is derived and its stationary analytical solution is numericallyanalyzed where the effect of collision is taken into account. It is found that the collision in thedusty plasma plays as a key role in dissipation for the propagation of DIA shock.



53

OL4-7

Equilibrium configuration of self gravitating dusty plasmas

Manish K ShuklaJawaharlal Nehru College, Pasighat, Arunachal Pradesh, India

Email: [email protected]

Using three dimensional molecular dynamics simulation, different equilibrium structures areobtained for self gravitating charged dust clouds. These equilibrium structures are sphericallysymmetric in nature which can be characterized by three parameters (i) number of particles in thecloud (ii) Temperature of the cloud, and (iii) a dimensionless parameter Γ� . The simulationresults are explained using the mean field theory where gravitational force density is balanced bythe sum of kinetic and electrostatic pressure of charged dust cloud. The significance of obtainedresults is also discussed in the context of structure formation in the astrophysical conditions.

References[1] M. K. Shukla and K Avinash, Phys. Plasmas 26, 013701 (2019).[2] K. Avinash, B. Eliasson, and P. Shukla, Phys. Lett. A 353, 105-108 (2006).[3] K. Avinash and P. K. Shukla, New J. Phys. 8, 2 (2006).[4] M. K. Shukla, K. Avinash, R. Mukherjee, and R. Ganesh, Phys. Plasmas 24, 113704 (2017).



54

OL4-8

Strong and collimated terahertz radiation by photo mixing of HermiteCosh Gaussian lasers in collisional plasma

Sheetal Chaudhary, Manendra and Anil K. MalikDepartment of Physics, Ch. Charan Singh University, Meerut.

e-mail:[email protected]

THz spectral region has become a focus of active and thriving research because of itspotential applications in remote sensing, topography, imaging, explosive detection,dentistry, chemical sciences, security identifications, terahertz time-domainspectroscopy (THz-TDS) [1-6]. An analytical model for terahertz (THz) wave emissionby frequency difference of Hermite Cosh Gaussian lasers in collisional plasma withperiodic density is developed. The effect of laser parameters (mode index �, decenteredparameter � and initial phase difference � ) and plasma parameters (plasma densitystructure, electron-neutral collisions) on emitted THz field profile is investigated. It isfound that the highest THz field is obtained for � = v,� = t, � = t,�, �� and � = ��(resonant excitation) at � = t . The study also reveals that electron neutral collisionsattenuate the field drastically. A very high THz field of G V m-1 and an efficiency of �3% is obtained in our scheme for optimised laser and plasma parameters.

References[1] B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26(2002).[2] D. Dragoman, M. Dragoman, Prog. Quantum Electron. 28, 10(2010).[3] W. P. Leemans, C. G. R. Geddes, J. Faure, C. Tóth, J. V. Tilborg, C. B. Schroeder, E.

Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J.Byrd, and

M. C. Martin, Phys. Rev. Lett. 91, 074802(2003).[4] S. Ebbinghaus, K. Schröck, J. C. Schauer, E. Bründermann, M. Heyden, G.Schwaab, M.

Böke, J. Winter, M. Tani, M. Havenith, Plasma Sources Sci. Technol. 15, 72(2006).[5] P. H. Siegel, IEEE Tran. Tera. Sci. Technol. 50, 910(2002).[6] F. Sizov, Opto Electron. Rev. 18, 10(2010).



55

OL4-9

Effect of laser pulse profile on controlling the growth ofRayleigh-Taylor instability in radiation pressure dominant regime

Krishna Kumar Soni, Shalu Jain, N. K. Jaiman, and K. P. MaheshwariDepartment of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)


In the radiation pressure dominant (RPD) regime the interaction of an intense relativistic laserpulse with an ultrathin, dense solid foil converts it into overdense plasma instantaneously. Thisplasma foil is accelerated as a whole by incident laser pulse. It becomes unstable due to the onsetof Rayleigh-Taylor instability (RTI). This RTI tears the foil into plasma clumps. It affects the ionacceleration process. The ion energy spectrum becomes broadened. In the comoving frame of theplasma foil the RTI makes it transparent for the incident radiation. The growth rate of RTIdepends on the pulse profile of the incident laser. So, by suitably tailored laser pulse one cancontrol the growth of RTI, and hence stabilize the ion acceleration. This paper presents acomparative study of energy and momentum transfer by the incident Gaussian and Lorentzianlaser pulse to the plasma ions. Numerical results for the comparison of incident laser pulse profilefor controlling the growth of RTI are presented.



56

OL4-10

Laser-driven radially polarized terahertz radiationgeneration in hot Plasma

Manendra and Anil K MalikDepartment of Physics, Chaudhary Charan Singh University Meerut, UP-250004, India


Bright radially polarized Terahertz (THz) radiation have invited great interest fromresearchers due to various potential application in the field of medical imaging, chemicalscience, spectroscopic identifications of complex molecules, explosive detection,security identification, topography, remote sensing, outer space communication andsubmillimeter radars [1 - 6]. We report radially polarized terahertz (THz) wavegeneration based on nonlinear mixing of two radially polarized beams in densitymodulated plasma. We incorporate in our model the effect of plasma electrontemperature (Te) on THz field intensity and efficiency. THz field intensity and efficiencyof THz monotonically increase with plasma electron temperature (Te). We observe thatthe effect of plasma electron temperature is more prominent around the resonanceexcitation i.e. �v − �� . The profile of THz depends only on the laser parametersand it is independent of plasma electron temperature. In our numerical investigationunder the optimized parameters, radially polarized THz radiation with the high electricfield and the efficiency can be obtained to meet the demands of the above mentionedpotential application. Radially polarized THz field is more suitable to penetrate deeplywithout any risk of collateral damage inside the skin layers thereby improved the safetyand efficacy of treatment [7].Key words: Terahertz radiation, Electron temperature, Plasma, Efficiency, Radiallypolarized

[1] D Dragoman, M Dragoman, Prog. Quant. Elect. 28 10 (2010).[2] W P Leemans, C G R Geddes, J. Faure, Tóth Cs, Tilborg J V, Schroeder C B,

Esarey E, Fubiani G, Auerbach D, Marcelis B, Carnahan M A, Kaindl R A, ByrdJ, and Martin M C, Phys. Rev. Lett. 91 074802 (2003).

[3] Schroeder C B, Esarey E , Tilborg J Van, Leemans W P, Phys. Rev. E 69 016501(2004).

[4] Ebbinghaus S , Schröck K, Schauer J C , Bründermann E, Heyden M, SchwaabG , Böke M, Winter J, Tani M, Havenith M, Plasma Sourc. Sci. Technol, 15 72(2006).

[5] P H Siegel, IEEE , 50 910 (2002).[6] F Sizov ,Opt. Electron. Rev. 18 10 (2010).[7] B Varghese, S Turco, V Bonito, and R Verhagen, Opt. Express 21 18304 (2013).



57

FullManuscript

PSC-1to

PSC-13



58

PSC -1

Simulation of runaway electron generation in fusion grade tokamakand suppression by impurity injection

Ansh Patel1, Santosh P. Pandya21School of Liberal Studies, PanditDeendayal Petroleum University, Gandhinagar, India

2Institute for Plasma Research, Bhat, Gandhinagar, India.


Abstract

During disruptions in fusion-grade tokamaks like ITER, large electric fields are inducedfollowing the thermal quench (TQ) period which can generate a substantial amount of RunawayElectrons (REs) that can carry up to 10 MA current with energies as high as several tens of MeV[1-3] in current quench phase (CQ). These runaway electrons can cause significant damage to theplasma-facing-components due to their localized energy deposition. To mitigate these effects,impurity injections of high-Z atoms have been proposed [1-3]. In this paper, we use aself-consistent 0D tokamak disruption model as implemented in PREDICT code [6] which hasbeen upgraded to take into account the effect of impurity injections on RE dynamics as suggestedin [4-5]. Dominant RE generation mechanisms such as the secondary avalanche mechanism aswell as primary RE-generation mechanisms namely Dreicer, hot-tail, tritium decay and Comptonscattering (from γ-rays emitted from activated walls) have been taken into account. Thesedifferent RE-generation mechanisms provides seed REs of different amount and correspondingmaximum amplitude of RE-current. In these simulations, the effect of impurities is taken intoaccount considering collisions of REs with free and bound electrons as well as scattering fromfull and partially-shielded nuclear charge. These corrections were also implemented in therelativistic test particle model to simulate RE-dynamics in momentum space. We show that thepresence of impurities has a non-uniform effect on the Runaway Electron Distribution function.Low energy RE lose their energy due to collisional dissipation while the high energy RE arescattered in momentum space and dissipate their energy due to higher synchrotron backreactiondue to its dependence on total energy and pitch-angle. We also show that the combined effect ofpitch-angle scattering induced by the collisions with impurity ions and synchrotron emission lossresults in the faster dissipation of RE-energy distribution function [7]. The variation of differentRE generation mechanisms during different phases of the disruption, mainly before and afterimpurity injections is reported.

Key words: Runaway electrons, collisional dissipation, impurity injection, avalanche mechanism

Introduction:Electrons in plasma are said to ‘run-away’ when the Coulomb collisional drag force acting onthem becomes smaller than the accelerating force due to an external electric field. WhileRunaway electrons (REs) are an interesting phenomenon, they can be very problematic forfusion-grade tokamaks like ITER, where large electric fields induced during the disruption phasecan multiply a RE seed population enormously by the avalanche effect [1]. These REs can carry



59

substantial amounts of the pre-disruption plasma current and have energies as high as few tens ofMeV. The uncontrolled loss of such REs should be avoided since they deposit their energies in ahighly localized manner on the plasma-facing-components and can damage them.

Massive material injection (MMI) is a possible solution to mitigate the detrimental effects of REenergy deposition [2]. Impurities such as He, Ne, Ar can be injected either in the form of solidpellets (SPI) or direct gas injection (MGI) which increases collisionality in the plasma leading tore-thermalization of low energy (~few MeV) REs and energy loss of high energy (~tens of MeV)REs.

The generation and suppression of RE during the CQ phase is the subject of this paper. Thegeneration of runaway electrons is considered by taking into account all significant primarygeneration mechanisms as well as avalanching. We utilize a self-consistent calculation of electricfield taking into account collisional and synchrotron drag force in the presence of impurities. Therest of the paper is structured as follows: the second section describes the model utilized for thenumerical study, and the results are presented in the third section.

Model:A 0-D model taking into account the evolution of plasma and runaway electron (RE) currentalong with runway energy has been implemented in the PREDICT code [6] for disruptionscenarios. The electric field is modelled taking into account replacement of ohmic current intoRE current as:

�� = �� − ��where ��,�� = ��,�� are the total and runaway plasma current densities and � is the plasmaresistivity. The total current Ip is evolved using:

�� =−

��t� ��

The RE density is calculated independently through the discharge due to various generationmechanisms [5]:

��

=��

��

+��

�㏨�ꘐ��伸�

+��

�−��쳌

+��

�−�䂺��䂺�

+��

�䂺�−��ꘐ

−��

ꘐ䂺��

from which the runaway current is calculated as�� = �� . No radial runaway lossesare considered which corresponds to the most pessimistic case with regards to RE generation indisruption scenarios. However re-thermalization of REs due to energy loss is considered by usingthe critical energy for RE generation as a cut-off point below which the test electrons are notconsidered as runaways.

The relativistic test particle equations that govern RE energy dynamics in momentum spaceincluding collisional and synchrotron-radiation induced losses are given as:

��

= �� −�h�� h��t

� � ��䂺ꘐꘐ � + v + ��− ��gc + �gy

��

�h��h��

��

��

= ��−�h�� h��t

��

��− ��gc + �gy

��

�h��h��

where �� and ��䂺ꘐꘐ�� are correctional factors that take into account the presence of impuritiesas calculated in [5].

Formation of runaway beamWe start our numerical study at the beginning of the current quench (CQ) phase and assume a REseed of 0.1kA generated due to incomplete thermalization of the electron energy distribution



60

function, also known as the hot-tail mechanism, with plasma temperature = 5 eV and deuteriumplasma density nD= 1020m-3.REs are then generated by other primary generation mechanisms:Dreicer generation, tritium decay, and Compton scattering sources taking into accountcorrections [5] due to the presence of impurities. The avalanching of thermal electrons (both freeand bound) into the RE region occurs due to induced high electric fields. The contribution due toall primary generation mechanisms during different phases of the current quench phase in fig.1(a)can be seen in fig.2(a). The high electric field causes avalanching of the runaway electrons whichsuppresses the electric field in return. The critical energy for RE generation increases gradually

with the drop in the electric field which suppresses further RE generation in the later part of theCQ phase. Fig.1(b) shows a temporal evolution of RE-beam energy considering differentgeneration mechanisms.

Fig. 1(a) RE generation due to various generation mechanisms. 1(b) RE beam energy due tovarious generation mechanisms (D: Dreicer, A: Avalanche, T:Tritium decay, C:Compton, H: Hot

tail)

In the baseline scenario with impurity, the MMI occurs at 30 ms and we assume that the impurityArgon atoms are assimilated completely and evenly inside the plasma. The RE current anddistribution function for the two baseline cases: without MMI and with nAr = 1020 m-3 injected at30 ms can be seen in fig. 2(c) and fig. 2(d).



61

Fig. 2(a) Contribution of various generation mechanisms in the beginning of the disruption andCQ phase. 2(b) RE beam energy in absence and presence of impurity. 2(c) Runaway electrondistribution function in absence of impurity. 2(d) Runaway electron distribution function in

presence of impurity injection.

The amount of hot-tail seed used here is a moderate estimation. The hot-tail seed is a strongfunction of the thermal quench (TQ) time and pre-disruption temperature [8] and can carry up toa few MeV of RE current for the most pessimistic scenario. However radial losses associatedwith the break-up of magnetic surfaces during the thermal quench phase also have to be takeninto account. Accurate estimates of the hot-tail seed would require 3D MHD simulationshowever it is reasonable to assume that some of the seed survives. Varying amounts of hot-tailseed due to varying discharge parameters have been shown in fig.3 (a) as calculated using ananalytical approximation derived in [8] assuming an exponential drop of temperature during thethermal quench.

Fig. 3(a) Hot tail seed RE due to varying pre-disruption temperature and Thermal Quench time(TQ).

Suppression of runaway beamThe RE beam starts dissipating its energy after the MMI due to collisional energy losses with theimpurity ions as well as synchrotron radiation losses. The RE current also decays due tore-thermalization of the REs. A higher amount of injected impurities causes faster decay of REcurrent and energy due to the higher amount of energy losses as can be seen in fig. 4(a). Lowenergy REs (~up to a few MeV) lose their energy mainly due to collisions with free, boundelectrons as well as with shielded, unshielded nuclear charge. High energy REs (~tens of MeV)are pitch angle scattered in momentum space due to interactions with partially ionized impuritiesleading to strong synchrotron radiation losses. As shown in fig. 4(b), the perpendicularmomentum of REs increases drastically on impurity injections which enhances synchrotronradiation losses and consequently thermalizes the REs. In fig.4 (c), the ratio of synchrotronbackreaction force to the collisional drag force is shown for two different RE fractions born atdifferent times during the discharge. For the early-born, high energy fraction (blue), the increasein perpendicular momentum enhances synchrotron losses significantly as compared to collisionallosses. In contrast, for the late-born, low-energy fraction (red), collisional and synchrotron lossesplay almost an equal role. Hence, the presence of impurities has a two-fold effect on RE energydissipation: the higher number of collisions decrease the RE energy and pitch-angle scattering ofREs in presence of impurities also enhances synchrotron losses, especially for high energy REs.

Contour level inAmpere



62

Fig.4(a) Effect of impurity amount on RE current. 4(b) 2D momentum space plot of RE showingpitch-angle scattering. 4(c) Ratio of synchrotron and collisional drag force for two different REs.

4(d) Effect of impurity amount on RE average energy

Conclusions:A numerical study of RE dynamics in the presence of impurities is performed using a 0Ddisruption model considering significant sources RE sources that would be present in a fusiongrade tokamak. The contribution of primary sources is shown to be considerable in the initial partof the CQ phase after which fast avalanching of RE current suppresses the electric field andconsequently primary generation mechanisms. The presence of impurities is shown to causedecay of RE current and energy with a higher amount of impurities leading to faster decay of bothparameters (RE-current and beam energy). Pitch angle scattering caused by collisions withimpurity ions enhance synchrotron emissions drastically and is very significant especially forhigh energy REs.

References[1] M. Lehnen, et.al.,Journal of Nuclear Materials, 463, pp39-48, (2015)[2] E. M. Hollmann, et. al., Physics of Plasmas, 22, 021802, (2015)[3] M. Lehnen, et.al., ITER Disruption mitigation workshop, Report:ITR-18-002, (2018)[4] J. R. Martín-Solís, et.al.,Physics of Plasmas, 22, 092512, (2015)[5] J. R. Martín-Solís, et.al.,Nucl. Fusion ,57, 066025 (2017)[6] Santosh P. Pandya, PhD thesis, AIXM0036, Aix-Marseille University, France, (2019)[7] Ansh Patel, et.al., PTS-2020, MF-02, Abstract#45, (2020)



63

[8] H. M. Smith and E. Verwichte, Physics of Plasmas 15, 072502 (2008)

PSC-2

Effects of flow Velocity and Density of Dust Layers on theKelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma:

Molecular Dynamic Study

Bivash Dolai and R. P. PrajapatiDepartment of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur-495009

(C.G.), India


Abstract

The effect of different velocities and density of flowing dusty plasma layers are investigated onhydrodynamic Kelvin-Helmholtz (K-H) instability. The dust particles are too massive ascompared to the electrons and ions. Therefore, the electron and ion fluids are taken to be lightBoltzmann fluid and they only contributes as the neutralizing background to the charged dustgrains. The dust particles are interacting through the Yukawa potential. Thus, the system can betermed as Yukawa one component fluid. The problem has been simulated using the MDsimulation technique through open source LAMMPS code.

We consider the two layers of such Yukawa one component fluids with same anddifferent dust density, and different velocity profiles. The effect of different flow velocities, flowdirection and different density are studied on the K-H instability. We have calculated the growthrate of the K-H instability for such configurations. For excitation of K-H instability, themagnitude of the equilibrium velocity of fluid must be greater than the dust thermal velocity. It isfound that the dust flow velocity and density gradient enhance the growth rate of the K-Hinstability.

Key words: Dusty plasma, Strongly coupled plasma, Kelvin-Helmholtz instability, Moleculardynamics simulation.

Introduction:The major examples of plasma in nature are high temperature weakly coupled plasma i.e., theaverage kinetic energy of the particles is larger than the average kinetic energy of the particlesdue to their thermal motions. Such type of plasma is generally called the ideal plasma. Also, thereexist examples of non-ideal plasma where the average potential energy dominates over theaverage kinetic energy of the particles [1]. The dusty or complex plasma is one of the goodexamples of such category. The dust grains may exist easily in the strongly coupled state due totheir high charges or in other words due to their extremely low charge to mass ratio [2]. Thecoupling between the particles is mathematically quantified through a dimensionless Coulombcoupling parameter (�) which is defined as the ratio of average potential energy to the averagekinetic energy of the particles,



64

……… (1)In case of Yukawa systems where screening parameter κ > 0, the plasma does not show the actuallong range crystalline behaviour at finite temperature (Td > 0) [3]. There exists an intermediatestate where the Yukawa system shows consequence of both liquid and solid like behaviour. In thecase of two-dimensional dusty plasma system with κ = 0.5 this state is limited to � =140. In thisregime, the medium behaves like a viscoelastic system. The fluid model is not adequate todescribe such Yukawa systems. There is phenomenological GHD model to describe suchYukawa dusty plasma systems [4]. Though GHD model is accepted and used widely [5] [6] tostudy such viscoelastic dusty plasma medium, the simulation studies [7] [8] [9] are also veryimportant to describe the phenomena in this regime.

The hydrodynamic Kelvin-Helmholtz (K-H) instability occurs when there exists relativevelocity between the different layers of the fluids. The dusty plasma has often encounter shearedflow in several situations viz. protoplanetory disks, Saturn ring and cometary tails. In theseobjects and also in several experimental situations, the sheared flow excites the K-H instability inthe dusty plasma medium. Theoretically, the state is described by the GHD model, but theimplication of this model for wide range of coupling parameter and screening parameter is aninteresting and open problem. Hence, the simulation studies are necessary to understand severalimportant phenomena in this regime, and in recent these studies also prevail great interests [7] [8].Several theoretical and experimental investigations are done in this regime to understand thecollective dynamics of this state.

The investigation of K-H instability close and beyond to the regime where crystallizationof the dusty plasma medium occurs is of great interest. In the MD simulation study of K-Hinstability, Ashwin and Ganesh (2010) have investigated the effect of coupling strength wellbelow the crystallization limit. In the present chapter, we investigate the K-H instability in theregime close and beyond the liquid-solid regime. We investigate the effect of different flowvelocity and flow direction, and also the effect of density gradient on the growth of the K-Hinstability using MD simulation.

Molecular Dynamics (MD) Model:The electrons and ions are considered to be light Boltzmann fluids and the dynamics of thecharged dust grains are considered in the simulation. The background plasma provides thescreening to the Coulomb interaction of the dust grains. Thus, the dust grains are interactingthrough the screened Coulomb potential or Yukawa potential, given by

………………… (2)where Qd is the constant charge on the dust grain, � and λD are inter-grain distance and Debyelength of the background plasma. The ratio ��λ� is an important plasma characteristic, and calledas screening parameter (κ). The acting force on the dust grains corresponding to the Yukawapotential is given by

…………………………. (3)The equation of motion for the dust particle following Newton’s second law of motion is givenby,

……………………………. (4)



65

The excitation of the K-H instability is produced by the external flow velocity in the x direction.In the above equation the term �㏨ is the force due to the external flow. We consider onlytwo-dimensional (X-Y) case in this simulation study.Simulation Details:We have used the open source LAMMPS code to carry out the MD simulation of the stronglycorrelated dust grains in the liquid-solid regime. We have considered a 2D simulation system assquare box along X and Y directions. with LX = LY = 400� (-200 � to 200 �). Here � = v� �� isthe Wigner-Seitz radius in the 2D dusty plasma layer and �� is the 2D density of the single dustyplasma layer. The particles are entered in the simulation box through the basis of hexagonal unitcells. A monolayer with 159803 number of particles are created. The boundaries are consideredas periodic. We use the typical simulation parameters as follows: dust grain charge Qd = 11940,grain mass md = 6.99×vt−v� kg, � = 4.18×vt−h m. The Debye length of the background plasmaλ� is taken as 8.36×vt−h m and hence the screening parameter κ remains 0.5 throughout thesimulations. The force cutoff distance is chosen to be 20 � in our simulation. The characteristicdust plasma frequency for these considered parameter is �� = 35.86 s-1 and correspondingresponse time scale ( �� ) of the dust particles is 0.175 s. The simulation is performed indimensionless unit (LJ in LAMMPS) and the Verlet algorithm is used to update the positions andvelocities of each particle. The time step is chosen critically so that the phenomena occurring inthe response time scale of the dust particles are easily observable and it is not high enough formoving a particle too much distance in a single step (to a nonphysical position).

Fig 1-3: variation in (1) Kinetic energy, (2) potential energy, and (3) Total energy in equilibration processfor ᴦ =140 and κ = 0.5.

Now our aim is to simulate the configured system for intermediate coupling parameters. Thecoupling parameter can be set to different values by changing � or dust temperature (��). Herewe fix the intergrain distance and change the dust temperature to acquire the desired couplingparameter. Since the dust particles are arranged initially in the simulation box through the basis ofhexagonal unit cells. The initial intergrain distance of the charged dust particle and hence theinitial coupling parameter of the system is determined by the lattice parameter of the unit cell. Toestablish the thermal equilibrium for a particular ᴦ, we evolve the system in canonical (NVT)ensemble using Noose-Hoover thermostat for 40 s. Then the canonical thermostat isdisconnected and the system is evolved for another 20 s in micro-canonical (NVE) thermostat.The energy plots for canonical and micro canonical equilibration run are shown in the figures 1-3.The total energy is the sum of the Yukawa potential energy and the thermal kinetic energy of theparticles. Here, the energies represent the total energies of the particles in the ensembles. Theenergy of any particle ensemble is minimum when they are arranged in any regular latticestructure, hence in the starting of the canonical run the energies of the ensemble start to increaseinitially, then after sufficient run energies show a little variation. From the figures 1-3, it is clearthat canonical run of 40 s is sufficient. Another 20 s of microcanonical run ensure the stablesystem for a desired � . The system is now ready for simulation. The simulation is performedfinally in the canonical thermostat.Results and Discussion:The initial state for the simulation is prepared by canonical and then microcanonical equilibrationrespectively. Thus, after achieving the thermal equilibrium the system is evolved with time step�t = 0.01 to observe the excitation of K-H instability. The screening parameter κ is kept constant



66

at 0.5 throughout the simulation process. We consider an equilibrium sheared flow velocity in the� direction. The velocity profile of the charged dust fluid layers is expressed as,

…………………….. (5)where �t is the equilibrium shear velocity, ㏨v is the amplitude of the perturbation, and � = �� is the perturbation wavenumber with � be the mode number of the perturbation.

The growth of the perturbed velocity field ㏨v from the equilibrium shear velocity willdemonstrate the instability in any simulation process. The amplitude of the sinusoidalperturbation is kept small ( ㏨v = thv ) in comparison of equilibrium shear velocity. Theconsidered shear flow speed is subsonic and the initial velocity profile satisfies theincompressibility condition (∇h� = t ). The sinusoidal perturbation grows as time passed. Theperturbed velocity ㏨v grows exponentially as time elapse. Tracking the power associated with thegrowing perturbed mode serves a good measure of the growth rate of the instability and thesaturation in the nonlinear stage. Here, we track the time evolution of the perturbed kineticenergy in the 쳌 direction to find the growth rate of a particular mode m. The perturbed kineticenergy is normalized to its initial value and expressed as,

…………………………… (6)The figure 4 shows the growth of the K-H instability as the time evolution of kinetic energy inthe y direction in log-linear scale. In the left subplot (a) of figure 4, the time evolution of kineticenergy is shown using log-linear scale for � =140, �t = th� and � = �. In the right subplot (b),the time evolution of kinetic energy is shown using log-linear scale for � = 140, �t = vhtand� = �.

Fig:4 Time evolution of perturbed kinetic energy in log-linear scale for � = 140, � = �, and (a) ㏨t = th�,(b) ㏨t = vht

In both figures initially the perturbed kinetic energy is growing exponentially as indicated by thelinear portion of the curves. As time passes the perturbed kinetic energy or velocity field achievehigh amplitude, which are comparable to the equilibrium values. As a result, the perturbed energyfinally saturates after initial exponential growth. The slope of the linear portion of the timeevolution curve of kinetic energy in the 쳌 direction gives value which is approximately twice ofthe growth rate of the linear K-H instability. The red lines in both subplots (a) and (b) of thefigure 4 show a linear fit to the initial linear growth rate regime of the K-H instability. In subplot(b), the black circle indicates the evolution of nonlinear stage of the unstable K-H mode, thegrowth later saturates in nonlinear stage.



67

The excitation of K-H instability for dispersive and compressible charged dust fluid has beenstudied. The K-H vorticity contours are shown in figures 5 and 6. The time evolution of perturbedkinetic energies in the y direction are studied for different mode m for several combinations ofphysical parameters. In the figure 5, the growth of K-H instability is shown for different values ofcoupling parameters. Three layers of charged dust fluids are presented. The upper and lower redcolored layers of particles are moving in the negative � direction and middle blue particle layer ismoving in the positive � direction with equilibrium flow velocity. The vorticity contours areshown in figure 5 for � =140 and 150 with different normalized times.

The initial equilibrium velocity is taken to be 1.0. The numerical growth rates of the linear K-Hinstability are determined from the slopes as described in figure 4. The normalized growth rate ofthe linear K-H instability is plotted against wavenumber k in the figure 7. This figure shows that,the growth rate of the linear K-H instability is increasing with increase in ᴦ. Thus, the couplingparameter ᴦ shows the destabilizing effect on the linear K-H instability in the regime near andabove dust crystallization. In the figure 6 growth of K-H instability is shown for different valuesof equilibrium velocities. The vorticity contours are shown in the figure 6 for V0 = 0.5 and 1.0with different normalized times. The coupling parameter � is taken constant as 140. The relativevelocity between the layers are 1.0 and 2.0 respectively. The normalized growth rate of the linear

Fig:5 The atomistic viewof the growth ofperturbation with timefor ㏨t = vht.

Fig:6 The atomistic viewof the growth ofperturbation with timefor � = vht.

Fig: The numerical normalized growth rate w of theK-H instability is determined through MD simulationand plotted against wavenumber k, (7) for ㏨t = th�and (8) for � = vht .

(8)(7)



68

K-H instability is plotted against wavenumber k in the figure 8. This figure shows that, the growthrate of the linear K-H instability increases with the magnitude of equilibrium flow velocity of thedust layers. Hence, the equilibrium shear flow have destabilizing influence on the linear K-Hinstability in the regime near and above dust crystallization. The figure shows very slowexcitation of instability when V0 = 0.5. To obtain the significant value of the growth rate ofinstability, the ratio of equilibrium flow velocity to the dust thermal velocity must be larger thanunity.

The velocity shear between fluid layers excites K-H instability. In real the fluid layersmay be of different densities. The initial equilibrium density of all the three layers of the chargeddust fluids are kept constant in the earlier discussions. Now we are interested to investigate theeffect of density gradients on the growth rate of the K-H instability. We consider the sharpdensity gradient between the layers of the charged dust fluids. The density of the upper and lowerfluid (colored as red) is kept equal and higher than the middle fluid layer (colored as blue). Thetemperature of the charged dust grain is kept constant throughout the whole simulation box. Theinitial coupling parameter will be different for upper and lower dust layers than the middle dustlayer, as their density and hence the interparticle distances are different. The three layers of thedust particles are equilibrated separately with 40 s of canonical and then 20 s of microcanonicalrun. The equilibrated positions of all the particles are added in the main simulation box. Thesinusoidal perturbations are imposed then similarly as stated in equation (8.4). The positions andvelocities of each particle are recorded as time evolved. The time step is taken as 0.0036 MD unit.The growth of the K-H instability in the interface for different time is shown in figure 9.

It is found that the sharp density gradient enhances thegrowth of the K-H instability. The density gradient excitesDAW which propagates from the interface to the lowerdense fluid. A compression and elongation of the lowerdense middle blue marked region can be seen in the figure9. Owing to the consideration of periodic boundarycondition the DAW excitation come back in the fluidthrough both upper and lower boundary of the simulationbox. But this is nonphysical, to inhibit this come back andto perform detail investigation of the combined excitationof DAW and K-H instability we need to extend thesimulation box in the y direction sufficiently. This isbeyond scope of the current work and will be investigatedin future. The influence of the direction of the equilibriumflow velocity has also been investigated. It is found that ifboth fluid layers flow in the same direction with relativevelocity then, the growth of the K-H vortex in y direction is

low and the vortexes propagate in the direction of flow velocity rapidly.Conclusions:The molecular dynamics (MD) simulation is performed to study the problem ofKelvin-Helmholtz (K-H) instability in dusty plasma. The effects of different flow velocities anddensity gradients have been investigated on the hydrodynamic K-H instability. The electron andion fluids are considered as light Boltzmann fluids and they are only providing the neutralizingbackground of plasma to the charged dust grains. Due to the high charges the dust particles arestrongly correlated. The dust particles are interacting through the Yukawa potential. Thus, thesystem can be termed as Yukawa one component fluid. The problem has been simulated inparticle level using the MD simulation through open source LAMMPS code.

The SCDP with screening parameter k = 0.5 shows long range orders around � = 140. Inthis work, we investigate the excitation of K-H instability close and beyond � =140. We considertwo layers of such Yukawa one component fluids with similar dust densities and differentvelocity profiles in the first case. The effects of different flow velocities and flow direction arestudied on the K-H instability. We have calculated the growth rate of the K-H instability for suchconfigurations. In the second configuration, we consider the density gradient in the two fluid

Fig:9 The atomistic view of thegrowth of the K-H instability withtime is shown for equilibrium flowvelocity ㏨t = vht.



69

layers and estimate the growth of K-H instability for different velocity profiles. Thedestabilization influence of coupling parameter is confirmed as reported by Ashwin and Ganesh[7]. The time evolution of small sinusoidal perturbation for different coupling parameters,equilibrium flow velocity and densities of fluid layers are analyzed. The time evolution of theK-H instability is observed in the present simulation study. It is found that, the different dust flowvelocities and density gradients enhance the growth rate of the K-H instability. For excitation ofK-H instability, the magnitude of the equilibrium velocity of fluid must be greater than the dustthermal velocity. Here we find that, the normalized equilibrium velocity V0 = 0.5, the growth ofthe K-H instability is very slow and the growth is linear. But, for V0 = 1.0, the growth is faster andlinear for very short duration, and the nonlinear development of K-H instability and mixingoccurs rapidly.References[1] S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982).[2] R. L. Merlino, and A. J. Goree, Phys. Today 57, 32 (2004).[3] Donkó, Z, Hartmann, P, and Kalman, G (2009). J. Phys. Conf. Ser. 162, p. 012016.[4] Frenkel, Y I (1946). Kinetic Theory of Liquids. Oxford: Clarendon Press.[5] Kaw, P K and Sen, A (1998). Phys. Plasmas 5, p. 3552.[6] Dolai, B and Prajapati, R P (2018). Phys. Plasmas 23, p. 083708.[7] Ashwin, J and Ganesh, R (2010). Phys. Rev. Lett. 104, p. 215003.[8] Tiwari, S K, Das, A, Angom, D, Patel, B G, and Kaw, P (2012). Phys. Plasmas 19, p. 073703.[9] Dharodi, V S, Tiwari, S K, and Das, A (2014). Phys. Plasmas 21, p. 073705.[10] Bonitz, M, Moldabekov, Zh A, and Ramazanov, T S (2019). Phys. Plasmas 26, p. 090601.



70

PSC-3

Study on ion re-circulation and potential well structure in an inertialelectrostatic confinement fusion device using PIC simulation

D. Bhattacharjee1, S. Adhikari2 and S. R. Mohanty1, 31Center of Plasma Physics-Institute for Plasma Research, Sonapur, Kamrup(m),

Assam-782402, India2Department of Physics, University of Oslo, PO Box 1048 Blindern, NO-0316 Oslo, Norway

3Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, 400094, India


Abstract

PIC (Particle-in-Cell) simulations are performed to study the ion behavior inside a table-topneutron source, Inertial Electrostatic Confinement Fusion (IECF) device. In this device, lighterions are accelerated, re-circulated and concentrated at the center by using an electrostatic field.These ions are capable of producing fusion at the central region of the cathode during highvoltage operations. An open source PIC code, XOOPIC is used to simulate the ion dynamics fordifferent experimental conditions. Ion re-circulation is visualized during run time and the phasespace of ions depicts the same, which resembles the star mode of discharge. Potential profileshave been studied in the voltage ranging from -1 to -5 kV and clear formation of double potentialwell is observed inside the cathode grids. Finally, the simulated results are compared with theexperimental results, measured using a cylindrical Langmuir probe.

Key words: IECF, PIC, Potential well, Neutrons.

Introduction:Magnetic or laser based devices are familiar for plasma confinement and to produce fusion.However, inertial electrostatic confinement fusion (IECF) is an alternate approach for producingfusion which is less complicated, easily realized and cost effective. The IECF is a portable,table-top device in which lighter ions are accelerated towards the center of the chamber due to theapplication of a purely electrostatic field. The cathode consists of cylindrical wire grids keptvertically at the center and is highly transparent through which the energetic ions generate to andfro motion or re-circulation. In this re-circulation process, the ions get confined inside thecathode, where, they collide with each other or with the neutrals (beam-beam orbeam-background collision) and finally produce fusion at the central region of the device.Although, the IECF device cannot be used for the purpose of thermonuclear energy productiondue to its small Q-value, it has very wide range of near term applications. The neutrons, which arethe basic products of the device, can be used in cancer treatment (BNCT), radiography, forexplosive material detection, in ion thrusters, etc. [1]. Moreover, x-ray production andradiography, ion irradiation, foil activation etc. are some other applications of the device. Thepioneer behind the development of the IEDF device is P. Farnsworth [2], and later, R. Hirsch [3]worked with him to upgrade the device as a fusion source. They have developed the ion gunspherical IECF device to confine the ions at the center of the device. Over the years, the devicehas been improved and promoted by many other researchers across the globe by introducingsingle, double and triple gridded system in both the cylindrical and spherical geometries [1].



71

The re-circulation of ions across the cathode openings is the basic process through which the ionsget confined at the center and finally produce fusion (at more than about -30 kV applied voltage).Also, formation of multiple potential well structure inside the cathode is another importantphenomena of the device to continue the ion re-circulation [1,3]. In this present work, we havefocused our study on ion re-circulation across the cathode grids and the formation of potentialwells inside the cathode during relatively lower cathode voltage operations (up to -5 kV). Wehave designed and simulated the cylindrical IECF device using particle-in-cell (PIC) method tostudy the ion dynamics and to obtain the potential profiles as well as the ion phase space tovisualize the ion re-circulation process. Lastly, we have compared the simulated profiles with theavailable experimental results, in this work.

Modeling:To visualize the ion behavior inside the cylindrical IECF device we have performed theelectrostatic PIC method using XOOPIC code [4] which is a 2D-3V object oriented PIC codewith an in-built Poisson solver. The code includes Monte Carlo Collision (MCC) algorithms tomodel the collisions of the particles. Multigrid Poisson’s solver is used which describes theboundary conditions of the simulation. The simulated domain and the parameters are designed torecreate the exact experimental environment with a cross section of the cylindrical deviceincluding the cross section of the cathode grids (having 8 numbers of grid wires), as shown in thefigure 1(b). We have also modeled the electron emitters to emit equal flux of electronscontinuously into the simulation domain. Deuterium is used as the background gas and theemitted electrons interacts with

Fig. 1: (a) Schematic of the cylindrical IECF device, (b) Cross-section of the simulation domainwith the cathode grids.

them to produce ions due to ionization. A high negative voltage is applied across the cathode as aresult of which the ions accelerated towards it. The time step (Δt) of the simulation is so chosen tosatisfy the Courant condition [5] and the spatial step (Δx) is considered such that it is always lessthan or equal to the Debye length of the system. The drift velocity of the fastest particle present inthe system decides the time step size [6]. Performing adequate calculations, the simulationparameters are determined. The time step is found to be ~10-11 s, and the specific weight taken, isof the order of 109 in this simulation. The primary electron and ion temperatures are assumed tobe 3 and 0.1 eV, respectively. The input file of the XOOPIC is prepared considering all theparameters and conditions mentioned here. A typical period to achieve the steady state is about 2– 3 days in our computer. Few scripts are also developed in MATLAB® in order to visualize thesimulation data.

(a) (b)



72

Fig. 2: (a) Ion phase space, (b) Bottom view during experiment, showing ion channels coming outof the central highly dense region.

Results and Discussion:As mentioned earlier, ion re-circulation is the primary process in such IECF devices. We canvisualize the re-circulation during run-time and the phase space of ions during -1 kV operationalso depicts it, as shown in figure 2(a). During the acceleration of the ions towards the highlytransparent cathode, some of the ions passed through the grid opening to the other side of thechamber. Again, some other ions collide at the center and get scattered to different directionsthrough the grid spacing, and some of them collide with the cathode grids and produce secondaryelectrons. The ions which pass through the cathode grid openings either directly or via scattering,re-circulates across it along some particular channels which can be observed in the simulatedprofile as well as in the actual experiment, as shown in figure (2). The experimental photograph(figure 2(b)) is taken from the bottom side of the chamber in which the channels (spokes) of ionsare vividly visible. This mode of discharge is popularly known as the star mode [1] in the IECFdevice.

Fig. 3: Surface plot of potential during -1kV cathode voltage.

Fig. 4: (a) Simulated, (b) experimental potential profiles from -1 to -5 kV cathode voltageoperations. At -5 kV voltage, formation of multiple (double) potential wells is observed.

(a) (b)

(a)

(b)

(b)



73

On the other hand, observation of the potential profiles shows some interesting phenomena. Thestructure of the potential profile, specially, inside the cathode grids become very important due tothe formation of space charge of both ions and electrons and multiple potential wells can beobserved during high voltage operations. Figure (3) shows the surface plot of the potential profileduring -1 kV cathode voltage operation. We have tried to study the structural changes in thepotential profiles from -1 to -5 kV cathode voltages. After reaching the steady state in thesimulation, we have plotted the equatorial profiles of potential for different applied voltages andare compared with the experimentally obtained profiles [7], as shown in figure (4). As weincrease the cathode voltage, acceleration of the ions towards the cathode grids will be increased,they will fall into the potential well made by the applied negative voltage to the cathode and theirconcentration inside the cathode will also increase. Due to the increased concentration of ionsinside the cathode, they will form a space charge of ions at some point of time. This space chargeof ions can be termed as the virtual anode inside the real cathode. Moreover, the virtual anode soformed will not allow further ions to accelerate towards it, rather the outside ions will be repelledand the secondary electrons will be attracted this time. These electrons will move into the virtualanode and their density may be increased if we further increase the cathode voltage. If theelectron density increases, they may form a space charge of electrons which may be termed as thevirtual cathode inside the real cathode. In the simulated profiles clear formation of the virtualanode (space charge of ions) is observed up to -4 kV cathode voltage operation. The depth of thepotential well and the height of the virtual anode increases with the increase in applied voltage.At -5 kV voltage, we have observed an indication of formation of another virtual electrode, i.e., avirtual cathode due to electron space charge at the center. In the experimental results using aLangmuir probe, we have observed similar kind of profiles. In fact, the formation multiplepotential well in -5 kV operation is more prominent in the experiment, as shown in figure 4(b).However, the maximum potential drop in the experimental results are less than that observed inthe simulation. For example, in case of -4 kV operation, the maximum negative potentialobserved during experiment is ~-2600V while it is around -3300V in case of simulation. This isdue to the presence of the probe inside the chamber which forms a sheath around it so that exactmeasurement of potential is a difficult task. On the other hand, due to the absence of any foreignbody during simulation, we don’t have such issues.

Conclusion:Continuous ion re-circulation and formation of multiple potential well inside the cathode are thebasis for the fusion reaction to occur in such IECF devices, during high voltage operations. Ionre-circulation can be visualized during run time of the XOOPIC simulation and from the ionphase space ion channels can be easily observed. Experimental photograph also shows the same.In the potential profiles, depth of the potential well is found to be increased with the increase inapplied negative voltage. During -5 kV, formation of double well is observed. Langmuir probemeasurements also supports the simulated results when observed experimentally. In future, weare planning to study other parameters like ion density, ion energy distribution function, etc.using XOOPIC simulation and will also try to improve the simulation further in order to visualizethe data during fusion relevant (more than -30 kV) energies.

Acknowledgment:I acknowledge my supervisor, Director of IPR, Center director of CPP-IPR, and my lab-mates fortheir support. I am also thankful to Department of Atomic Energy (DAE) for their financialsupport to carried out my work.

References[1] G. H. Miley and S. K. Murali, Inertial electrostatic confinement (iec) fusion, Fundamentals

and Applications, Springer (2014).



74

[2] P. T. Farnsworth, Electric discharge device for producing interactions between nuclei(1966), US Patent 3,258,402.

[3] R. Hirsch, Inertial-electrostatic confinement of ionized fusion gases, Journal of AppliedPhysics 38, 4522 (1967).

[4] J. P. Verboncoeur, A. B. Langdon, and N. Gladd, An object-oriented electromagnetic piccode, Computer Physics Communications 87, 199 (1995).

[5] C. De Moura, C. Kubrusly, and S. Carlos, The courant-friedrichs-lewy (c) condition, ApplMath Comput 10, 12 (2013).

[6] C. Birdsall and A. Langdon, Plasma physics via computer simulation (CRC press, 2004).[7] D. Bhattacharjee, D. Jigdung, N. Buzarbaruah, S. R. Mohanty, and H. Bailung, Studies on

virtual electrode and ion sheath characteristics in a cylindrical inertial electrostaticconfinement fusion device, Physics of Plasmas 26, 073514 (2019).



75

PSC-4

Slow and fast modulation instability and envelope soliton of ionacoustic waves in fully relativistic plasma having

nonthermal electrons

Indrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,21 Department of Physics, Jadavpur University, Kolkata-700032, India

2East Kolkata Centre for Science Education and ResearchP-1, B.P.Township, Kolkata-700 094, India.


Abstract

Slow and fast modulation instability, envelope soliton of ion acoustic wave have beentheoretically studied in cold unmagnetized fully relativistic plasma consisting of coldpositive ions having constant stream velocity and nonthermal electrons using Fried andIchikawa method. The expression of nonlinear Schrodinger equation in fullyrelativistic plasma has been derived for slow- and fast- mode of the wave and theconditions for the existence of modulation instabilities are obtained. From the nonlinearSchrodinger equation, the solution for envelope solitons for slow- and fast- modes of thewave are also obtained. The profiles of bright- and dark-envelope solitons are drawn anddiscussed taking different values of ion-stream velocity and nonthermal electrons. Theresults are new and would be applicable in astrophysical plasma.Keywords: Relativistic plasma, Ion acoustic wave, Two temperature electrons, Modulationinstability, Envelope solitons, Nonlinear Schrodinger equation , Fried and Ichikawa method.

1. Introduction

In weakly relativistic plasma, Das and Paul [1,2] have first derived the Korteweg-deVries(K-dV) equation using reductive perturbation method of Washimi and Taniuti [3 ] tostudy ion acoustic solitary waves (IASWs) considering a collision less andunmagnetized weakly relativistic plasma consisting of cold ions and isothermal electrons.It was first shown that relativistic effect gives significant contribution to IASWs only inpresence of streaming of ions. Later, various authors have considered differentparameters in weakly relativistic plasma , e.g. ion-temperature, negative ions beam ionstwo-temperature electrons , nonisothermal electrons etc. for the studies of ion-acousticsolitary waves. However, solitary waves in relativistic plasma in presence of nonthermalelectrons gives rise to some interesting results. But, few authors have studied themodulation instability of ion acoustic waves in fully relativistic plasma. Ghosh andBanerjee [4] have theoretically studied nonlinear amplitude modulation of ion-acousticwaves (IAWs) in fully relativistic unmagnetized two-fluid plasma by using complete setof fully relativistic dynamic equations. The growth rate is shown to decrease withincrease in the relativistic effect. We are interested here to study modulation instabilityand envelope solitons in a fully relativistic plasma composed of cold relativistic ions



76

andnonthermal electrons. We have derived the nonlinear Schrodinger equation by usingthe Fried and Ichikawa method [5] instead of multiple scale perturbation technique.2.FormulationThe plasma is assumed to be fully relativistic unmagnetized collision less having

nonthermal electrons . So, the basic equations describing the plasma dynamics innon-dimensional form can be written as:

( ) 0ii i

n n ut x

- - - (1), ( )i iru u

t x x

- - - (2),2

2 e in nx

- - - (3)

where,

12 2

2/ , 1- ii

uu uir c

,

ϕ is the electrostatic potential, in and iu are the density and velocity of ions, iru is therelativistic velocity of ions, c is the velocity of light; en is the density of electrons, In theabove Eqs. (1)-(3) the densities of electrons are normalized with respect to theequilibrium density of ions 0n , the distances are normalized by the Debye length, time bythe ion plasma period, velocity by ion-acoustic speed and potential by /B eT e .

The boundary conditions are : 0 , 1i iu u n and 0 as x .Since we assume the electrons to be nonthermally distributed, the electron density en inEq. (3) is given by

2(1 )exp( )en (4)where, 4 / (1 3 )p p , measures the deviation from thermalized state p determinesthe number of nonthermal electrons in the plasma.Using Fried and Ichikawa [5] we have derived the Nonlinear Schrodinger (NLS)equation given by

22

2( ) 0gi C P Qt x x

(5)

where, P is the dispersive coefficient P and Q is the nonlinear coefficient Q .

The nonlinear coefficient Q of NLS equation (5 ) for slow and fast wave are obtained as4

2 2 1 36 5/23 1 1 46 6 2 3/2

1 1 1 2 1

(2 3 )3 10(2 )2 3 ( )

f ff f

f

Q

(6a)4

6 5/2 2 2 1 33 1 1 46 6 2 3/2

1 1 1 2 1

(2 3 )3 10(2 )2 3 ( )

s ss s

s

Q

(6b)



77

Where, 2 2 3 32 2

2 2 22 2 2 2 2

4 44 2 2 2 4 2 2 2

, , 1 , 1 ,

5 8 5 85 , 5

f o s of f o s s o f s

f o f o fo s o s o o sf s

V u V uV u V uc c

V u V u Vu V u V u u Vc c c c c c c c

The dispersive coefficient P for fast and slow mode of the wave is obtained as3/21

2 5/21

12 ( )Fast

kPk

,3/21

2 5/21

12 ( )Slow

kPk

(7)

In (6) and (7), the parameters 1 2 31 (1 3 )(1 ), ,2 6

,

2

1 21 iouc

3. Results and discussions

A) The modulation instability

The amplitude modulation of ion acoustic waves (IAW) in fully relativistic plasma

consisting of inertial cold ions and isothermal twotemperature can be studied by using

the NLS equation (6).

The maximum growth rate of modulation instability of ion acoustic wave is20m Q . (8)

α0 is a real constant and 20Q is the amplitude dependent frequency shift. The sign

of the product PQ determines the stability / instability of the ion-acoustic wave. If theproduct PQ is negative (i.e. PQ < 0) the ion acoustic wave will be unstable relativelymodulation. But, the wave will be stable relatively modulation if PQ ( i.e. PQ > 0) ispositive.

Growth rate of unstable wavesThe growth rates of unstable IAW wave given by Eq.(12 ) are numerically estimatedand graphically shown in Fig.1(a) and Fig.1(b) for different values of ion streamvelocity and nonthermal parameter of electrons in fully relativistic plasma.



78

4 6 8 100

1 10 7

2 10 7

3 10 7

Wave Number

Gro

th R

ate

X2 j 3

X2 j 4

X2 j 5

X2 j 6

k j

0.2 0.4 0.6 0.8 10

20

40

60

Xsj 1

Xsj 3

Xsj 5

Xsj 6

kj

Fig.1(a). Growth rate for slow mode ion acoustic wave different relativistic streamvelocity. The red, blue, green and magenta graphs represent u0/c=0.4, 0.533,0.667 and0.8 respectively, =0.3,c=1.5; Fig.1(b) -Growth Rate of slow mode for different valuesof . The red, blue, green and magenta curves represent =0.1. 0.3, 0.5 and 0.6;u0/c=0.6, c=2.

B) Envelope Soliton

The solitary wave solutions of ion acoustic wave (IAW ) may be obtained from the NLSequation (5). The product PQmay be positive or negative which give two types localizedsolitary wave solutions. For PQ < 0 , the wave is modulationally unstable and the bright-envelope-soliton (or bright soliton) is excited. But, when PQ > 0 the wave ismodulationally stable and gives a dark-envelope-soliton (or dark soliton). In fact, brightsolitons are localized large-amplitude excitations on the envelope of certain carrierwaves. Their formation requires an attractive or focusing nonlinearity. The dark solitonsare dips or holes in a large-amplitude wave background. Their formation requires arepulsive or defocusing nonlinearity. The profiles of bright-envelope solitons and darkenvelope solitons for different values of ion stream velocity nonthermal parameter ofelectrons are shown in Figs.2(a) and 2(b) for bright solitons.



79

5 0 50

0.02

0.04

0.06

0.08

Brig

ht S

olito

n Pr

ofile

j 2

j 4

j 5

j

5 0 50

0.05

0.1

Brigh

t Soli

ton P

rofil

e bs j 1

bs j 2

bs j 4

j

Fig.2 (a) Profiles of bright soliton for slow mode of the wave different valuesrelativistic ion stream velocity (u0/c).The red, blue, green and magenta linescorrespond to u0/c =0.267, 0.533, 0.667 ; Other parameters are and =0.3,c=1.5;Fig.2(b) Profiles of bright soliton for slow mode of the wave for different values .Thered, blue and green lines correspond to =0.1, 0.2 and 0.6; Other parameters are .c=2,u0/c=0.6

4. Conclusion

In this paper we have theoretically studied modulation instability of slow and fast modeof ion acoustic waves along with the possible generation of both dark- and bright-envelope soliton in a fully relativistic plasma consisting of cold ions and nonthermalelectrons using Fried and Ichikawa method.In our analysis, the form of envelope solitonis derived from the NLS equation and structures of bright and dark envelope solitons forslow and fast mode are graphically shown and discussed.

i) Growth Rate: The growth rates of unstable slow- mode slowly increaseswith ion stream velocity 0 /u c and wave number k .The growth rate of slow- modeincreases with the increase of and wave number k.

ii) Bright Solitons: The bright solitons of slow- mode for different values of0 /u c with fixed values of k ( k =1) are compressive in nature the amplitude decreases

with the increase of ion stream velocity. The bright soliton of slow- mode for differentvalues of and fixed values of k are compressive in nature and its amplitudeincreases with the increase of .

The relativistic plasmas occur in a variety of situations, such as, space-plasmas,laser- plasma interaction , plasma sheet boundary layer of earth’s magnetosphere . Therelativistic motion in plasmas is assumed to exist during the early evolution of theUniverse . In astrophysical observations it has been found that particles are ejected withhigh velocities during solar bursts or the explosion of stars huge amounts of matter in theform of ionized gases are ejected from these astrophysical objects at very high velocities .

References

[1] G C Das and S N Paul (1983) , XVI International Conf. Phenomena in Ionized Gases,August 29-September 2, 1983.[2] G C Das and S N Paul ,. The Physics of Fluids 28, 823( 1985).[3] H Washimi and T Taniuti, Physical Review Letters 17, 996 (1966).[4] B Ghosh and S Banerjee , Journal of Plasma Physics 81, 905810308 (2015).[5] B D Fried and Y H Ichikawa, Journal of Physical Society of Japan 34, 1073(1973).



80

PSC -5

Effect of negative charge dust on ion-acoustic dressed solitons inunmagnetized plasmas

J. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2Department of Physics, Govt. College Tonk, Rajasthan, India-3040011Seth RLS Govt. College, Kaladera, Rajasthan, India-303801

2Govt. College, Dholpur, Rajasthan, India-328001


Abstract

Propagation of an ion-acoustic soliton in a plasma consisting of negative charge dust isconsidered the reductive perturbation method (RPM). The well known RPM has beenused to derive the KdV equation. This exact solution reduce to the dressed solitonsolution when mach number is expanded in terms of soliton velocity. Variation ofamplitude and width for the KdV soliton, core structure, dressed soliton and exact solitonare graphically represented to different values of negative ions and mach number.The present study of this paper may be helpful in space and astrophysical plasma systemwhere negative charge dust ions are present.

Key words: Soliton, RPM , Dusty Plasma, soliton

Introduction:In recent years, interest in study of dusty plasmas has arisen because of its

occurrence in space and astrophysics. Vladimirov et al. [1] studied the ion acoustic waves incomplex laboratory plasmas containing dust grains and negative ions, where effects of relevantprocesses were considered. Mamun and Shukla [2] used two models for negative iondistributions, i.e., Boltzmannian and the streaming, and found that the negative ion numberdensity and streaming velocity could greatly affect the dust surface potential, and therefore thedust charge. Baluku et al. [3] investigated dust ion acoustic solitons in an unmagnetized dustyplasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a kappadistribution using both small amplitude and arbitrary amplitude techniques. A theoreticalinvestigation of dusty plasma consisting of ion fluid, non-thermal electrons and fluctuatingimmobile dust particles has been made by Alinejad [4].Ichikawa et al. [6] and Sugimoto and Kakutani [7] have been studied the dressed soliton inplasmas. Ion acoustic dressed soliton in EPI [8-9], ion beam [10] and dusty [11] plasmas havebeen studied using sagdeev potential technique and RPM. They discuss the characteristics of thesoliton such as amplitude, width and velocity. Chatterjee et al. [12] and Roy and Chatterjee [13]have been studied the dressed soliton in quantum plasmas and dusty pair-ion plasma. Effect of thequantum parameters and characteristics of soliton such as amplitude and width.

Tiwari [9] studied only the effect of fractional concentration on amplitude and width thesoliton. The aim of this research paper have been studied the propagation of ion-acoustic dressedsoliton in nonthermal electrons in plasmas by considering the RBM, the first and second coupled



81

evolution equation, namely the KdV equations is derived. Through elimination of the secularterms, the KdV soliton, core structure, dressed soliton and exact soliton are determined.

Basic equations:We consider a collisionless unmagnetized plasma consisting of ions and dust. The dynamics ofthe plasma is given by following set of normalized fluid equation:

0

xVN

tN iii (1)

xxVV

tV i

ii

(2)

0

xVN

tN ddd (3)

xxVV

tV d

dd

(4)

id NNex

12

2

(5)

Here N and V are the normalized density and fluid velocity of the plasma ions respectively. isthe electric potential. ,/ dd MZ ,/ idd mmM ,/ 00 id nn and . dZ Thesequantities have been rendered dimensionless in terms of equilibrium plasma density ),( 0n ion

sound speed 2/1)/( ie mT and characteristic potential ),/( eTe respectively. The space coordinate

speed )(x has been normalized in terms of Debye length speed 2/1200 )/( enTeD and time

coordinates by the inverse of ion plasma frequency.

Stationary solitons solution :We introduce the usual transformation in equation (1) – (5) and obtain stationary soliton solution

Mtx (6)Where M is the Mach number of soliton. Integrating Eqs. (1) - (5) and using the necessaryboundary conditions (Ni,d → 1, and Vi,d → 0 as ) for a soliton structure, gives

22

MMN i

(7)

22

MMN d

(8)Integrating the value of Ni in (7) and Nd in (8), multiplying both side by ,/ dd integratingonce and using the necessary boundary conditions (Ni,d → 1, and Vi,d → 0 as ) we getthe following relation

0)()(21 2 Vd (9)

where the Sagdeev potential V is given by

2

22

2 21121111)(M

MM

MeV

(10)



82

I expand the value of ...62

132

e and using this Taylor series expansion in (9) and

include also the effect of fourth-order nonlinearities of electric potential ).( The equation (9)reduces to 4

33

22

12 d (11)

Where

221

11MM

(12)

311

4

2

42

MM(13)

66

3

3 45

45

121

MM (14)

Integrating of eq. (11) with respect to and using the boundary conditions( ,0/ dd 0 as ) gives stationary exact soliton solution as

11)(cosh241

/2

22/1

22

31

21

A

(15)

Where2/1

1

4

A (16)

The exact soliton solution (15) is the same results to (9a) earlier investigation [9]. We denote (15)as small amplitude as compared with the KdV soliton, because its expansion in small amplitudelimit can give rises to the KdV soliton and dressed soliton solution when the RPM is used for theanalysis.We expand the Mach number (M) of soliton velocity as 1M in (12) – (14), and

retaining terms up to 2 in ,1 and terms up to in ,2 and keeping ,3 independent of such that each terms on R.H.S. of (11) is of fourth order in combined nonlinearities of and .we find out

21 3211 (17)

42 R (18)

3

3 1512

1 (19)

where

2

2

13113

R (20)

We using (17) – (19) and retain terms up to the order of 2 in (15)

221

2

1 kkk (21)

Rk

413

2

3 (22)



83

...6

4141 1

44

62/1

2

31

kkk

(23)where

R

k

11(24)

21

12414R

Rk (25)

and

3

2

216831116

RRRk

(26)

Substituting (17) - (19) in (15) and retain terms up to the order of 2 in the expansion, we canwrite the dressed soliton solution as

AAhAh ~tanh~sec~sec 222

21 (27)

where

Rkkkkkkkkk

Rkk

Rkkkkkkkkkkk 31

32

132223

23

2

32

131132

1 842816242

(28)

Rkkkkkkkk

Rkkkkkkk 31

32

13223

2

3132

2 822842

(29)Including the contribution of 2 term in (15), we can expressed A~ as

2/12/11

21

4~

A (30)

Keeping terms of order only soliton solution (27) reduces to the KdV soliton

Ah2sec2

3 (31)

where2/1

4

A (32)

Equation (27) is following first (core structure) and second terms (cloud structure) Ahcore

~sec 21 (33)

AAhcloud~tanh~sec 22

2 (34)Results and Discussion:We present the variations of amplitude, width and product of amplitude and square of width (P =amplitude × Width2) of the KdV soliton ,k core structure ,c cloud structure ,cl dressedsoliton ,d and the small amplitude exact soliton solution .sFigure (1) shows the variation of S (solid blue color line), KdV (dashed red color line), core(dotted black color line), dS (dotted green color line) and cloud (solid yellow color line) versus for different value of = 0.006, 0.007 and 0.008 at the Md = 10000, Zd= -100, and M = 1.2.



84

Here we find that as finite increases, the small amplitude of S , KdV , core , dS and cloudcorresponding to also increases but the potential of the KdV soliton )( KdV is constant.

Fig. Cap.Fig. 1. Variation of S (solid blue color line), KdV (dashed red color line), core (dotted blackcolor line), dS (dotted green color line) and cloud (solid yellow color line) vs for differentvalue of = 0.006,0.007 and 0.008 at the Md = 10000, Zd= -100, and M = 1.2.

Conclusions:The small amplitude exact soliton solution, KdV soliton, core and cloud structure and dressedsoliton solution which described the ion-acoustic dressed soliton in unmagnetized plasma withnonthermal electron is derived. The main conclusion of this paper are the followingFor a given value of soliton velocity, the amplitude of exact soliton and core structure (KdVsoliton and dressed soliton) decreases (constant) as nonthermal increases but for a given value of , the amplitude of exact soliton, core structure, KdV soliton and dressed soliton increases assoliton velocity increases.

References[1] S V Vladimirov, K Ostrikov, M Y Yu, and G E Morfill, Phys. Rev. E 67, 036406 (2003).[2] A A Mamun and P K Shukla, Phys. Plasmas 10, 1518 (2003).[3] H Alinejad, Astrophys Space Sci, Volume 327, Issue 1, pp 131-137 (2010).[4] T K Baluku, M A Hellberg, I Kourakis and N S Saini, Phys. Plasmas 17, 053702 (2010).[5] S L Jain, R S Tiwari and M K Mishra, Astrophysics and Space Science 357 (1), 57 (2015).[6] Y H Ichikawa, T Mitsu-Hashi and K Konno J. Phys. Soc. Jpn. 41, 1382 (1976).[7] N Sugimoto and T Kakutani J. Phys. Soc. Jpn. 43, 1469 (1977).[8] R S Tiwari, AKaushik, M K Mishra Physics Letters A 365, 335 (2007).[9] R S Tiwari Physics Letters A 372, 3461 (2008).[10] Yashvir, R S Tiwari and S R Sharma Canadian Journal of Physics 66, 824 (1988).[11] R S Tiwari and M K Mishra Physics of Plasmas 13, 062112 (2006).[12] P Chatterjee, K Roy, G Mondal, S V Muniandy, S L Yap and C S Wong Physics of

Plasmas 16, 122112 (2009).P Chatterjee, K Roy, S V Muniandy and C S Wong Physics of Plasmas 16, 112106 (2009).

[13] K Roy and P Chatterjee Indian Journal of Physics 85, 1653 (2011).



85

PSC-6

Inductive Energy Storage System with Plasma Opening Switch: Areview

Kanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,21Homi Bhabha National Institute, Mumbai-400094,

2Pulsed Power & Electro-Magnetics Division, Bhabha Atomic Research Centre Facility,Atchutapuram, Visakhapatnam, Andhra Pradesh, India-531011,


Abstract

Pulse compression technique is used to generate high powers in the range of Terawatt withsecondary energy storage device as inductive energy store (IES) with plasma opening switch(POS) having charging time is in the range of microseconds and output pulse duration innanoseconds. The inductive energy store is more advantage compared to most widely usedcapacitive energy storage devices with respect to energy density which is 10 -100 times high [1].The parameters that define the performance of IES system are peak output voltage, peak outputcurrent, rise times and pulse widths of current and voltage. Employing of POS results inmultiplication of voltage and power with good energy coupling between the source and load. Theuse of POS improves the load current rise times as well [1]. The IES with POS technology is usedin different applications include generation of particle beams, radiation sources, fusion researchand defense applications. Some of the facilities of plasma opening switch for mega-ampere areGIT-16 [2], MAGPIE [3], COBRA [4], DECADE [5], ACE-4 [6]. The experimental results ofthese facilities gives details of current conduction phase and opening phase of micro second POS.This paper provides details of different facilities of POS technology and simulation of idealmodel of inductive energy system with different functions of variation of POS switch resistanceconnected to resistive load.

Key words: Inductive Energy Storage, Plasma Opening Switch, mega-ampere

Introduction:In pulsed power engineering, the applications of inductive energy storage systems have goodinterest. The IES with POS is a solution for many problems which includes power enhancement,output pulse width and rise time reduction, prepulse elimination and design of pulse generatorswith low cost for different applications. The Fig-1 shows the IES with plasma opening switch.



86

Fig.1: Schematic view of POS operationThe working of POS is as follows: a plasma path is formed between the high voltage electrodeand grounded electrode parallel to load. On conduction of the path due to plasma puffing, theenergy stored in capacitor is transferred to inductive store. Due to changes of plasma parameters,the path becomes non-conducting suddenly (POS opens), which generates high voltage acrossthe switch and load. Under these conditions, the total energy stored in inductor is transferred toload [7]. This paper provides the review on different POS technologies available in literature inSection-I and simulation of ideal IES system in section II. The section-III gives the conclusion ofpaper.

I. Facilities of POS Technology

1. GIT-16 (S. P. Bugaev et.al)The GIT technology was developed by High Current Electronics Institute, Russia for theexperiments on high-temperature plasmas generated by gas puff and wire array implosions. TheGIT-16 is a 6.8 mega-joule pulsed power generator in which the technology of direct pumping ofan IES from Marx capacitor bank [8] and delivery of energy to a Z-pinch [9] load withmicrosecond POS employed. Each module consists of a primary energy store (set of Marxgenerators), a vacuum bushing insulator and a vacuum transmission line. The primary energystore consists of two sections connected in parallel in which each sections contains 12-stage Marxgenerator. The GIT-16 pulse generator has negative output voltage generation of 2MV withcurrent as 7.6MA [10]. The currents in this is monitored by Rogowski coils.

2. MAGPIEMAGPIE is pulsed power facility in Imperial College London. MAGPIE consists of four Marxcapacitor banks which is discharged in to four independent pulse forming lines (PFLs) [11].These are combined into single vertical transmission line which delivers maximum of 1.4MA ofcurrent within 250ns to load as vacuum chamber [12]. The peak electron density measuredthrough interferometry technique is 2.5×1018 per cm3 [13].

3. DECADEThe DECADE pulsed power generator is developed by US based Physics International Company.This generator is multi-module system working in X-ray explosive emission diodes. The mainparts of module are Marx generator (570kJ of energy) [5], the intermediate storage capacitor, thetriggered closing switches, a water line, the vacuum insulator, the inductive store is designedusing magnetically insulated transmission line, the POS and the diode load. When POS in fullconduction state, the maximum current reached up to 1.8 MA within 300 ns. The primary energystore Marx generator consists of six modules, each containing twelve stages 85 kV per stage. Theoutput voltage of the Marx generator reached to 1MV. The intermediate energy storage capacitoris discharged through six simultaneously operated triggered gas switches. The plasma sources arecoaxial cable guns that produce a plasma density of approximately 1015 cm-3 [14].



87

4. ACE-4The ACE-4 pulsed power facility is Mega joule system capable of delivering 4MJ [6] developedby Maxwell Company, USA. Power Conditioning is performed using IES with POS. Theflashboards are used as plasma sources for the ACE-4. The Marx module consist of 24 generators.In conduction phase, the maximum current in the POS builds up to 5 MA in 1.6 µs. Duringconduction phase current front propagates down the plasma in a snowplow mode, pushing theplasma ahead and to the sides, until the current channel reaches the end of the POS region. Theexisting plasma in the regions of POS eventually thins such that it will not allow the current toflow, and a gap is formed, transferring the current to the load. The current is typically transferredto the electron diode load in 100 ns. The electron density measured using the laser basedinterference technique is approximately ~1015/cm3 to maximum of 1018/cm3 according toliterature [14, 15].

5. COBRAThe COBRA pulsed power facility is designed at Cornell University for wire array X pinchstudies. The two applications for which the COBRA designed is to study X pinch as loads and todevelop X pinches in return current path as source of point-projection radiography of wire arrays.The primary source consists of storage capacitor charged to 70kV. The output of primary sourcecharges the four coaxial water pulse forming lines having resistance of 1.8 ohm with line delay as30ns. The intermediate capacitive store charged from two pairs of water PFLs is dischargedthrough two self-breaking gas switch. The four charged output PFLs from intermediate sourcedischarged independently using laser triggered spark gap switches. The discharge current of1MA has rise time of 230ns with full width and half maximum of 350ns [16].

II. Simulation of Ideal Model of OS with IES

The Opening Switches play important role in the IES system. The Fig-6 shows theinductive energy storage system. The main circuit of IES contains a primary storage device, atriggered closing switch, storage inductor (secondary storage device), an OS and a load. Thedesign and development of opening switch is the challenge in the present scenario. The OSshould have less resistance while conducting, high resistance while in open state, capability ofinterrupting high currents in short duration, high dielectric strength and fast recovery response.The rise of the resistance increase of OS should be less such that it can interrupt the highamplitudes of currents in short time i.e., the pulse width is in the order of micro or nano seconds.The rate of change of resistance in OS is the parameter that describes its performance.

Fig. 2: IES with Primary storage device as capacitorsOperation Principle:The basic operation of the IESS, in which the energy is be stored in the form of magnetic fieldduring the current flowing through inductor. The inductor is charged through the sources likecapacitors, battery, magnetic flux compression generators, etc. As the OS is closed, primarycurrent flows in the circuit which charges the inductor and a practical inductor contains on ESR(R) depends purely on the design of inductor. We have to design the inductor such that it has less



88

�t�� losses in primary loop and the time constant of the circuit (L/R) must be greater than time (t)

to trigger the switches from the charging of the source. The charging time of inductor is based onthe time constant of primary loop. The current in the OS is interrupted such that the total currentwill be transferred to the load generating high voltages across the load terminals.

Circuit Analysis:The circuit shown in the Fig-6 is the simplest and ideal IES which was considered here foranalysis reported by Pai. S.T. The voltage source in series with the inductor is considered as thecurrent source �䂺 in the primary loop to charge the storage inductor. Here the OS is consideredequivalent to time dependent resistor R(t). The different cases of variation of OS resistance isdiscussed in detail.Case(i): The OS is considered as the linearly rising resistance switch with time. The switchresistance is defined as � � = ��. Where k is the slope which is constant. The circuit voltage andcurrent equations

�䂺 = �� + �� + �� = t (1)

�� = ��The solution of the load current is obtained by applying the boundary conditions i.e., at t=0, �䂺 =�䂺,

�L = �䂺��

��+��exp  ��

��ln �� + �� − �� (2)the time at which the maximum current can be obtained is calculated by equating the derivative ofthe �L to zero and given by

�� =��

(3)

Fig. 3: Switch current profile and Load current profile for case (i) with different switching speeds

Case(ii): In this case the resistance of the OS is considered as the step function, with conditionsas, at t=0, R=0 and as t > 0, constant value of R=Rf. This variation of resistance is represented be

� = �� v − �−�� (4)By applying the boundary conditions and considering the load as inductive load (LL) the loadcurrent is expressed as

�L = ��䂺 v − �−�� (5)Where constants, � = �

�+��, � = ��

��From the above equation if the initial value of the current and Rf is made high then the power atthe load terminals will be high.



89

Case(iii): Now, if the resistance variation of the OS is considered as step rise i.e., � � t �䂺�in step. If the load is inductive load then from the law of conservation of the magnetic flux, theload current is expressed as

�L = ��䂺 (6)Where, constant ‘a’ is already defined above.

Fig. 4: Switch current profile and Load current profile for (a) case (ii) (b) case(iii)

Conclusions

In this paper, the plasma opening switch based inductive energy storage pulse generatortechnologies developed by various laboratories and researches are reviewed and there current andvoltage ratings were reported. The simulations of ideal model of opening switch based IESsystem with variation of switch resistance is carried out and results were reported. We aim todesign a nanosecond plasma opening switch based inductive energy system which can delivercurrent in the range of mega amperes, output voltage in the range of mega volts and energy of40kJ.

References[7] R. A. Meger et. al., Appl. Phys. Lett., 42, 943(1983).[8] S. P. Bugaev et.al., Russian Physics Journal, 40, 1154-1161(1997).[9] G. N.Hall et al., Review of Scientific Instruments, 85, 943-945(2014).[10] Shelkovenko, Tatiana A et al., IEEE transactions on plasma science, 34, 2336-2341(2006).[11] P. Sincerny et al., Tenth IEEE International Pulsed Power Conference, 3-6 July 1995,

Albuquerque, NM, USA, 405-416(1995).[12] R. Crumley, D. Husovsky and J. Thompson, 12th IEEE International Pulsed Power

Conference, 27-30 June 1999, Monterey, CA, USA, 1118-1121(1999).[13] B. V. Weber et al., IEEE Transactions on Plasma Science, 19(5), 757-766(1991).[14] W. J. Carey and J. R. Mayes, Conference Record of the Twenty-Fifth International Power

Modulator Symposium, 2002 and 2002 High-Voltage Workshop, 30 June-3 July 2002, CA,USA, 625-628(2002),

[15] M G Haines, Plasma Physics and Controlled Fusion: IOP Science, 53(9), 093001(2011).[16] https://www.hcei.tsc.ru/en/cat/fields/fields.html for information on[17] Liansheng Xia et al., Review of Scientific Instruments, 79, 086113(2014).



90

[18] https://www.imperial.ac.uk/plasma-physics/magpie/[19] T. Clayson et al., IEEE Transactions on Plasma Science, 46(11), 3734-3740(2018).[20] Pulse Generators with Plasma Opening Switches. In: Pulsed Power. Springer, Boston, MA,

2005.[21] Niansheng Qi et. al., IEEE transactions on plasma science, 30(1), 227-238(2002).[22] https://www.lps.cornell.edu/project/cobra/



91

PSC-7

Simulation Study of Planar Anode Micro Hollow Cathode DischargeUsing Dielectric Layer

Khushboo Meena1, R P Lamba11CSIR-Central Electronics Engineering Research Institute (CSIR-CEERI),

Pilani-333031, Rajasthan, India.


Abstract

Microdischarges are very popular for a long time and they have many advantages. Micro HollowCathode Discharge is one of the micro discharges which is formed in the cylindrical shapedhollow cathode and responsible for the generation of high electron density discharge, but it has avery short period of a lifetime due to the sputtering effect on the cathode walls and moving of thedischarge from glow to arc region. There is another type of discharge called Dielectric BarrierDischarge; it has the advantage of low electrode erosion.In this paper, a 2D-axis symmetric model is designed and simulated using the Plasma Module ofCOMSOL 5.4 Software. This model includes the MHCD as well as DBD discharge. In this model,a dielectric layer of 40µm is placed on the inside wall of the anode. In this model, a planar anodeis used which is covering one side of the hollow cathode. The diameter of the hollow cathode is500µm and a height of 500µm is used. Argon gas is used for the discharge at atmosphericpressure. Pulsed voltage is applied to have the 1000ns period cycle. In this model for the ignitionof the discharge takes place at the minimum distance between anode and cathode. After thatdischarge gets sustained in the hollow cathode cavity and attains the stable abnormal glowdischarge having high electron density in the order of 1018 m-3.

Key words: Microdischarges, Dielectric Barrier, Hollow cathode

Introduction:The microdischarges are very popular due to their small sizes and many other advantages overmacro discharges. The Micro hollow cathode discharges (MHCD) are firstly introduced by theA.D. White in 1959[1]. From there it covers the long journey of many decades and evolvedduring this time. The MHCD is used in different technologies such as laser technology, UVgenerators, material processing, etc. They conduct the high discharge current as comparativelyconventional discharge [4-5]. Two scaling laws are followed by the MHCD first is pd (pressureand distance between the electrodes) law which depends on Paschen’s curve for the breakdownvoltage and another law is pD (pressure and Diameter of the hollow cathode) scaling law or AllisWhite law. The pendulum effect is responsible for the hollow cathode effect which iselectrostatic trapping of the fast electrons which causes oscillating motion within the cathodehollow cavity. But it has the disadvantage of a short period of life-time due to the sputteringeffect on the cathode walls caused by electrodes and glow to arc transition of discharge.



92

The Dielectric barrier discharge [DBD] which is also called the silent discharge is also verypopular because of its capability of ozone generation. These discharges have less electron densityas compared to the MHCD but it forms a steady uniform glow discharge and prevents the glow toarc transition. In this discharge dielectric layer is used between electrodes, it may be singledielectric or double dielectric as peruse.

In this paper, we have tried to coaxially use the MHCD and DBD [2]. We have used the singledielectric layer on the planar anode and placed it on the hollow cathode. For simulation we haveused the COMSOL 5.4 software and the 2D- axis-symmetric model is designed in the plasmamodule it has been explained in First Section [3]. In Second section simulation studies and resulthas been shown with the help of spatial distribution discharge and other results. In the last section,the conclusion has been noted regarding the results.

Simulation studies and Results:In this paper COMSOL 5.4 software is used to simulate the designed model. A 2D-axissymmetric model is designed using the plasma module. In figure 1 schematic diagram of thedesigned model is shown. In this model Micro hollow cathode of diameter 500 µm is used havingthe height of the 500µm to maintain the aspect ratio as 1:1. In this model, a planar anode is usedon the one window of the cathode cavity and a dielectric layer is placed between the anode andcathode of 40µm as shown in the figure. Simulation has been carried out at the atmosphericpressure in the presence of argon gas. We are using a square pulse with a rise time of 100ns andpulse width is 1000ns per cycle. This Nanosecond square pulse is used to provide the hollowcathode effect at higher pD values because according to the Allis white law pD range for hollowcathode discharge is 0.1-10 Torr cm. But because we are using a single dielectric layer in thismodel it opens up the higher range for pD value.

Fig. 1: Schematic diagram of the designed MHCD

Spatial distribution of discharge: Spatial distribution of the discharge is shown by theIso-surface plot of a given model in figure 2. In this design discharge ignites near theanode wall and after ignition discharge moves towards the cathode cavity where it getssustained. This process repeats itself for every pulse. In given figure 2(a) ignition of the



93

discharge is shown at 1kV. After the ignition at around 100ns discharge gets collectedinside the hollow cathode due to the pendulum effect with the high electron density orderof 1018 m-3 as shown in figure 2(b).

(a) (b)

(c) (d)

Fig. 2: Iso-surface plot of the discharge in the given design at 1kV for 50kHz frequency.

During the deceiving pulse at around 900ns, it starts again confining the discharge andconfined at 1000ns as seen in figure 2(c) and 2(d). It shows that for the nanosecond pulsecycle even for higher pD values discharge takes place in the hollow cathode. And due tothe dielectric layer discharge did not move towards the glow to arc region and confinedfor higher electron density.

VI- Characteristics: For each cycle, current peaks are observed during the rise time andfall time as in given figure 3 at rising pulse during 0-100ns current peak is coming of2.5mA. After that during the plain pulse width from 100ns -900 ns current startsdecreasing and becomes zero. Again for the fall time from 900ns-1000ns current isshowing the peak value of range 3mA but in negative due to the fall cycle. There is also asecond peak which is due to the hollow cathode effect.



94

Fig. 3: IV- Characteristics of the designed model at 1kV for square wave nanosecond pulsedcycle.

Mass Fraction: In MHCD mass fraction of metastable atoms are higher than the Argonions which are due to the hollow cathode effect (HCE). The pendulum effect of fastelectrons is responsible for this cause. As shown in figure 4 we are getting a higher valueof metastable atoms than the Argon Ions which shows the presence of HCE.

Fig. 4: Mass fraction plot of Metastable and Argon Ions.

Conclusions:In this paper by simulating the Planar Anode design model it has been observed that byusing the dielectric layer we can have the high electron density in hollow cathode without



95

moving from glow to arc discharge. It has been seen that due to the use of a dielectriclayer pD value can be increased. The Ignition of the discharge dielectric barrier plays animportant role and at 1kV breakdown occurs according to Paschen’s law. This value ofhigher breakdown voltage occurs due to the high thickness and low dielectric constant ofthe dielectric material.

It has been observed that due to the pulsed voltage-current peaks are occurring at the riseand fall times and after that, it moves towards the zero. With the help of the mass fractionplot, it was also being verified that this design is showing the hollow cathode effectwhich is responsible for the high electron density of the order of 1018 m-3.

References[1] A.D. White, “New hollow cathode glow discharge”, J. Appl. Phys. 30 711–719(1959).[2] C. Meyer, Daniel Demecz, E. L. Gurevich, U. Marggraf, G. Jestel, J. Franzke, J.

Anal. At. Spectrom., 27, 677, (2012).[3] COMSOL Multiphysics Documentation, 2019, [online] Available:

http://www.comsol.co.in.[4] K. H. Schoenbach, A. El-Habachi, W. Shi, and M. Ciocca, “High-pressure hollow

cathodedischarges,” PlasmaSources Science and Technology, vol. 6, no. 4, p. 468, 1997.

[5] K. Becker, K. Schoenbach, and J. Eden, “Microplasmas and applications,” Journal ofPhysics D: Applied Physics, vol. 39, no. 3, p. R55, 2006.



96

PSC-8

Effect of laser pulse profile on controlling the growth ofRayleigh-Taylor instability in radiation pressure dominant regime

Krishna Kumar Soni, Shalu Jain, N.K. Jaiman, and K.P. MaheshwariDepartment of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)


Abstract

In the radiation pressure dominant (RPD) regime the interaction of an intense relativistic laserpulse with an ultrathin, dense solid foil converts it into overdense plasma instantaneously. Thisplasma foil is accelerated as a whole by incident laser pulse. It becomes unstable due to the onsetof Rayleigh-Taylor instability (RTI). This RTI tears the foil into plasma clumps. It affects the ionacceleration process. The ion energy spectrum becomes broadened. In the co-moving frame ofthe plasma foil the RTI makes it transparent for the incident radiation. The growth rate of RTIdepends on the pulse profile of the incident laser. So, by suitably tailored laser pulse one cancontrol the growth of RTI, and hence stabilize the ion acceleration. This paper presents acomparative study of energy and momentum transfer by the incident Gaussian and Lorentzianlaser pulse to the plasma ions. Numerical results for the comparison of incident laser pulse profilefor controlling the growth of RTI are presented.

Key words: Laser plasma interaction, Ion acceleration, Rayleigh-Taylor instability

Introduction:Laser driven ion acceleration mechanism is a very important mechanism of ion acceleration dueto its smaller in size, cost effective, and compactness [1, 2]. Increasing the laser intensities ~

22219 /1010 cmW by chirped pulse amplification technique the interaction of the laser pulsewith ultrathin dense solid foil becomes nonlinear [3, 4]. Beyond this stage of laser intensity, i.e. at

223 /10~ cmWI we meet a new regime of ion acceleration known as radiation pressure dominantregime [2, 5-6]. In the RPD regime an intense laser pulse interacts with an ultrathin, solid metalfoil made of electrons and ions. As a result of this interaction the metal foil get converts into anoverdense plasma foil instantly which reflects the incident laser pulse and acts as a relativisticplasma mirror [5-8]. The radiation pressure of the incident laser pulse pushes the electron layer inthe forward direction and the intense electric field so created pulls the ions along with them withalmost the same speed as that of electrons and thus have a kinetic energy above that of theelectrons [5]. The plasma foil gains energy which is proportional to the incident laser pulseenergy [5].Due to extremely high radiation pressure (~ 30 tera-bar) associated with the incident intense laserpulse having intensity ~ 223 /10 cmW plasma exhibits relativistic nonlinearities through thereflected and transmitted radiation from it and becomes unstable due to onset of Rayleigh-Taylorinstability [1, 6, 9-10]. The RTI occurs when a lighter fluid accelerates a heavier fluid. This RTIcan disrupt the acceleration process and tear the plasma foil into clumps of denser lower energyplasma [6, 9]. It follows that a controlled growth of the RTI can stabilize the foil opacity andacceleration process. The growth-rate of the RTI depends upon the phase profile of the incident



97

laser pulse. One can control the growth of the RTI by choosing an appropriate profile of theincident laser pulse.In this paper we give our analytical and numerical results of laser pulse profile for controlling thegrowth of the RTI. Numerical results for ion energy and momentum are also presented. We findthat a Gaussian pulse profile is better than a Lorentzian pulse for controlling the growth of RTI.This paper is organized as follows. In section 2 of this paper we give the equation of motion of thethin plasma foil and its solution in terms of ion momentum in the RPD regime. Section 3 dealswith the equations describing the Rayleigh-Taylor instability. Numerical results and discussionare given in section 4. Conclusions are drawn in the last section.

2. Equation of motion:The equation of motion of a surface element of a perfectly reflecting plasma mirror in thelaboratory frame is [6, 9]:

// dtpd (1)where p is the momentum of the ions in the plasma foil, is the radiation pressure, is the unitvector normal to the foil surface, and is the surface density. Let the mirror velocity and themirror normal vector remain in the yx plane then the equation of motion (1) for the targetelement can therefore be written as [9]

syP

tp x

0, and

sxP

tp y

0. (2)

Here, xp and yp are the component of the ion momentum in the x and y direction,

respectively, 000 ln , 0 is the initial plasma density, and 0l is the initial thickness of the foil.Let the electromagnetic (EM) wave propagate along the x - axis then the radiation pressure of thenormally incident EM wave on the foil surface can be written in the lab frame as

11

2

20EP , where 222/ xix pcmp , (3)

is the normalized velocity of the foil in the lab frame, 0E is the electric field of the laser pulse,

im is the mass of the ion, and c is the speed of light in vacuum. Lagrangian coordinates, and

are chosen such that ),,(,, tyxyx and 2/122 ddds . Let the unperturbed mirrormoves along the x - axis so that 0d , and dsd .Since the electric field of incident EM wave depends on time in the lab frame as

ctxtEE /00 . So introducing the new variable ctxt /00 , which is the wave

phase at the unperturbed mirror element position with 0 the laser pulse frequency in the lab

frame, we obtained 00 1/ xdtd . Here, 0

x is the unperturbed mirror velocity along thex - axis. Using the variable we can write Eq. (2) as:

0202

202

00

20

0

2xxi

xix

ppcm

pcmEddp

. (4)

Here, 0xp is the unperturbed x component of ion momentum. Introducing the average

normalized intensity of the EM wave

0 0

dRw , with 200

20

imE

R , and

00

2 c

, by using initial condition 000 xp the solution of Eq. (4) will be given by :

www

cmp ix

12

20 . (5)



98

Kinetic energy of the accelerated ions can be calculate as: 22022, cmcpcm ixikini .

By using Eq. (5) kinetic energy will be given by

wwcmikini

12

22

, . (6)

3. Rayleigh-Taylor instability:The plasma foil accelerated by the radiation pressure of the laser pulse is unstable due to the onsetof the Rayleigh-Taylor instability. To investigate the linear stability of the accelerated foil withrespect to perturbations tx ,1 , and ty ,1 , we linearize Eq. (2) around the solution 0

xp ,we obtain [6, 9]

110

2 yxi

x Rcm

p

, and

11

0 2 xyx

i Rp

cm

. (7)

Here, we retain only the terms that are in the ultrarelativistic limit. One can obtain WKB solutionsof Eq. (7) in the form [9]

0

1 ''exp, kidi . (8)

Substituting Eq. (8) in Eq. (7), we find (with growth-rate >>1) 2/Rk , with 011 /~ xiyx pcmi . (9)

4. Results and Discussion:From Eq. (9) we see that the growth of the RTI depends on the phase profile of the incident laserpulse. By choosing an appropriate profile of the incident EM pulse we can control the growth ofRTI and hence stabilize the foil acceleration. To obtain the analytical and numerical results forthe effect of laser pulse profile on the growth of RTI, we choose the following pulse shapes(A) Gaussian pulse 2

00 67.1exp EE , and(B) Lorentzian pulse 2

00 29.11/ EE .Using these expressions in Eq. (5) we obtain the momentum of the accelerated ions as

67.168.6// 000 erfRcmp ix and 29.1tan58.2// 1

000 Rcmp ix for

Gaussian and Lorentzian pulse, respectively which depend on the pulse profiles of the incidentlaser pulse. With the use of Eq. (9) the profile dependent exponential growth

d0 of the RTI are

1809.1

3618.220 erfRk and

29.1sinh29.11

210 Rk

for Gaussian and Lorentzian pulse profiles, respectively.

Numerical results are obtained with the help of MATLAB software for the following set of laserpulse and plasma parameters: laser pulse intensity 223 /1037.1~ cmWI (that is expected forproposed superpower lasers such as HiPER and ELI [11]), plasma density 322

0 /105.5 cmn ,foil thickness 00 5.0 l , m 10 , 1836/ ei mm . Fig: 1 depicts the variation of momentumof the accelerated ions with wave phase for Gaussian and Lorentzian laser pulse profiles. Fromthis figure we see that the ion momentum increases with increasing the wave phase for both thelaser pulses. The momentum imparted to the ions are 0.32 GeV/ c and 0.16 GeV/ c for the valueof 10 for Lorentzian and Gaussian laser pulse, respectively. In fig: 2 we shows the variationof energy of the accelerated ions with wave phase of the incident laser pulse having Gaussianand Lorentzian pulse profiles. This curve show that the ion energy increases with increasing thewave phase for both the laser pulses. For 10 there are 0.05 GeV and 0.02 GeV energy of theaccelerated ions for Lorentzian and Gaussian laser pulse, respectively. Fig: 3 shows the



99

exponential growth of the RTI with wave phase in case of Gaussian and Lorentzian pulseprofiles of the incident laser pulse. From this figure we see that for the value 10 the growth ofRTI in case of Lorentzian pulse is 3.3 times higher than the case of Gaussian laser pulse. Since forthe stability of the ion acceleration process against RTI we need a laser pulse for which thegrowth of instability must be minimal. So Gaussian laser pulse is better suited than the Lorentzianpulse in controlling the growth of RTI.

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Norm

alize

d Mo

men

tum

Gaussian laser pulseLorentzian laser pulse

Fig. 1: Shows the variation of normalized momentum cmp ix /0 of the ions with wave phase for Gaussian and Lorentzian pulse.

0 2 4 6 8 100

0.01

0.02

0.03

0.04

0.05

0.06

Norm

alize

d Ene

rgy

Gaussian laser pulseLorentzian laser pulse

Fig. 2: Shows the variation of normalized energy 2, / cmikini of the ions with wave phase for

Gaussian and Lorentzian pulse.

0 2 4 6 8 100

0.5

1

1.5

Grow

th of

Ray

leigh

-Tay

lor in

stabil

ity

Gaussian pulseLorentzian pulse



100

Fig. 3: Shows the exponential growth-rate of the RTI with wave phase for Gaussian andLorentzian pulse.

5. Conclusions:In the RPD regime the momentum/energy transferred from laser pulse to the plasma ions dependson the pulse profile of the incident laser pulse. In this regime the momentum and energy transferto the ions by the Lorentzian pulse is 1.54 times and 2.67 times that of the Gaussian pulse,respectively. We see that in case of Lorentzian laser pulse the instability grows much faster withthe wave phase. So by comparing the numerical results for growth of RTI we find that theGaussian laser pulse is better suited than the Lorentzian pulse for controlling the growth of RTI.

AcknowledgemetsFinancial support from the Department of Atomic Energy (DAE), Board of Research in NuclearSciences (BRNS) Mumbai, (Government of India) under the research project no.39/14/07/2018-BRNS is thankfully acknowledged. Thanks are due to Professor Sudip Senguptafor several academic discussion and support.

References[1] F. Pegoraro, and S. V. Bulanov, Eur. Phys. J. D, 55, 399-405 (2009).[2] A. Macchi, M. Borghesi, and M. Passoni, Rev. Mod. Phys., 85, 751-793 (2013).[3] T. Brabec, and F. Krausz, Rev. Mod. Phys., 72, 545-591 (2000).[4] G. A. Mourou, T. Tajima, and S. V. Bulanov, Rev. Mod. Phys., 78, 309-371 (2006).[5] T. Zh. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phys. Rev. Lett.,

92, 175003 (2004).[6] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys. Usp.,

56, 429-464 (2013).[7] Krishna Kumar Soni, and K. P. Maheshwari, Pramana J. Phys., 87, 1-6 (2016).[8] F. Mackenroth, and S. S. Bulanov, Phys. Plasmas, 26, 023103 (2019).[9] F. Pegoraro, and S. V. Bulanov, Phys. Rev. Lett., 99, 065002 (2007).[10] A. Sgattoni, S. Sinigardi, L. Fedeli, F. Pegoraro, and A. Macchi, Phys. Rev. E, 91, 013106

(2015).[11] M. Dunne, Nature Phys., 2, 2-5 (2006).



101

PSC-9

Effect of the nonthermal electrons on ion-acoustic cnoidal wave inunmagnetized plasmas

P. C. Singhadiya1, J. K. Chawla2, S. K. Jain1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801

2Department of Physics, Govt. College Tonk, Rajasthan, India-304001Govt. College, Dholpur, Rajasthan, India-328001


Abstract

Using reductive perturbation method, Korteweg de Vries (KdV) equation is derived for aunmagnetized plasma having warm ions and nonthermal electrons. The cnoidal wave solution ofthe KdV equation is discussed in detail. The effect of nonthermal electron on the characteristicsof the cnoidal wave and soliton are also discussed. It is found that nonthermal electron has asignificant effect on the amplitude and width of the cnoidal waves, while it also affects the widthand amplitude of the soliton in plasmas. The numerical results are plotted within the plasmaparameters for laboratory and space plasmas for illustration.

Key words: KdV equation, cnoidal wave, solitonIntroduction:Many researcher studied the characteristics of nonlinear periodic waves in plasmas [1-24]. Thecnoidal waves can be expected to play an important role in the nonlinear transport processes inplasma [1-3]. The nonlinear periodic waves (NPWs) expressed in terms of Jacobianelliptical-functions, like sn, cn and dn waves, are finding important applications in diverse areasof physics. One of them is the nonlinear transport phenomena. Yadav et al. [14] have beenstudied the ion acoustic cnoidal wave (IACW) in a magnetized plasma. They found that increasethe angle of obliqueness then increase the amplitude of the IACW. Yadav et al. [16] studied theion acoustic nonlinear periodic waves (IANPWs) in plasma with two-electron-temperature.Tiwari et al. [18] studied the IACW in a unmagnetized plasma. They found the averagednonlinear ion flux, using the RPM. Yadav and Sayal [19] have been studied the obliquelypropagating dust acoustic cnoidal waves in a magnetized dusty plasma. They discussed thecharacteristics of dust acoustic cnoidal waves and soliton. IACWs in unmagnetized plasma withhot isothermal electrons, cold ions and dust have been studied by Jain et al. [20]. The effect ofdust concentration, charge on dust grains and mass ratio of dust grains on amplitude, phasevelocity and averaged nonlinear ion flux of the dusty plasma discussed in details. Wang et al. [21]studied the IAW in a magnetized plasma with positrons, using the Painleve expansion method.The IACWs in a dense magnetoplasma have been studied by El-Shamy [22]. They have derivedthe KdV equation with using the pseudo potential approach and discussed its cnoidal wavesolution for relativistic degenerate electrons in magnetized plasma. Kaur et al. [23-24] have beenstudied the cnoidal and solitary waves in magnetized and unmagnetized plasma. They discussedcharacteristics of dust magnetosonic periodic (cnoidal) and solitary waves in details.

In the past years, several authors studied the ion-acoustic wave (IAW) in unmagnetized[25,27,29,34-35] and magnetized [27,28,30,33,36,37] plasma having non-thermal electrons.



102

Sabry et al. [30] and El-labany et al. [31] examine the effect of nonthermal electrons on theproperties of the ion-acoustic waves in magnetized plasma. The effect of the nonthermalelectrons and positron concentrations on IAWs in a plasma have been studied by Pakzad andTribeche [34]. They discuss the effect of nonthermal parameters on the characteristics on theIAWs. Rufai [36] studied the auroral electrostatic solitons and supersolitons in a magnetizednonthermal plasma. It is found that increase the value of the nonthermal parameters thenamplitude of soliton decreases. Chawla et al. [37] studied the effect of nonthermal electron andpositron on ion-acoustic solitary wave in magnetized plasmas.Basic equations:We consider collisionless unmagnetized plasma consisting of ions and nonthermal electrons. Thenonlinear dynamics behavior of ion acoustic waves is governed by the following normalizedusual equations:

0)( nvn xt (1)nnvvv xxxt (2)

nenex 22 1 (3)Where , n and v are the electric potential, normalized density and fluid velocity of the plasmarespectively. , ei TT / and 2/12

00 )/( enTeD are nonthermal parameter, ionictemperature ratio and Debye length speed respectively.Derivation of the KdV equation using the RPM:In order to investigate the NLPWs in plasma, we employ the standard RPM to derive the KdVequation. The independent variables are stretched and as: ),(2/1 tx t2/3 where is a small parameter and is the phase velocity of the wave.The dependent variables are then expended as

...1 )2(2)1( nnn ...)2(2)1( vvv ...)2(2)1( (4)

Substituting there expressions along with stretched coordinates into (1) - (3) and we obtain thefirst order quantities as

)1()1( 1 n (5)

1)1()1( 1 Cv (6)

Here C1 is an integration constant which may depend on the variable .Thus, we obtain the following phase velocity ( ) of the cnoidal wave in the ion-acoustic waveframe

1

112 (7)

We get a relationship among the second order

)(21

4111 2

)1(22)1(2

)2()2( 2

Cv

(8)

Where )(2 C is the second integration constant which is independent of but may depend on. In the derivation of (8), the periodic boundary condition implies that

01 Ct (9)There C1 is independent of and .We obtain the following KdV equation, using first and second order equation

03111 yCx (10)

Where



103

,12

11132

332

1

x 21 12

1

y

(11)In (10) is used in place in .)1(Cnoidal wave solution of the Kdv equation:In order to determine the steady state solution of the KdV equation (10), we consider

1u (12)Where 1u is a constant velocity.Integrating equation (10) twice with respect to , we obtain

0)(21 2 d (13)

where the Sagdeev potential )( is given by

262)(

20

03

1

12

1

yx

yu

(14)

0 and 0 are respectively, the charge density and electric field when vanishes. We find theion acoustic soliton solution

)/(sec 2 Whm , (15)

where the amplitude of the soliton 11 /3 xum and width of the soliton 2/111 )/4( uyW .

Results and Discussion:To investigate the existence regions and nature of the ion - acoustic cnoidal wave andsoliton in nonthermal plasma, we have done numerical calculations for different set ofplasma parameters ( , ,u , 0 and 0 ). The Sagdeev potential and phase plane plotwith the change in nonthrmal parameter are shown in figure (1) - (4).The numericalresults are displayed in figure (1) (Eqn. 13), where we have plotted the phase plane forthe fixed values of the parameters as taken in figure (2). In the dotted line (i.e.,

002.00 and 007.00 ) nonthermal parameter = 0 (blue color), 0.1 (blackcolor), 0.15 (green color) and 0.2 (red color) of figure (1). On the other side, the solidphase curve (i.e., 00 and 00 ) nonthermal parameter = 0 (blue color), 0.1(black color), 0.15 (green color) and 0.2 (red color) in figure (1). It shows that if weincrease the value of the nonthermal parameter , the electric potential of thecnoidal wave and soliton increases. In figure (2) (Eqn. 13), we have potted the phasecurve for the fixed values of parameters ( , ,u 0 and 0 ) as taken in figure (1) buthaving different value of ionic temperature ratio ( ) = 0.2. It shows that if we increasethe value of the nonthermal parameter , the electric potential of the cnoidal waveand soliton decreases. A comparison of figure (1) and (2) shows that for the fixed valuesof parameters, if we increases the value of ionic temperature ratio ),( the electricpotential slightly decreases. The change in the amplitude of the Sagdeev potential with respect to potential given by equation (14). For the different values of

nonthermal parameter is illustrated in figure (3) with the finite value of 007.00 and ,002.00 the dotted line: nonthermal parameter = 0 (blue color), 0.1 (blackcolor), 0.15 (green color) and 0.2 (red color) curves represent the Sagdeev potentialcorresponding to cnoidal waves whereas the solid curve represents the soliton with

00 and ,00 and nonthermal parameter = 0 (blue color), 0.1 (black color), 0.15



104

(green color) and 0.2 (red color). It shows that if we increase the value of nonthermalparameter , the amplitude of the cnoidal wave and soliton increases. In figure (4),represents the variation in the Sagdeev potential with respect to potential for thefixed values of parameters ( , ,u 0 and 0 ) as taken in figure (3), but having differentvalue of nonthermal electron )( at ionic temperature ratio .2.0 A comparison offigures (3) and (4) shows that for the fixed value of parameters ( ,u 0 and 0 ), if weincrease the value of , the amplitude of the cnoidal wave and soliton slightlydecreases.

Fig. Cap.Figure 1. Variation of d with respect to potential for different value of 007.00 and

002.00 (dotted line), 00 and 00 (solid line), at phase velocity ,015.0u ionictemperature ratio ,1.0 and nonthermal electron )( = 0 (blue color), 0.1(black color), 0.15(green color) and 0.2 (blue color).Figure 2. Variation of d with respect to potential for different value of 007.00 and

002.00 (dotted line), 00 and 00 (solid line), at phase velocity ,015.0u ionictemperature ratio ,2.0 and nonthermal electron )( = 0 (blue color), 0.1 (black color), 0.15(green color) and 0.2 (blue color).Figure 3. Variation of Sagdeev potential vs. potential for different value of

007.00 and 002.00 (dotted line), 00 and 00 (solid line), at phase velocity,015.0u ionic temperature ratio ,1.0 and nonthermal electron )( = 0 (blue color),

0.1(black color), 0.15(green color) and 0.2 (red color).Figure 4. Variation of Sagdeev potential vs. potential for different value of

007.00 and 002.00 (dotted line), 00 and 00 (solid line), at phase velocity,015.0u ionic temperature ratio ,2.0 and nonthermal electron )( = 0 (blue color),

0.1(black color), 0.15 (green color) and 0.2 (red color).Conclusions:In summary, we have addressed the problem of the cnoidal wave and soliton in unmagnetizedplasma with nonthermal electrons and ions. The KdV equation is derived using the reductiveperturbation method. The effect of different ranges of nonthermal parameters on cnoidal waveand soliton is studied. The results obtained in this study may be useful to explain nonlinearperiodic waves associated with ion-acoustic waves in the astrophysical environment whereunmagnetized ions and nonthermal electrons are present.References[1] H. Schamel, Plasma Phys. 14, 905 (1972).[2] Y. H. Ichikawa, Phys. Scr. 20, 296 (1979).[3] K. Konno, T. Mitsuhashi and Y. H. Ichikawa, Soc. Jpn. 46, 1907 (1979).[4] L. C. Lee and J. R. Kan, Phys. Fluids 24, 430 (1981).[5] M. Temrin, K. Cerny, W. Lotko and F. S. Mozer, Phys. Rev. Lett. 48, 1175 (1982).[6] Yashvir, T. N. Bhatnagar and S. R. Sharma, Plasma Phys. Controlled Fusion 26, 1303

(1984).[7] R. Boström, G. Gustafsson, B. Holback, G. Holmgren, H. Kustem and P. Kinter, Phys. Rev.



105

Lett. 61, 82 (1988).[8] A. V. Gurevich and L. Stenflo, Phys. Scr. 38, 855 (1988).[9] A. Roychowdhary, G. Pakira and S. N. Paul, J. Plasma Phys. 41, 447 (1989).[10] U. Kauschke and H. Schlüter, Plasma Phys. Controlled Fusion 33, 1309 (1990).[11] K. P. Das, F. W. Sluijter and F. Verheest, Phys. Scr. 45, 358 (1992).[12] W. J. Pierson, Jr., M. A. Donelan and W. H. Hui, J. Geophys. Res. 97, 5607 (1992,).[13] U. Kauschke and H. Schlüter, Plasma Phys. Controlled Fusion 34, 935 (1992).[14] L. L. Yadav, R. S. Tiwari and S. R. Sharma, J. Plasma Phys. 51, 355 (1994).[15]. L. L. Yadav, R. S. Tiwari and S. R. Sharma, Phys. Scr. 40, 245 (1994).[16] L. L. Yadav, R. S. Tiwari, K. P. Maheshawari and S. R. Sharma, Phys. Rev. E

52, 3045 (1995).[17] Y. V. Kartashov, Y. A. Vysloukh and L. Torner, Phys. Rev. E 67, 066612 (2003).[18] R. S. Tiwari, S. L. Jain and J. K. Chawla, Phys. Plasmas 14, 022106 (2007).[19] L. L. Yadav and V. K. Sayal, Phys. Plasmas 16, 113703 (2009).[20] S. L. Jain, R. S. Tiwari and M. K. Mishra, Phys. Plasmas 19, 103702 (2012).[21] J. Y. Wang, X. P. Cheng, X. Y. Tang, J. R. Yang and B. Ren, Phys. Plasmas 21,

032111 (2014).[22] E. F. El-Shamy, Phys. Rev. E 91, 03105 (2015).[23] N. Kaur, M. Singh, R. Kohli and N. S. Saini, IEEE Trans. Plasma Sci. PP, 1-7 (2017).[24] N. Kaur, M. Singh and N. S. Saini, Phys. Plasmas 25, 043704 (2018).[25] G. C. Das and S. G. Tagare, Plasma Phys. 17, 1025 (1975).[26] R. A. Crains, A. A. Mamun, R. Bingham and P. K. Shukla, Physica Scripta T 63, 80 (1996).[27] A. A. Mamun, Phys. Rev. E 55, 1852 (1997).[28] A. Bandyopadhayay and K. P. Das, Physica Scripta 61, 92 (2000).[29] T. S. Gill, P. Bala, H. Kaur, N. S. Saini, S. Bansal and J. Kaur, Eur. Phys. J. D 31, 91

(2004).[30] R. Sabry, W. M. Moslem and P. K. Shukla, Plasma Phys. 16, 032302 (2009).[31] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Plasma Phys. 17,

042301 (2010).[32] M. K. Mishra and S. K. Jain, J. Plasma Phys. 79, 893 (2012).[33] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Astro Phys Space

Sci 340, 77 (2012).[34] H. R. Pakzad and M. Tribeche, J. Fusion Energy DOI: 10.1007/s/0894-.012-9503-9 (2012).[35] A. Mannan, A. A. Mamun and P. K. Shukla, Phys. Scr. 85, 065501 (2012).[36] O. R. Rufai, Plasma Phys. 22, 052309 (2015).[37] J. K. Chawla, P. C. Singhadiya and R. S. Tiwari, Pramana- J. Phys. 94, 13 (2020).



106

PSC -10

Target Shape Effects on the Energy of Ions Accelerated in theRadiation Pressure Dominated (RPD) Regime

S. Jain, K. K. Soni, N. K. Jaiman, K. P. MaheshwariDepartment of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)


Abstract

The study of the interaction of an ultra-intense laser pulse with a thin dense plasma foil is offundamental importance for different research fields such as efficient ion acceleration, highfrequency intense radiation sources, medical applications, investigation of high energy collectivephenomena in relativistic astrophysics [1]. We consider the interaction of an ultrashort,ultra-intense laser with ultrathin plasma layer leading in the generation of ion beam [2]. In thisreference, we evaluate the energy and luminosity of the ion beam and their dependence on thelaser and target parameters. Numerical results are presented for the Gaussian shaped foil targetand flat target. The effect of plasma foil thickness on the accelerated ion energy and theluminosity has also been studied.

Key words: Radiation pressure acceleration (RPA), Gaussian shaped foil target, Flat target.

Introduction:High density ultra-short relativistic ion beam is generated when an ultra-short EM wave interactswith ultrathin foil. Higher laser intensities ( 220 /10 cmWI ) allow us to use laser inducedparticle acceleration for novel high-energy-physics applications [1, 2]. Various regimes havebeen discussed in the framework of this concept [1, 3]. Recently, a new mechanism for laserdriven ion acceleration was proposed, where particles gain energy directly from the radiationpressure (RP) exerted onto the target by the laser beam [4]. The RPA mechanism predictssuperior scaling in terms of ion energy and conversion efficiency [2]. In this RPA regime theelectromagnetic (EM) wave is totally reflected by a plasma mirror prompted by an EM wave.This anticipates the energy conversion efficiency defined as the ratio of the mechanical energy of

the plasma foil to the electromagnetic energy given by

1

2and c

V . Here, V is

the instantaneous foil velocity and c is the speed of light. In the limit 1 , this accelerationmechanism becomes more efficient i.e. 1 .For RPA to become dominant, a thin foil is irradiated by a circularly polarized laser pulse atnormal incidence. Owing to the absence of an oscillating component in the Bv

force, electron

heating is strongly suppressed. Instead, electrons are compressed to a highly dense electron layergathering in front of the laser pulse which in turn accelerates ions [5]. By choosing the laser



107

intensity, target thickness, and density such that the radiation pressure equals the restoring forcegiven by the charge separation field, the whole focal volume therefore propagates ballistically asa quasineutral plasma bunch and continually gaining energy from the laser field. In this scenario,all particle species are accelerated to the same velocity, which substantially results in amonochromatic spectrum [6]. Thus, RPA scheme has important fundamental features such as thedependence of ion energy on the laser pulse fluence, narrow energy spectrum, low divergenceand high acceleration efficiency [7, 8].In addition to the requirement of obtaining the maximum ion energy for high-energy physicsapplication, we come to include an important parameter such as the luminosity of an ion beamcharacterizing the number of accelerated ions crossing a unit area of the beam in unit time. Inparticular, the generated ion beam should possess high luminosity. This can be achieved byfocusing the particle beam into a focal spot or by irradiating the foil with an appropriatelymodulated laser pulse.Theoretical models have shown very optimistic results for quasi monoenergetic ion beams foradequately long driver laser pulses [6]. However, multidimensional simulations show theinevitable dispersion of charged particles, electrons and ions, when the target is deformed [9].In this paper, we restudy the problem by considering the different shapes of target and give ouranalytical and numerical results depicting the effect of target shaping on ion-energy gain andluminosity of an ion beam. Numerical results are also obtained for different target thickness inrespect of the wavelength of incident laser pulse. This paper is organized as follows: section 2gives the equation of motion of thin plasma foil in RPD regime. Numerical results and discussionare given in section 3. Conclusions are drawn in the last section.

Equation of motion of thin plasma foil:At first, we study about the deformation of target under the interaction of a laser pulse. From themomentum conservation law between the laser and the target, the evolution of the targetnormalized velocity can be described by the following equation of motion of the thin plasmafoil under the RPA scheme as [10]:

11

2

2

Rcmlndt

d

ie

LE . (1)

Here, 211 , LE is the electric field associated with the laser pulse, which depends

on the variable txt , en is the plasma density, l is the foil thickness, im is the ion mass, R is the reflectivity of thin plasma foil in the rest frame of the foil,

11 , is the frequency of the incident laser pulse. In the simplest case,

when the foil is initially at rest i.e. 0)0( and assuming total reflection i.e. 1R , thenone obtains the general solution for the ion velocity as [1, 11]:

22

22

WW

WW (2)

Here, lnF

We

L2 and

dE

F LL

0

2

4represents the fluence of the laser beam. Thus

the kinetic energy of the accelerated ions is given by the expression1

22

WWcmii .

If the areal density lne is shaped properly then the target can be kept flat. One can use atarget with the Gaussian thickness distribution as follows [9]:

m

T

rlll 2

2

01 exp,max

. (3)



108

Here, r is the transverse distance to the laser axis, 1l , 0l , T , m are the shape parameters.Parameter of fundamental importance such as the luminosity of the beam of ions accelerated inthe RPD regime is mathematically expressed by [1]:

][101010

10 12242

1234

scmcmN

kHzfL tot

(4)

Here, totN is the number of accelerated ions, is the transverse size of the beam and f is thelaser repetition rate.

Results and Discussion:We solve equation (1) by making use of MATLAB software and the numerical results are shownin below figures. For numerical calculation we have taken the typical set of parameters: peaklaser intensity 222

0 10 cmWI , laser pulse duration fs50 , focal spot radius m10 , laser

repetition rate kHzf 10 , transverse size of the laser beam 10 , laser wavelength

m 1 , plasma density Cre nn 169 , where 32122 /101.14 cmemn eCr is thecritical density. Layout of both Flat target and Gaussian shaped foil target may be differentiatedby taking different sets of 0l and 1l values. For the sake of simplicity, we present our results for a

Gaussian shaped foil target whose parameters are 3.00 l , 7T , 15.01 l , 1m . For

the flat target, we just set 3.01 l , other parameters are the same.

0 200 400 6000

0.4

0.8

1.2

Normalized Time

Nor

mal

ized

Ene

rgy

Shaped Foil Target

FLAT Target

Fig. 1: Normalized energy as a function of normalized time t for different target shapes

0 100 200 300 400 500 6000

1

2x 10

36

Normalized Time

Lum

inos

ity

Shaped Foil Target

FLAT Target

Fig. 2: Luminosity of ion beam as a function of normalized time t for different target shapes

Fig. 1 and 2 show the variation of normalized energy

2cmi

i of the accelerated ions and

luminosity with normalized time t , respectively for 2 types of target, viz. Gaussian shaped



109

foil target and flat target. These curves indicate that for a fixed value of fst 300~ , the ionenergy is ~ 1170.6 MeV and ~ 766.35 MeV corresponding to Gaussian shaped foil target and flattarget (FT), respectively. The corresponding luminosity for both Gaussian shaped and Flat targetis found to be 1234108.1 scm and 1234102.4 scm , respectively.

0 200 400 600 8000

0.2

0.4

0.6

Normalized Time

Nor

mal

ized

Ene

rgy

l <

l =

l >

Fig. 3: Normalized energy as a function of normalized time for different values of foil thickness

Fig. 3 and 4 show the variation of normalized energy

2cmi

i of the accelerated ions and ion

beam luminosity with normalized time t , respectively for three different values of the targetfoil thickness, i.e., nml 800 , nm1000 and nm1200 . These curvesindicate that for a fixed value of fst 300~ , the accelerated ion energy for l , l and

l is ~367.41 MeV, ~299.97 MeV and ~255.79 MeV, respectively. We also estimate thecorresponding luminosity of

100 200 300 400 500 600 700 800 9000

2

4

6

8

10

12

14

16

18x 10

35

Normalized Time

Lum

inos

ity

l < l = l >

Fig. 4: Luminosity as a function of normalized time for different values of foil thicknessaccelerated ions originating from the focal spot of the laser. It is found to be 12341019 scm ,

1234104.27 scm and 1234107.37 scm , respectively for l , l and l .

Conclusions:Electron-ion layer moving at a relativistic speed almost fully reflects the incident laser pulse inthe radiation pressure dominant regime. The reflection coefficient being dependent on thepolarization of the incident laser pulse influences the energy transfer. Moreover, a properlyshaped target can lead to an efficient transfer of energy and momentum to the ions as a result ofthe interaction between the incident laser pulse and thin plasma foil. From our results, we foundan interesting fact that the energy of the accelerated ions is more (~ 1170.6 MeV) when theshaped foil target is irradiated by the incident laser pulse. From this finding, one can concludethat the total number of ions in the center part of the shaped foil target is originally less than that



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in the case of the flat target and the luminosity is higher for Flat target which will be favorable forsolving the problems of fundamental physics applications. Our result also depicts that themaximum energy corresponding to fst 133~ is estimated to be 0.75 GeV when the ions getacceleration by Gaussian shaped foil target, which is close to the Chen simulation result asillustrated in [13, Fig. 1(b)]. Having made a comparative study of plasma foil thickness we foundthat one of the plasma foils possess the minimum thickness accelerates the ions more efficientlyin comparison to the thick foils. The increasing value of foil thickness makes the accelerated ionenergy smaller. The maximum energy obtained by the ions is ~ 367.41 MeV corresponding to

)(800 nml . This energy value diminishes gradually when the thickness rises and reaches~ 255.79 MeV for )(1000 nml .

AcknowledgementFinancial support from the Department of Science & Technology, New Delhi, (Government ofIndia) under the research project no. DST/INSPIRE Fellowship/ 2017/IF170835 is thankfullyacknowledged.

References[1] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys.Uspekhi, 56, 429-464 (2013).[2] T. Zh. Esirpekov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phy. Rev. Lett., 92,175003 (2004).[3] A. Macchi, M. Borghesi, and M. Passoni, Rev. Mod. Phys., 85, 751 (2013).[4] A. Macchi, F. Cattani, T. V. Liseykina, and F. Cornolti, Phys. Rev. Lett., 94, 165003(2005).[5] A. Henig et. al., Phy. Rev. Lett., 103, 245003 (2009).[6] O. Klimo, J. Psikal, and J. Limpouch, Phys. Rev. ST Accel. Beams, 11, 031301 (2008).[7] S. Kar et. al., Phys. Rev. Lett., 109, 185006 (2012).[8] A. Maachi, S. Veghini, T. V. Liseykina, and F. Pegoraro, New J. Phys., 12, 045013 (2010).[9] M. Chen , A. Pukhov, and T. P. Tu, Phy. Rev. Lett., 103, 024081 (2009).[10] S. S. Bulanov, E. Esarey, C. B. Schroeder, S. V. Bulanov, T. Zh. Esirkepov, M. Kando, F.Pegoraro, and W. P. Leemans, Phys. Plasmas, 23, 056703 (2016).[11] E. Yu. Echkina, I. N. Innovenkov, T. Zh. Esirkepov, F. Pegoraro, M. Borghesi, and S. V.Bulanov, Plasma Phys. Rep., 36, 15-29 (2010).



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PSC-11

Effect of magnetic field on the sheath width of a 13.56 MHz radiofrequency capacitive argon discharge

S Binwal1, S K Karkari2, L Nair11Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi, 110025, India

2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar, Gujarat, 382428, India


Abstract

A 13.56 MHz, parallel plate capacitive discharge is investigated in the presence of magnetic field.A non-invasive method of estimating the sheath width has been demonstrated using the electricalimpedance measurements. Further, the effect of magnetic field, discharge current and pressure onthe capacitive sheaths is investigated. The experimental results report almost 55.5 % reduction inthe sheath width for the argon discharge operating at 1.0 Pa background pressure and 7.0 mT ofapplied magnetic field compared with the unmagnetized case.

Key words: capacitive discharge, magnetic field, sheath width, non-intrusive technique,electrical measurements

Introduction:The sheath is a positive space charge region that separates the quasineutral plasma from theelectrode surface. Almost the entire voltage applied to the discharge plates gets dropped acrossthe sheath region. The positive ions on entering the sheath with an initial Bohm velocity arefurther accelerated inside the sheath and bombard the electrode surface with high kinetic energy.Therefore, sheath plays an important role in the surface modification on the substrate by ionbombardment. In case of a capacitive coupled radio frequency (CCRF) discharge, in the timescale �� , the electrons respond instantaneously to the time varying electric fieldwhereas ions respond to the time averaged sheath potential. The parameters that control the iondynamics in RF sheath are the mean free path of ions (pressure) and the ion transit time across thesheath (τion). These parameters depend on the sheath width which is a function of sheath voltageand plasma density [1]. For achieving high etch rates, mono-energetic ions are preferred.Therefore, low pressure and high plasma density is generally suitable. A transverse magneticfield can be introduced to achieve high density plasma at low operating pressure. The magneticfield influences the ion energy and ion angular distribution through the sheath width.

Although, both fluid [2] and PIC simulation [3- 5] studies have demonstrated the effect ofmagnetic field on the sheath. Fewer experimental works has been carried to investigate the role ofapplied magnetic field on the sheath width in a symmetric CCRF discharge [6-7]. In this paper weanalyzed the effect of magnetic field on the capacitive RF sheaths. A non-invasive method ofestimating the sheath width has also been demonstrated using the electrical impedancemeasurements.



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Experimental setup:The schematic of the experimental chamber is given in Ref-[8-10]. It consists of two rectangularparallel plate electrodes which are 40 cm long and 10 cm wide, separated by a distance of 8 cmhoused inside a cylindrical glass chamber. The electrodes are driven by a 13.56 MHz RFgenerator via automatic impedance tuner having an L-type matching circuit. The output of thematching circuit is connected to the parallel plates through an isolation transformer in a push-pullconfiguration. The chamber is equipped with a set of turbo and rotary vacuum pumps to achievea base pressure of 6 × 10−6 Pa. The system is placed between a pair of race-track shapeelectromagnetic coils providing uniform transverse magnetic field along the width of the plates.The potential between the plates is measured by a pair of high voltage Tektronics capacitivevoltage probe. The discharge current is measured by IPC miniature current transformer. Theexperimental system is calibrated prior to the experiment to account for the inherent delaysintroduced because of the length of the cables of voltage /current probes and stray capacitances[8-10].

Model to estimate maximum sheath width:In the homogenous discharge model [11], the ion density can be simply treated uniformthroughout the discharge and the electron density has a step like profile. If the potential on thewall (�) is transiently large and negative such that �� − ��, electrons are repelled from thesheath. This leaves behind a matrix of positive ions. The potential in the sheath in 1-dimensioncan be expressed by Poisson’s equation as follows:��

=− ��t�t

(1)Here, �t is the ion/electron density at the plasma- sheath boundary ��t = �� .Equation (1) is integrated with wall potential � = − ��伸 with respect to the plasma. The meansheath width can be expressed as [12]:

�� = ��伸��t

v��(2)

In equation (2), the information of plasma density and voltage drop across the sheath is requiredto estimate the sheath width. In capacitive discharge most of the applied voltage (�� ) isdropped across the sheath. Therefore, it is reasonable to assume ��伸 � ��. The information ofdensity is usually obtained from the probe measurements. To avoid using Langmuir probe whichis an intrusive diagnostic, the value of n0 is estimated from the externally measured RF current.The RF current has three components namely the displacement current (�� , which is due tovariation in the sheath width with RF cycle, a constant ion current��䂺�� and the electron current( �� ) which has an exponential dependence on the sheath voltage [12]. In one RF cycle, theconstant ion current needs to be balanced by the electron current. The sheath region is devoid ofelectrons. The electron can reach the electrodes only at an instant on RF cycle when the sheathcollapses at the electrode. In this phase, the displacement current becomes zero and the small ioncurrent contribution can be neglected in comparison to the electron thermal current. At this time,the sheath at the opposing electrode attains maximum sheath width (�� ). This reduces the RFcurrent to, �� =

�t㏨�伸 ��h

and the expression can be rewritten in terms of �t as follows:

�t =h ��㏨�伸 ��

(3)Here � = htt × vt−� �� is the electrode area and ㏨�伸 the thermal velocity of electrons givenas ㏨�伸 = �h� × vt� �� −v . The RF current, �� can be replaced in (3) by theexperimentally measured current, �� which denotes the net RF current flowing through theplasma.�� = �� + �� (4)



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The values R and X can be estimated by following the procedure discussed in Ref:[8].Thus, using equation (2), (3) and (4) the expression for maximum sheath width can be written as:

�� = �h� × vt� × ��䂺��

v��v�h (5)

In this expression, the temperature dependence on sheath width is minimal against RF potential.Therefore, it is reasonable to approximate Te in the range of 2- 4 eV. In the subsequent section,maximum sheath width is estimated using equations (5) by assuming Te= 4 eV.

Results and Discussion:(a) Variation of sheath width with discharge current

In Fig-1 it is seen that in the un-magnetized case, sm rises with a slow pace almost linearly onincreasing Irms. However, an opposing trend is observed when the magnetic field is applied asshown in fig-2. In this case, sm decreases to reach a saturation value as Irms is increased.Fundamentally, the sheath width is inversely proportional to the electron density sm ∝1/ne anddirectly proportional to the sheath voltage sm ∝Vsh [12]. In the low pressure unmagnetizedcapacitive discharge, increasing discharge current or power does not guaranty the increase inplasma density. It is found in the literature that in an unmagnetized CCRF discharge a largefraction of discharge power is dissipated in ion acceleration in the sheath. The power dissipationby ions in the sheath results in a higher Vsh value and a saturation in plasma density. Therefore,the sheath width slightly increases with increasing the discharge current.

In case of B=7.0 mT, higher fraction of power is coupled to the electrons in the bulk. Thisresults in an enhancement of electron density with the discharge current. Although, Vsh alsolinearly vary with discharge current but the rate of change of density is more dominant. Hence thesheath width monotonically decreases with the discharge current.

Fig-1: Plot of the sheath width vs dischargecurrent for unmagnetized case at 1.0 Pa to 5.0

Pa.

Fig-2: Plot of the sheath width vs dischargecurrent for B=7.0 mT at 1.0 Pa to 5.0 Pa.

(b) Pressure effects on sheath widthWith increase in the background pressure, more ionizing neutrals are available in the discharge.This results in an increase in plasma density. Therefore, the sheath width is expected to fall withpressure. This is clearly observed for the unmagnetized case. However, in the magnetized case,the increase in plasma density with pressure is also associated with an enhancement in crossB-field diffusion losses. Therefore the variation in sheath width with pressure is relatively smallas compared to the un-magnetized case.

(a) Effect of magnetic field on sheath width



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Fig-3 represents the sheath width vs magnetic field plots for two different discharge currentvalues. It is seen that with increase in magnetic field there is a monotonic fall in the sheath width.The application of transverse magnetic field reduces the radial losses and therefore enhances thedensity of the discharge. The amplitude of the discharge voltage is also significantly reduced inpresence of magnetic field. Accordingly, there will be a reduction in the amplitude of voltagedrop across sheath. Both these effects will commutatively reduce the sheath width in themagnetized discharge.

Fig-3: Plot of the sheath width vs magnetic field for two discharge current values at 1.0 Pa.

Similar effect of magnetic field on the RF sheath in a symmetric discharge was reported in aparticle in cell simulation study by Sharma et al [3]. They demonstrated that in a single frequencyCCRF discharge, simultaneous control of the ion flux and ion energy bombarding on a surface ispossible by a suitable choice of a transverse magnetic field. Their results showed that the sheathwidth was reduced by 60% of the value by applying a transverse static magnetic field of 3.5 mTin a Helium discharge. They also reported a 4-fold increment in the ion flux at the electrode.These results suggest that the application of magnetic field of the strength such that the electronsare strongly magnetized while the ions remain unmagnetized can induce the similar effect asusing a dual frequency.

This simulation study supports our experimental results, where we have also observedalmost 55.6 % reduction in the sheath width at 7.0 mT of transverse magnetic field [c.f fig-3]. It isalso noteworthy to mention that although in past a model for sheath width estimation for themagnetized CCRF discharge has been reported by Park et al [6]. However, the model requiresplasma density as an input parameter which is usually measured using a Langmuir probe. Theapplication of probes is not desirable in industrial plasma processing reactors due to limitationssuch as high oscillating potential, contamination & perturbation introduced by the probe [13].The method presented here thus becomes imperative where only external measurements havebeen used to estimate the sheath width.

Summary and Conclusions:In this paper, maximum sheath width is estimated non- invasively using the electricalmeasurements. Effect of discharge current, pressure and magnetic field on the sheath width isinvestigated. The ion dynamics is not directly influenced by the magnetic field as ions areunmagnetized in B=7.0 mT. However, magnetic field influences the electron plasma density andthe sheath voltage which inturn controls the ion flux and ion energy in the sheath region.Therefore, the ion dynamics is basically getting controlled by the sheath dynamics. The presentwork also confirms the PIC simulation study by Sharma et al [3] which reported almost 60 %reduction in the sheath width in presence of magnetic field. Our experimental work confirms



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these results and we report almost 55.5 % reduction in the sheath width for the argon dischargeoperating at 1.0 Pa background pressure and 7.0 mT of applied magnetic field.

In conclusion, the results suggest that the magnetic field can be used as a controlling knob to tunethe sheath width/ ion bombarding energy in a single frequency CCRF discharge. This can enablethe user to optimize the processing window in a desirable manner.

References[1] T. Panagopoulos and D. J. Economou. Journal of Applied Physics 85.7 pp. 3435–3443

(1999).[2] M.M. Hatami, Physics of Plasmas 22.4, p. 043510, (2015).[3] S. Sharma et al, Physics of Plasmas 25.8, p. 080704, (2018).[4] J. Moritz et al, Physics of Plasmas 23.6, p. 062509(2016).[5] N. S. Krasheninnikova, X.Tang, and V. S. Roytershteyn, Physics of Plasmas 17.5, p.057103(2010).[6] J.C. Park and B. Kang, IEEE Transactions on Plasma Science 25.3, pp. 499– 506, (June1997).[7] S. J. You et al, Surface and Coatings Technology 171.1,pp. 226–230, (2003).[8] S. Binwal et al, Physics of Plasmas 25.3, p. 033506(2018).[9] J. K Joshi et al, Journal of Applied Physics 123.11, p. 113301, (2018).[10] S. Binwal et al, Physics of Plasmas 27.3, p. 033506, (2020).[11] M. A. Lieberman and A. J. Lichtenberg. “Principles of plasma discharges and materialsprocessing”. In: MRS Bulletin 30.12 (1994).[12] P. Chabert and N. Braithwaite. Physics of radio-frequency plasmas. Cambridge UniversityPress, (2011).[13] S.K. Karkari, A.R. Ellingboe, and C. Gaman, Applied Physics Letters 93.7, p. 071501,(2008).



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PSC- 12

Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO)plasma region

S. P. Acharya1, a, A. Mukherjee2, b, and M. S. Janaki1, c1Saha Institute of Nuclear Physics, Kolkata, India

2National University of Science and Technology, “MISiS”, Moscow, Russia

e-mail: [email protected], b [email protected], c [email protected]

Abstract

We consider the system consisting of the plasma environment in the Low Earth Orbital (LEO)region in presence of charged space debris objects. This system is modelled for the first time as aweakly coupled dusty plasma; where the charged space debris objects are treated as weaklycoupled dust particles with two dimensional space and time dependences. The dynamics of theion acoustic waves in the system is found to be governed by a forced Kadomtsev-Petviashvili(KP) type model equation, where the forcing term depends on the distribution of debris objects.Exact accelerated planar solitary wave solutions are obtained from the forced KP equation upontransferring the frame of reference, and applying a specific non holonomic constraint condition.For a different constraint condition, the forced KP equation also admits lump wave solutions. Thedynamics of exact accelerated lump wave solutions, which are happened to be pinned, is alsoexplored. Approximate dust ion acoustic wave solutions with time dependent amplitudes andvelocities for different types of localized space debris functions are analyzed. Our work providesa much clearer insight of the debris dynamics in the plasma medium in the LEO region, revealingsome novel results that are immensely helpful for various space missions. Different perspectivesfor practical applications of our theoretical results are discussed in detail..

Key words: Space debris, Low Earth Orbital, forced Kadomtsev-Petviashvili equation, planarsoliton, lump wave.

Introduction:

Upsurge in research endeavours encompassing dynamics of space debris objects in near-earthatmospheres has been gaining significant attention by numerous scientists across countries fromrecent years. Space debris objects [1] include dead satellites, meteoroids, destroyed spacecrafts,other inactive materials resulting from many natural phenomena etc. which are being levitated inextraterrestrial regions especially in near-earth space. The space debris objects are substantiallyfound in the Low Earth Orbital (LEO) [2] and Geosynchronous Earth Orbital (GEO) regions.Also, their number is continuously being increased nowadays due to various artificial spacemissions which result in dead satellites, destroyed spacecrafts etc. and many natural hazardsoccurring in space. These debris objects are of varying sizes and shapes, and move with different



117

velocities [3]; thus, cause significant harm to running spacecrafts. Therefore, to avoid thesedeteriorating effects, active debris removal (ADR) has become a challenging problem intwenty-first century. Some indirect detection techniques for space debris have also beendeveloped by different authors [4, 5, 6]. This paper interprets a much more realistic situation;which is not considered by these authors and may provide more justifiable indirect evidence ofpresence of debris objects.

We model, for the first time, the system consisting of the plasma environment in presence ofspace debris objects in the Low Earth Orbital (LEO) region as a weakly coupled dusty plasmasystem. Space debris objects become charged in a plasma medium because of differentmechanisms such as photo-emission, electron and ion collection, secondary electron emission [7]etc. These charged debris objects of varying sizes ranging from as small as microns to as big ascentimetres, and, in certain conditions, even more than centimetres [3, 8] move with differentvelocities. Therefore, there can be finite chances that the individual dynamics of charged debrisobjects are mutually correlated; which results in weak coupling among them. Numerous recentworks on dynamics of space debris are performed without taking into account this paramounteffect as far as our knowledge goes. In this work, the weak coupling effect among charged debrisobjects is accomplished with the introduction of a two dimensional space and time dependentforcing function arising out of debris objects. Consequently the forcing function dependsphysically on the distribution of space debris objects in the LEO plasma region, and their possiblerelative motions. This new generalized forcing function represents a two dimensional extensionof recent works done by Sen et al. [5], and Mukherjee et al. [6].

Derivation of nonlinear evolution equation:We consider the propagation of finite amplitude nonlinear dust ion acoustic waves (DIAWs) inthe Low Earth Orbital (LEO) region due to the motion of orbital charged debris objects. TheLEO region consists of a low temperature low density plasma along with the abundance of debrisobjects. We assume that the ion species is treated as a cold species, i.e. the ion pressure isneglected and the electrons obey the Boltzmann distribution. The basic normalized system ofequations in this system in (2+1) dimensions is given by

��+ �

�� + �

�쳌�㏨ = t, (1)

��+ �

��+ ㏨ �

�쳌+ �t

��= t, (2)

�㏨��+ �㏨

��+ ㏨ �㏨

�쳌+ �t

�쳌= t, (3)

��t��

+ ��t�쳌�

− �t + � − �� − �� = �� ,(4)

��+ ∇h� �� ㏨�� = t (5)

�㏨��+ ㏨��h∇�� ㏨�� = t (6)

where the following normalizations have been used:� � �

λ�� 쳌 � 쳌

λ��

λ��

�t��

��t�

� �� ㏨ � ㏨

�� t � �t

��,

(7)where λ� is electron Debye length, Cs is ion acoustic speed, �� is Boltzmann constant, �� iselectron temperature, �t� is equilibrium electron density, and �t� is equilibrium ion density.Equations (1), (2), (3), and (4) represent ion continuity equation, ion momentum conservationequations in x and y directions, and Poisson's equation respectively; where n, u, and t denote thedensity, velocity, and electrostatic potential of the ion species respectively. Similarly, ��, ��, and㏨�� denote dust charge in electron units, dust density, and dust velocity respectively, andequations (5) and (6) represent dust continuity and dust momentum equation respectively. Theterm S(x, y, t) in the RHS of equation (4) represents a charge density source arising due to theweakly coupled charged debris objects having two dimensional space and time dependences.Therefore, S(x, y, t) also depends on the distribution of debris objects in the LEO region. In the



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pioneering work done by Sen et al. [5], they have considered the source term to have onedimensional space and time dependences. Also, Sen et al. have taken both ion acoustic solutionand forcing term to have the form of line solitons with constant amplitudes and constantvelocities; which is subsequently generalized by Mukherjee et al. [6] by considering morerealistic time dependent amplitudes and velocities for both ion acoustic solution and forcing term.We generalize both the work done by Sen et al. and Mukherjee et al. to consider a forcing term intwo spatial and one temporal dimensions in order to accomplish the weakly coupled nature oforbital debris objects. We do not follow any restrictions as taken by Sen et al. as well.We derive the evolution equation corresponding to the nonlinear DIAWs in our systemfollowing the well-known reductive perturbation technique (RPT) [9]; where we expand thedependent variables of the system as:

� = v + ��v + �h�� +�, (8) = ��v + �h� +�, (9)㏨ = ��㏨v + ��㏨� +�, (10)t = ��tv + �ht� +�, (11)�� = v + ��v + �� +�,

(12)�� = ��tv + ��t� +�, (13)

where � is a small dimensionless expansion parameter characterizing the strength of nonlinearityin the system. We consider a weak space-time dependent localized debris function whichvanishes at space infinities. After scaling we have� �,쳌,� = �h��,쳌,��, (14)where f(x, y, t) can have any spatially localized form that is consistent with the weakly coupledcharged debris dynamics as per our approach. Similarly, the independent variables are alsorescaled as:� = � � − ㏨�� = �� = ��쳌, (15)where ㏨� is the phase velocity of the wave in x direction. Putting these expanded and rescaledvariables in equation (1) and collecting different powers of �, we get� �� : − ㏨�

��v��+ �v

��= t, (16)

� �� : − ㏨��+ ��v

��+ �

�� + �vv + �㏨v

��= t. (17)

Similarly, using equation (2), we get� �� : − ㏨�

�v��+ �tv

��= t, (18)

� �� : − ㏨��+ �v

��+ v

�v��+ �t�

��= t. (19)

Again, using equation (3), we get� �h : − ㏨�

�㏨v��+ �tv

��= t. (20)

Finally, equation (4) yields:� �� : − tv + �v = t, (21)

� �� : ��tv��

− t� −tv

�

�+ �� = �. (22)

From equations (16), (18), (20) and (21), we obtain�v = tv =� v� ㏨�� = v� �㏨v

��=� �tv

��h (23)

Then, upon differentiating equation (22) wrt � partially, and substituting equations (17), (19) and(23), we get the final nonlinear evolution equation after some simplifications as:

� � ��v� + ��v�v� + �v�� + �v�� = ��, (24)which is the forced Kadomtsev-Petviashvili (KP) equation, i.e. the generalization of forced KdVequation, with the subscripts denote partial derivatives. In order to get a convenient form, weapply the frame transformation:

�v = �h� � = �� =� �� = v�� = ��h (25)

Then, equation (24) reduces to



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�h� + �hh� +h�� + �h�� = ��, (26)The above equation represents the final evolution equation which is analysed extensively in thefollowing subsections.Solutions of nonlinear evolution equation: We know that KP, modified KP, coupled KP [10],generalized KP [11], and nonplanar KP [12] equations are very well-known and differentmethods of solutions are already known [13, 14]. Also, KP Burgers equation, different solutions[15] and their dynamical evolution have been analysed for plasmas. These analyses have beenperformed without taking into account the forcing term. We analyse different types of solutionsof forced KP equation (26) in this section.(A) Planar solitary wave solution:The equation (26), upon applying a transformation � �− � and � �− �, admits exact dust ionacoustic accelerated planar soliton solution when the forcing function � satisfies a nonholonomic constraint:�� + hh�� + �h�� + �� =− ��h��, (27)where �� represents the time dependent amplitude of the forcing function �h Here, wegeneralize the constraint condition taken by Mukherjee et al. [6] to solve forced Korteweg-deVries (KdV) equation to two dimension in order to apply the same for forced KP equation. Then,after some simplifications, the exact dust ion acoustic accelerated planar soliton solution is givenby

h �,�,� = � �� + �쳌� ��伸��+ �쳌�+ �� + �쳌 � � �+ �� ,

(28)where �� and �쳌 represent the � and 쳌 components of wave number, and � denotes the phase ofthe solitary wave solution respectively. Typically this planar soliton solution is as shown in figure1.

Fig. 1: Planar solution at T=1.5�.

Similarly, the forcing function is given by� �,�,� =− ��伸��+ �쳌�+ �� + �쳌 � � �+ ��. (29)

Therefore, it is concluded that both amplitude and velocity of the forcing function changewhereas only velocity of the dust ion acoustic soliton changes. This is two dimensional extensionof the recent work done by Mukherjee et al. [6] on exact accelerated solitons.(B) Lump wave solution: The lump wave solution of the forced KP equation (26) are discussedbelow.(i) Solution by constraint condition: Following Yong et al. [16], we approximate the forcingfunction as:

� =− ��. (30)In contrast to Yong et al., we have taken a slightly different constraint condition

�� = �� +h�, (31)then it satisfies lump wave solution which is typically of the form

h = h� �−��+vthy�−� �+��−yhh��v+ �−��+vthy�−v �+��−yhh��

.(32)This is obtained using the famous Hirota bilinear method [17]. This lump wave solution is plottedin figure 2.



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Fig.2: Lump solution at T=0.

(ii) Solution by frame transformation: We apply a frame transformation:�� = � + t

�� = �� = �(33)along with the approximation that � = ��h. As a result, equation (26) turns into an unforcedKP equation

�h�� + �hh�� + h�� + �h�� = t ,(34)which admits the solution:

h �,�,� = −��+ t� � � ��+��+��−�� +��+��+v��

��+ t� � � ��+��+��−�� +��+��+v��

. (35)

This shows accelerating features due to presence of the terrm t�� .

(C) Perturbative solution: We can also approximate the solution of forced KP equation (26)through perturbation technique following the work done by Moroz [18]. We get a perturbativesolution, in this case, as

h = ht + hv +�, (36)where ht and hv denote zeroth and first order perturbed quantities respectively. Here, htrepresents the solution of equation (26) in absence of external forcing � . The other perturbedquantities depend upon ht and the nature of forcing function �. This perturbed solution is morerealistic as compared to solutions by constraint conditions.

Discussions and applications:In this work, we obtain exact accelerated lump wave solutions, as explored in previous section,due to the presence of forcing function � in (2+1) dimensions. Again, these accelerated lumpsolutions are happened to be 'pinned', i.e. both source or forcing function and analytical solutionmove with the same velocity. We also obtain accelerated planar solitary wave solution when theforcing function � satisfies a certain constraint condition as represented by equation (27), andlump wave solutions when the constraint condition changes to that represented by equation (31).But the condition that forcing function obey a certain constraint is not more realistic. Therefore,from a practical point of view, there are more chances that pinned accelerated lump wavesolutions are to be resulted as consequences of the presence of weakly coupled debris objects,which are self-consistently related to the dust ion acoustic solution. We obtain this inference afterwe generalize the debris problem taken by Sen et al. [5] to two dimensions to model as aweakly coupled dusty plasma system in order to make the solutions more realistic and practicable,after considering time dependent amplitudes of the forcing functions.We know that lump wave solutions are special kinds of rational function solutions that arelocalized in all directions in space whereas solitary wave solutions are exponentially localizedsolutions in certain directions. Therefore, lump waves can be more stable as compared to solitarywaves resulting from KP equation and are detectable by external means. Recently, Sen et al. [5]devise an indirect method of detection of centimetre-sized debris objects by observation ofprecursor line solitons. But they neglected many crucial effects including the time dependence ofamplitudes of forcing function which represents debris objects. This may imply the observationof a debris object even when no line soliton is to be detected in its vicinity. Therefore, ourobservation of pinned accelerated lump wave solutions due to presence of debris objects maypave a novel way of detection of debris objects through observation of lump waves irrespectiveof the sizes and shapes of debris objects by advanced sensors or technologies equipped in



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space-crafts. This also happens to be the generalization of the work done by Kulikov et al. [4]where they conclude the detection of debris objects through growth of amplitudes. From anabstract point of view, our work provides a much clearer insight of space debris dynamics in theLEO plasma region through mathematical modelling.

Conclusions:. Our work provides a detailed theoretical investigation of space debris dynamics in the LEOplasma region through mathematical modeling. This will be extremely helpful for different spacemissions by various space agencies in the world.References:[1] H. Klinkrad, Space Debris: Models and Risk Analysis, Springer Praxis Books, PraxisPublishing Ltd, Chichester, UK.[2] J. C. Sampaio, E. Wnuk, R. Vilhena de Moraes, and S. S. Fernandes, Resonant OrbitalDynamics in LEO Region: Space Debris in Focus, Mathematical Problems in Engineering,Volume 2014, Article ID 929810.[3] Rules of Thumb and Data for Space Debris Studies, Australian Space Academy.[4] I. Kulikov and M. Zak, Detection of Moving Targets Using Soliton Resonance Effect,Advances in Remote Sensing, Vol. 1, No. 3, December 2012.[5] A. Sen, S. Tiwari, S. Mishra and P. Kaw, Nonlinear wave excitations by orbiting chargedspace debris objects, Advances in Space Research, Vol. 56, Issue 3, Pages 429-435, 1 August2015.[6] A. Mukherjee, S. P. Acharya, and M. S. Janaki, Exact accelerated solitons by orbiting chargedspace debris, arXiv:2001.11817v1 [nlin.PS], 26 Jan 2020.[7] M. Horanyi, Charged dust dynamics in the solar system, Annual Review of Astronomy andAstrophysics, Vol. 34, Pages 383-418, November 2003.[8] Technical Report on Space Debris, United Nations Publication, ISBN 92-1-100813-1, NewYork, 1999.[9] R. A. Kraenkel, J. G. Pereira and M. A. Manna, The reductive perturbation method and theKorteweg-de Vries hierarchy, Acta Appl Math 39, 389-403 (1995).[10] M. Lin, and W. Duan, The Kadomtsev-Petviashvili (KP), MKP, and coupled KP equationsfor two-ion-temperature dusty plasmas, Chaos, Solitons and Fractals, Volume 23, Issue 3, Pages929-937, 2005.[11] J. Yu, F. Wang, W. Ma, Y. Sun, and C. M. Khalique, Multiple-soliton solutions and lumps ofa (3+1)-dimensional generalized KP equation, Nonlinear Dynamics, Vol. 95, pages 1687{1692(2019).[12] S. Reyad, M. M. Selim, A. EL-Depsy, and S. K. El-Labany, Solutions of nonplanarKP-equations for dusty plasma system with GE-method Physics of Plasmas, Vol. 25, 083701(2018).[13] A. R. Seadawy, and K. El-Rashidy, Dispersive solitary wave solutions ofKadomtsev-Petviashvili and modi_ed Kadomtsev-Petviashvili dynamical equations inunmagnetized dust plasma, Results in Physics, Volume 8, Pages 1216-1222, 2018.[14] A. A. Minzoni, and N. F. Smyth, Evolution of lump solutions for the KP equation, WaveMotion, Vol. 24, Issue 3, Pages 291-305, 1996.[15] M. S. Janaki, B. K. Som, B. Dasgupta, and M. R. Gupta, K-P Burgers Equation for the Decayof Solitary Magnetosonic Waves Propagating Obliquely in a Warm Collisional Plasma, Journalof the Physical Society of Japan, Vol. 60, No. 9, Pages 2977-2984, 1991.[16] X. Yong, W. X. Ma, Y. Huang, and Y. Liu, Lump solutions to the Kadomtsev-Petviashvili Iequation with a self-consistent source, Computers and Mathematics with Applications 75 (2018)3414-3419.[17] R. Hirota, Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions ofSolitons Phys. Rev. Lett. 27, 1192 (1971).[18] I. M. Moroz, The Kadomtsev-Petviashvili equation under rapid forcing, Journal of

Mathematical Physics 38, 3110 (1997).



122

PSC -13

Large amplitude ion-acoustic solitons in plasmas with positrons andtwo superthermal electrons

S. K. Jain1, P. C. Singhadiya2 and J. K. Chawla1Govt. College, Dholpur, Rajasthan, India-328001

2Seth RLS Govt. College, Kaladera, Rajasthan, India-303801Department of Physics, Govt. College Tonk, Rajasthan, India-304001


Abstract

The large amplitude of ion-acoustic solitons in plasma consisting of ions, positrons and cold andhot superthermal electrons is considered the pseudo-potential method (SPM). An energy integralequation for the system has been derived with the help of SPM. It is found that compressivesolitons exist in the plasma system for selected set of plasma parameters. The effect of thespectral indexes of hot electrons (kh), spectral indexes of cold electrons (kc), temperature ratio oftwo species of electron ),( 1 positron concentration ),( ionic temperature ratio ),( positrontemperature ratio )( and Mach number (M) on the characteristics of the large amplitudeion-acoustic solitons are discussed in detail. The amplitude of the solitons increases with increasein positron concentration ),( ionic temperature ratio ),( positron temperature ratio )( andMach number (M) however an decrease in spectral indexes (kh, kc), increases the amplitude of thesolitons.The present study of this paper may be helpful in space and astrophysical plasma system wherepositrons and superthermal electrons are present.

Key words: Large amplitude, pseudo-potential method , superthermal electrons , solitonIntroduction:The study of the linear and nonlinear wave phenomena in electron-positron-ion (EPI) plasma hasbeen a subject of significant importance for researchers. The pair production generate naturallyelectron-positron plasmas such as pulsar magnetosphere [1,3], in early universe [2,4], in nucleonstars, active galactic nuclei [6] and star atmosphere [8]. Several authors [7,10,20] studied theion-acoustic waves in EPI plasmas.Many researchers using the SPM for study large amplitude ion-acoustic waves with two distinctgroups of hot electrons [5,15], negative ion [9], EPI [11,15], charge dust grains [14,18],superthermal electrons [19] in plasmas. Bharuthram and Shukla [5] investigated the effect of twodistinct groups of hot electrons on large amplitude ion-acoustic solitons (IASLs) in plasmas.The effect of superthermal electrons observed in astrophysical environment deviates fromMaxwellian distribution and found to obey kappa distribution. The effect of superthermalelectrons on ion-acoustic waves in plasmas has been studied by Hellberg et al. [12] andBoubakour et al. [13]. El-shamy [16] studied the characteristics of the ion acoustic solitary wavesin plasmas with superthermal electrons. Saini et al. [17] examined that effect of hot and coldsuperthermal electrons on ion-acoustic waves in magnetized plasma.



123

Basic equations:We consider a collisionless plasma consisting of ions, positrons and superthermal electrons. Thedynamics of the plasma is given by the continuity equation, equation of motion and Poisson’sequation:

0)( nvn xt

(1) nnvvv xxxt

(2) nnnn pchx 12 (3)The superthermal electrons having two distinct temperature follow kappa distribution andpositrons may be given by

2/1

2/31

ck

cc kn (4)

(5)

...

621

3322 en p (6)

Where ,0

0

e

c

nn

,0

0

e

h

nn

,0

0

e

p

nn

,)32(12

32121 1

1

h

h

c

c

kk

kk

2

221

2

2

2 )32(214

322141

h

h

c

c

kk

kk

and kc,h is the k-distribution corresponding to cold and

hot species of electrons.In the above equations n, np, nc and nh and v are denote the normalized density of ions, positron,

cold and hot electrons, fluid velocity of the ion respectively. The ion-acoustic speedmT

C es

andeTe is the normalized electrostatic wave potential. The space variable (x) and time

variable (t) have been normalized by Debye length 204 enTe

D and inverse of the ion

plasma frequency in the mixture ,4 2

0

1

enm

pi respectively. ,/ ep TT ,/ ei TT and

hc TT /1 are the ratio of positron and electron temperature, the ratio of ion and electrontemperature, the ratio of cold to hot electron temperature respectively.

Stationary solitons solution :Let us find out the Sagdeev pseudopotential from basic equations (1) – (3) with introduce theusual transformation

Mtx (7)where M is the Mach number of DLs.Using the equation (7) in Eqs. (1) – (3), the fluid equations be written as

2/1

1

2/31

hk

hh kn



124

0)( nvnM (8)

nnvvvM

(9) nnn pe 12 (10)Using the Eqs. (4) – (6), in the equation (10) and integrating Eqs. (8) - (9) with using appropriateboundary conditions for the unperturbed plasma at , n = 1, v = 0, 0 and

.0dFind the quadratic equations

(11)From equation (11) the ion density (n) is given by

2/12/12222 422

2

MMM

Mn

(12)

Integrating equation (10) with respect to , we obtain

021 2 Vd (13)

where V is the Sagdeev potential which is given by

31

4)2(23

4

4)2(2

21

123

21123

211

2

2/32222

2

2222

23

23

1

1

M

MMM

M

MMMM

ekk

Vch k

c

k

h

(14)

For the existence of large amplitude solitons, the Sagdeev potential must satisfy the followingconditions ,0V and ,0Vd at 0 (15)

,0 mV 0 m

Vd 0m (16)

0V for ,0 m (17)

0)2( 2224 MnMn



125

Here m , represents the maximum value of potential.

0

31

4)2(23

4

4)2(2

21

123

21123

211

2

2/32222

2

2222

23

23

1

1

M

MMM

M

MMMM

ekk

mm

mm

k

c

mk

h

m m

ch

(18)……. for m ……….. and …>0 …….. for mResults and Discussion:In the present investigation, it is found that for the selected set of plasma parameters, the systemsupports only IACSs depending upon the spectral indexes of hot electrons (kh), spectral indexesof cold electrons (kc), temperature ratio of two species of electron ),( 1 positron concentration

),( ionic temperature ratio ),( positron temperature ratio )( and Mach number (M).In fig. (1), Sagdeev potential )( curves have been plotted to investigate the effect of spectralindexes of hot electrons (kh). The graphical representation reveals that for decreasing the value ofkh, the amplitude of the IACSs increases. In fig. (2), Sagdeev potential )( curves have beenplotted to investigate the effect of spectral indexes of cold electrons (kc). The graphicalrepresentation reveals that for decreasing the value of kc, the amplitude of the IACSs increases.In figure 3 the Sagdeev potential )( against potential for different values of positrontemperature ratio . It is found that increasing values of results increases in amplitude of theSP of the ion-acoustic compressive soliton.In figure 4 the Sagdeev potential )( against potential for different values of positronconcentration ).( It is found that increasing values of results increases in amplitude of theSP of the ion-acoustic compressive soliton.

Fig. Cap.Fig. (1) Variation of the Sagdeev potential )(V with potential of the compressiveion-acoustic solitons for M = 2.1, kh = 2, = 0.1, 1 = 0.1, = 0.01, = 0.001 and = 0.001having different values of kc = 8.0 (red color dashed line), 9.0 (blue color dotted line) and 1.9259(black color solid line).Fig. (2) Variation of the Sagdeev potential )(V with potential of the compressiveion-acoustic solitons for M = 2.1, kc = 8, = 0.1, 1 = 0.1, = 0.01, = 0.001 and = 0.001having different values of kh = 2.0 (red color dashed line), 2.01 (blue color dotted line) and1.9259 (black color solid line).



126

Fig. (6) Variation of the Sagdeev potential )(V with potential of the compressiveion-acoustic solitons for kh = 2.0, kc = 8, M = 2.1, = 0.1, 1 = 0.1, = 0.01 and = 0.001having different values of = 0.001 (red color dashed line), 0.005 (blue color dotted line) and0.009 (black color solid line).Fig. (7) Variation of the Sagdeev potential )(V with potential of the compressiveion-acoustic solitons for kh = 2.0, kc = 8, M = 2.1, = 0.1, 1 = 0.1, = 0.01 and = 0.001having different values of = 0.001 (red color dashed line), 0.01 (blue color dotted line) and 0.1(black color solid line).Conclusions:In the present paper, the effect of spectral indexes of cold and hot electrons, temperature ratio oftwo species of electron, positron concentration, ionic temperature ratio, positron temperatureratio and Mach number on the large amplitude of the IACSs are investigated in plasmas. Forgiven set of plasma parameters on increasing indexes of cold and hot electrons, the amplitude ofIACSs decreases, but it decreases with increase in positron concentration and positrontemperature ratio. The finding results of this paper may be useful for understanding of nonlinearion-acoustic solitons in plasma containing positrons, ions and nonthermal electrons in space andlaboratory plasmas.References[1] P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 (1969).[2] W. Misner, K. S. Throne and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p.

763.[3] F. C. Michel, Rev. Mod. Phys. 54, 1 (1982).[4] M. J. Rees, in The Very Early Universe, edited by G. W. Gibbons, S. W. Hawking and S.

Siklas (Cambridge University Press, Cambridge, 1983).[5] R. Bharuthram and P. K. Shukla, Phys. Fluids 29, 3214 (1986).[6] H. R. Miller and P. J. Witter, Active Galactic Nuclei, Springer, Berlin 1987 p. 202.[7] F. B. Rizzato, Plasma Phys. Control. Fusion 40, 289 (1988).[8] E. Tandberg–Hansen and A. G. Emshie, The Physics of Solar Flares (Cambridge University

Press, Cambridge, 1988), p. 124.[9] S. L. Jain, R. S. Tiwari and S. R. Sharma, Can. J. Phys 68, 474 (1990).[10] S. I. Popel, S. V. Vladimirov, P. K. Shukla, Phys. Plasmas 2, 716 (1995).[11] Y. N. Nejoh, Phys. Plasma 3, 1447 (1996).[12] M. A. Hellberg, R. L. Mace, T. K. Baluku, I. Kourakis and N. S. Saini, Phys. Plasmas 16,

094701 (2009).[13] N. Boubakour, M. Tribeche and K. Aoutou, Phys. Scr. 79, 065503 (2009).[14] R. S. Tiwari, S. L. Jain and M. K. Mishra, Phys Plasmas 18, 083702 (2011).[15] S. K. Jain and M. K. Mishra, J Plasma Physics 79, 893 (2013).

S. K. Jain and M. K. Mishra, Astrophys Space Sci 346, 395 (2013).[16] E. F. El-Shamy, Phys. Plasmas 21, 082110 (2014).[17] N. S. Saini, B. S. Chahal, A. S. Bains and C. Bedi, Phys. Plasmas, 21, 022114 (2014).[18] S. L. Jain, R. S. Tiwari and M. K. Mishra, Astrophys Space Sci 357, 57 (2015).

S. L. Jain, R. S. Tiwari and M. K. Mishra, J. Plasma Phys 81, 1 (2015).[19] K. Kumar and M. K. Mishra, AIP Advances 7, 115114 (2017).[20] J. K. Chawla, P. C. Singhadiya, R. S. Tiwari, Pramana J. Phys. 94, 13 (2020).

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