VASIMR DANISHA:A Hall Thruster Space Odyssey

VASIMR DANISHA

A Hall Thruster Space Odyssey

By Dr.A.B.Rajib Hazarika, PhD, FRAS, AES

VASIMR DANISHA: A HALL THRUSTER SPACE ODYSSEY

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Dr.A.B.Rajib Hazarik,PhD,FRAS,AES

Page no.(i)

Dr.A.B.Rajib Hazarika, A.E.S. MSc, PhD, MIAMP (Germany), FRAS (Lond.), MWASET, MFFS (USA), MIBC (UK), MNPSS (USA) Assistant Professor, Dept. of Mathematics, Diphu Govt. College, Diphu, Karbi Anglong, Assam, India ,Pin- 782462, M- 9435166881 Res: “Anjena Manzil”, Kadomtola, Modhupur, P.O. Modhupur, Dist: Nagaon, Assam, India Pin - 782001 Ph- 03672-256327 ************************************************************************


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Page no.(ii)

PREFACE ABOUT THE AUTHOR

As available on website: http://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika

User:Drabrh/Dr.A.B.Rajib Hazarika

From Wikipedia, the free encyclopedia < User:Drabrh Jump to: navigation, search " A.B.Rajib Hazarika" redirects here. For Dr.A.B.Rajib Hazarika, see Dr.A.B.Rajib Hazarika.

Dr.A.B.Rajib Hazarika

[[File:Dr.A.B.Rajib Hazarika & his two kids.jpg [1]

|frameless|alt=]]

Dr.A.B.Rajib Hazarika with Laquit(son) and Danisha(daughter)

Born

Azad Bin Rajib Hazarika

July 2, 1970 (age 40)

Jammu, Jammu and Kashmir, India

Residence Nagaon, Assam, India

Nationality Indian

Ethnicity Assamese Muslim


3


Citizenship India

Education PhD, PDF, FRAS

Alma mater

University of Jodhpur

Jai Narayan Vyas University

Institute of Advanced Study in Science & Technology

</ref>http://www.iasst.in/]

Kendriya Vidyalaya[1] http://www.akipoonacollege.com/

OccupationAssistant Professor (Lecturer), Diphu Govt. College ,

Diphu,Assam,India

Years

active 2004- onwards

Employer Diphu Government College

Government of Assam ,Assam Education Service

Known for Lecturer ,Assistant Professor,Mathematician, Academician

,Fusion,Astronomy

Home town Nagaon, Assam, India

Salary Rs 40000 per month

Height 6 feet and 2 inches

Weight 100 kg


4


Title Doctorate, Dr., FRAS (London), Assam Education Service,

AES

Board

member of

Member of Scientific and Technical committee & Editorial

review board of Natuaral and Applied sciences World Academy

of Science ,Engineering & Technology</ref>

http://www.waset.org/NaturalandAppliedSciences.php?page=45

Religion Sunni Islam,

Spouse Helmin Begum Hazarika

Children Laquit Ali Hazarika(son), Danisha Begum Hazarika(daughter)

Parents Rosmat Ali Hazarika@Rostam Ali Hazarika@Roufat Ali

Hazarika and Anjena Begum Hazarika

Call-sign Drabrh or Raja

Website

http://www.facebook.com/Drabrajib

http://in.linkedin.com/pub/dr-a-b-rajib-hazarika/25/506/549

http://en.wikipedia.org/wiki/Special:Contributions/Drabrh

http://www.diphugovtcollege.org/

http://www.karbianglong.nic.in/diphugovtcollege.org/teaching.html


5


Dr.A.B.Rajib Hazarika,PhD,FRAS,AES (born July 02, 1970, in Jammu, Jammu and Kashmir, India) is Assistant Professor(Lecturer) Diphu Government College ,Diphu in KarbiAnglong district , Government of Assam[2], [3] , KarbiAnglong,Assam's largest conglomerate by Government of Assam . He is also the Fellow of Royal Astronomical Society[4],London ,Member of International Association of Mathematical Physics, World Academy of Science ,Engineering & Technology , Focus Fusion Society, Dense Plasma Focus, Plasma Science Society of India, International Biographical centre, Assam Science Society, Assam Academy of Mathematics,International Atomic Energy Agency,Nuclear and Plasma Society,Society of Industrial and Applied Mathematics,German Academy of Mathematics and Mechanics,Fusion Science & Technology Society,Indian National Science Academy,Indian Science Congress Association,Advisory Committee of Mathematical Education, Royal Society,International Biographical Centre.

Contents

• 1 Early life o 1.1 Early career

1.1.1 Currently working • 2 Career • 3 Research • 4 Patent & Innovation • 5 Research Guidence • 6 Personal life • 7 Quotes • 8 Awards and recognition • 9 References • 10 External links


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Early life

Dr.A.B.Rajib Hazarika was born into the famous Hazarika family, a prominent family belonging to Dhing's wealthy Muslim Assamese community of Nagaon district. He was born to Anjena Begum Hazarika and Rusmat Ali Hazarika. He is eldest of two childrens of his parents younger one is a Shamim Ara Rahman(nee Hazarika)daughter .

Early career

Dr.A.B.Rajib Hazarika completed his PhD degree in Mathematics from J N Vyas University of Jodhpur in 1995 with specialization in Plasma instability, the thesis was awarded “best thesis” by Association of Indian Universities in 1998 and the Post-Doctoral Fellow Program from Institute of Advanced Study in Science & Technology [5] in Guwahati Assam in 1998 as Research Associate in Plasma Physics Division in theory group studying the Sheath phenomenon. As a Part-time Lecturer in Nowgong college, Assam before joining the present position in Diphu Government College ,Diphu in KarbiAnglong district [6],[7] He is a member of the wikipedia[8], [9]. He is Fellow of Royal Astronomical Society [10],member of International Association Mathematical Physics [11], member of World Academy of Science,Engineering & Technology [12], [13],member of Plasma Science Society of India [14] , [15] ,member of Focus Fusion Society forum [16] ,member of Dense Plasma Focus [17], Member of Assam Science Society [18], Member of Assam Academy of Mathematics [19]

Currently working

He joined the Diphu Government College[20] in July 2004 as Lecturer in Mathematics (Gazetted officer) through Assam Public Service commission[21] in Assam


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Education Service [22] ,AES-I. [23] now redesignated as Assistant Professor.

Career

In May 1993, Dr.A.B.Rajib Hazarika was awarded Junior Research Fellowship, University Grants Commission, National Eligibility Test and eligibility for Lecturership ,Govt. of India and worked as JRF(UGC,NET) in Department of Mathematics and Statistics of J N Vyas University in Jodhpur. Later on in May 1995 got Senior Research Fellowship(UGC,NET) and continued research for completion of PhD on 27th Dec 1995 .From 1993 onwards taught in Kamala Nehru College for women, Jodhpur and in Faculty of Science in J N Vyas University in Jodhpur up to the completion of PhD .In 1998 May joined Plasma Physics Division of Institute of Advanced Study in Science & Technology in Guwahati as Research Associate for PDF in theory group to study the sheath phenomena of National Fusion Programme [24] of Govt. of India . Then joined Nowgong College as a part-time Lecturer after which in 2004, July joined the present position of Lecturer in Diphu Government College which is redesignated as Assistant Professor.

Research

During PhD </ref> http://www.iopscience.iop.org/1402-4896/51/6/012/pdf/physcr_51_6_012.pdf </ref> http://www.iopsciences.iop.org/1402-4896/53/1/011/pdf/1402-4896_53_1_011.pdf </ref> http://www.niscair.res.in/sciencecommunication/abstractingjournals/isa_1jul08.asp </ref> http://en.wiktionary.org/wiki/Wikitionary:Sandbox </ref> http://adsabs.harvard.edu/abs/1996PhyS..53...578


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during PDF the research was based on Astronomy, Astrophysics, Geophysics , for plasma instability with the title of thesis as “Some Problems of instabilities in partially ionized and fully ionized plasmas” which later on in 1998 was assessed as best thesis of the year by Association of Indian Universities in New Delhi. His current interest lies in Astronomy, Astrophysics, Geophysics, Fusion Plasma, and innovation of fusion devices, design of fusion devices, simulation codes and theoretical mathematical modeling.He is known for his theoretical research work on Gravitational instability and gravitational collapse M=23/2 Msun as a new formula for Chandrasekhar limit now known as Bhatia-Hazarika Limit , when the rotating neutron star, pulsars are formed .When the mass of the star is more than this limit a neutron star shrinks or abberates due to gravitational collapse up to a point size in space. As it is known that when the star passes limit of the size of old star more than three times that of mass of sun it passes the Schwarchild radius and there on is a black hole from where we can receive no more information as its gravitational field is too intense to permit anything , even photons to escape.Research at Diphu Govt. College </ref> http://en.wikipedia.org/wiki/Special:Contributions/Drabrh/File:Drabrhdouble_trios_saiph_star01.pdf </ref> http://en.wikipedia.org/wiki/File:Drabrh_bayer_rti.pdf </ref> http://en.wikipedia.org/wiki/File:Columb_drabrh.pdf </ref> http://en.wikipedia.org/wiki/File:Drabrh_double_trios.pdf </ref> http://en.wikipedia.org/wiki/File:Drabrhiterparabolic2007.pdf </ref> http://en.wikipedia.org/wiki/File:Drabrh_mctc_feedbackloop.pdf </ref> http://en.wikipedia.org/wiki/File:Drabrh_tasso_07.pdf </ref> http://en.wikipedia.org/wiki/File:Abstracts.pdf?page=2

Patent & Innovation

Applied for patent in US patent and trademarks office has innovated three future fusion devices Double Tokomak collider


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(DTC), Magnetic confinement Tokomak collider (MCTC) hub, Duo Triad Tokomak collider (DTTC) hub .A Hall thruster as diffusion associated neoclassical indigenous system of Hall assembly (DANISHA)is designed applied for international application No.PCT/IB2009/008024 in World Intellectual Property Organisation[25].He has innovated a new simulation code Fuzzy Differential Inclusion Code in 2003 for fusion process.[26], [27]

Research Guidence

Research guidence is given to two students in Mathematics for MPhil degree

Personal life

Dr.A.B.Rajib Hazarika has a metallic Scarlet red Tata Indigo CS of Tata motors make and loves to drive himself.

Quotes

• "Fakir(saint) and lakir(line) stops at nothing but at destination"

• "Expert criticizes the wrong but demonstrates the right thing"

• “Intellectuals are measured by their brain not by their age and experience”

• “Two type of persons are happy in life one who knows everything another who doesn’t know anything”

• “Implosion in device to prove every notion wrong for fusion”

• “Meditation gives fakir(saint) long life and fusion devices the long lasting confinement”


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Awards and recognition

Dr.A.B.Rajib Hazarika got Junior Research Fellowship,Government of India Senior Research Fellowship,Government of India Research AssociateshipDSTGovernment of India Fellow of Royal Astronomical Society [28] Member of Advisory committee of Mathematical Education Royal Society London Member of Scientific and Technical committee & editorial review board on Natural and applied sciences of World Academy of Science ,Engineering &Technology [29] Leading professional of the world-2010 as noted and eminent professional from International Biographical Centre Cambridge

References

1. ^ http://www.kvafsdigaru.org/ Poona College of Arts, Science &Commerce

• Template:Http://en.wikipedia.org/wiki/Special:contributions/Drabrh

External links

Wikimedia Commons has media related to: Drabrh/Dr.A.B.Rajib Hazarika

• [30] • Dr.A.B.Rajib Hazarika's profile on the Linkedin Website • [31]]]

dr ab rajib hazarika aes 19:01, 16 October 2010 (UTC) dr ab rajib hazarika aes


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Categories: Jai Narayan Vyas University alumni | Institute of Advanced Study in Science & Technology alumni | List of Indian mathematician | List of Indians by state | List of people of Assam | PhD | PDF | Assamese | Nuclear fusion people | Hazarika family | Poona college of Arts ,Science & Commerce alumni | Fellow of Royal Astronomical Society | 1970 births | Living people | Sunni Islam people | Kendriya Vidyalaya alumni | Academician | Indian Sunni muslim

• User:Drabrh/Dr.A.B.Rajib Hazarika English

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… …

D I F F U S I O N A S S O C I A T E D N E O C L A S S I C A L

I N D I G E N O U S S Y S T E M O F H A L L A S S E M B L Y ( D A N I S H A )

Histor y

Hall thrusters were studied independently in the US and the USSR in the 1950s and '60s. However, the concept of a Hall thruster was only developed into an efficient propulsion device in the former Soviet Union, whereas in the US, scientists focused instead on developing gridded ion thrusters.

Two types of Hall thrusters were developed in the Soviet Union:

• thrusters with wide acceleration zone, SPD (Russian: СПД, стационарный плазменный двигатель; English:


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SPT, Stationary Plasma Thruster) at Design Bureau Fakel

• thrusters with narrow acceleration zone, DAS (Russian: ДАС, двигатель с анодным слоем; English: TAL, Thruster with Anode Layer), at the Central Research Institute for Machine Building (TsNIIMASH).

Soviet and Russian SPD thrusters

The common SPD design was largely the work of A. I. Morozov.[1] SPD engines were operated since 1972. They were mainly used for satellite stabilization in North-South and in East-West directions. Since then until the late 1990s 118 SPD engines completed their mission and some 50 continued to be operated. Thrust of the first generation of SPD engines, SPD-50 and SPD-60 was 20 and 30 mN respectively. In 1982 SPD-70 and SPD-100 were introduced, their thrust being 40 mN and 83 mN. In the post-Soviet Russia high-power (a few kilowatts) SPD-140,

SPD-160, SPD-180, T-160 and low-power (less than 500 W) SPD-35 were introduced.[2]


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Soviet and Russian DAS-type engines include D-38 and D-55.[2]

Soviet-built thrusters were introduced to the West in 1992 after a team of electric propulsion specialists, under the support of the Ballistic Missile Defense Organization, visited Soviet laboratories and experimentally evaluated the SPD-100 (i.e., a 100 mm diameter SPT thruster). Over 200 Hall thrusters have been flown on Soviet/Russian satellites in the past thirty years. They were used mainly for station keeping and small orbital corrections. Currently Hall Thruster research, design, and theoretical modelling is led by experts at NASA Glenn Research Center and the Jet Propulsion Laboratory. A considerable amount of development is being conducted in industry, such as Aerojet and Busek Co.

This technology was used on the European lunar mission SMART-1 and is used on a number of commercial geostationary satellites.[3]

Introduction

What's a Hall Thruster?

The Hall thruster is a type of plasma-based propulsion systems for space vehicles. The amount of fuel that must be carried by a satellite depends on the speed with which the thruster can eject it. Chemical rockets have very limited fuel exhaust speed. Plasmas can be ejected at much higher speeds, therefore less fuel need be carried on board.

The Hall thruster was invented in the late 1950's. Until the mid 1990's, it has been developed primarily by the Russians. During the past 30 years, the Russian placed in orbit more than 100 Hall thrusters. However, the vast majority of satellites worldwide have relied on chemical thrusters and, to a lesser extent, arc jet thrusters and ion thrusters.


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A conventional electrostatic ion thruster consists of two grids, an anode and a cathode, between which a voltage drop occurs. Positively charged ions accelerate away from the anode toward the cathode grid and through it. After the ions get past the cathode, electrons are added to the flow, neutralizing the output to keep it moving. A thrust is exerted on the anode-cathode system, in a direction opposite to that of the flow. Unfortunately, a positive charge builds up in the space between the grids, limiting the ion flow and, therefore, the magnitude of the thrust that can be attained.

In a Hall thruster, electrons injected into a radial magnetic field neutralize the space charge. The magnitude of the applied magnetic field is approximately 100- 200 gauss, strong enough to trap the electrons by causing them to spiral around the field lines in the coaxial channel. The magnetic field and a trapped electron cloud together serve as a virtual cathode. The ions, too heavy to be affected by the field, continue their journey through the virtual cathode. The movement of the positive and negative electrical charges through the system results in a net force (thrust) on the thruster in a direction opposite that of the ion flow. Existing Hall thrusters can produce large jet velocities 10-30 km/s within the input power in the range from hundred watts to tens of kilowatts. For the state-of-the-art thrusters operating in the power range of above kilowatt, 50-60% of the input electric power goes to the kinetic power of the plasma jet. These thrusters are capable to produce the thrust in the range 0.1-1 N. Since ion acceleration takes place in quasi-neutral plasma, Hall thrusters are not limited by space-charge build up. Hence, higher current and thrust densities than conventional ion thrusters can be achieved at discharge voltages from hundreds volts to a few kilovolts. With such performance capabilities Hall thrusters can be used to keep satellites on geosynchronous orbit (GEO), to compensate for atmospheric drag on satellite in low-earth orbits (LEO), to raise a satellite from LEO to GEO and for interplanetary missions. Besides space applications, Hall thrusters can be also useful for industrial applications such as plasma processing of materials.


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The Hall Thruster Concept

Presently in use

"Princeton Plasma Physics Laboratory: Fueling the Future" presents an overview of the Laboratory's research program. The video includes a basic introduction to the principles of magnetic fusion energy, a mission synopsis of PPPL's current major fusion experiment, the National Spherical Torus Experiment, and descriptions of fusion devices proposed for the future. These include the National Compact Stellarator Experiment, being built at PPPL, and the international ITER project. Information on the


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application of plasma physics to solve near-term problems is also presented.

Operation

The essential working principle of the Hall thruster is that it uses an electrostatic potential to accelerate ions up to high speeds. In a Hall thruster the attractive negative charge is provided by electron plasma at the open end of the thruster instead of a grid. A radial magnetic field of a few milli-Teslas [4] is used to hold the electrons in place, where the combination of the magnetic field and an attraction to the anode force a fast circulating electron current around the axis of the thruster and only a slow axial drift towards the anode occurs.


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Hall thrusters are largely axially symmetric. This is a cross-section containing that axis.

A schematic of a Hall thruster is shown in the image to the right. An electric potential on the order of 300 volts is applied between the anode and cathode.

The central spike forms one pole of an electromagnet and is surrounded by an annular space and around that is the other pole of the electromagnet, with a radial magnetic field in-between.

The propellant, such as xenon gas is fed through the anode, which has numerous small holes in it to act as a gas distributor. Xenon propellant is used because of its high molecular weight and low ionization potential. As the neutral xenon atoms diffuse into the channel of the thruster, they are ionized by collisions with high energy circulating electrons (10–20 eV or 100,000 to 250,000 °C). Once ionized the xenon ions typically have a charge of +1 though a small fraction (~10%) are +2.

The xenon ions are then accelerated by the electric field between the anode and the cathode. The ions quickly reach speeds of around 15,000 m/s for a specific impulse of 1,500 seconds (15 kN·s/kg). Upon exiting however, the ions pull an equal number of electrons with them, creating a plume with no net charge.

The axial magnetic field is designed to be strong enough to substantially deflect the low-mass electrons, but not the high-mass ions which have a much larger gyro radius and are hardly impeded. The majority of electrons are thus stuck orbiting in the region of high radial magnetic field near the thruster exit plane, trapped in E×B (axial electric field and radial magnetic field). This orbital rotation of the electrons is a circulating Hall current and it is from this that the Hall thruster gets its name. Collisions and instabilities allow some of the electrons to be freed from the magnetic field and they drift towards the anode.


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About 30% of the discharge current is an electron current which doesn't produce thrust, which limits the energetic efficiency of the thruster; the other 70% of the current is in the ions. Because the majority of electrons are trapped in the Hall current, they have a long residence time inside the thruster and are able to ionize almost all (~90%) of the xenon propellant. The ionization efficiency of the thruster is thus around 90%, while the discharge current efficiency is around 70% for a combined thruster efficiency of around 63% (= 90% × 70%).

The magnetic field thus ensures that the discharge power predominately goes into accelerating the xenon propellant and not the electrons, and the thruster turns out to be reasonably efficient. Compared to chemical rockets the thrust is very small, on the order of 80 mN for a typical thruster. For comparison, the weight of a coin like the U.S. quarter or a 20-cent Euro coin is approximately 60 mN.

However, Hall thrusters operate at the high specific impulses that are achieved with ion thrusters. One particular advantage of Hall thrusters, as compared to an ion thruster, is that the generation and acceleration of the ions takes place in a quasi-neutral plasma and so there is no Child-Langmuir charge (space charge) saturated current limitation on the thrust density, and thus thrust is high for electrically accelerated thrusters.

Another advantage is that these thrusters can use a wider variety of propellants supplied to the anode, even oxygen, although something easily ionized is needed at the cathode.[5] One propellant that is starting to be used is liquid bismuth due to its low cost, high mass and low partial pressure.

THEORY In this study, we developed three computational techniques for the ECE radiation analysis of the Hall thruster.


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The first one is the single particle approximation analysis. This is the simplest one among the approaches. We modeled the plasma region of the Hall thruster with three parameters, the magnetic field, electron temperature, and electron density distributions. These parameters are constant in a cell. We calculated the radiation with the parameter distributions according to the observation angle. The frequency of a cell is determined by the magnetic field of the cell. This analysis is easy to approach and does not require a high computing performance. However, the results of this analysis don’t have detail results. The radiated electric field is derived from the power, so there is no polarization information on the electric field. We moved on more sophisticated analysis. The next one is the Particle-In-Cell (PIC) analysis. PIC is for analysis of microscopic phenomena. Particle motions in the thruster channel region are simulated with the PIC method. We selected electrons from the Maxwell-Boltzmann distribution for the speed of electrons. The Monte-Carlo method was adopted in this selection. We solved the Lorentz force equation to get the motion data of the electrons and analyzed the radiated electric field with the particle motions. Then, we took the Fourier transform of the electric field to consider the radiation in the frequency domain. This approach is from definition, the radiation is from charge acceleration. It is more realistic approach to the plasma. It uses same parameter distributions, but the parameter in a cell is not constant any more because of adopting the Monte-Carlo method. It also shows the polarization information of the radiation. However, we assume in this analysis that the radiation is in free space. The channel plasma is considered as current sources for radiation. The material constants of the plasma are concerned as free space. The last approach adopted is to consider the non free space and inhomogeneous media. The hybrid FEM/MoM (hybrid element method) was suggested to exploit advantages of finite element


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method (FEM) and method of moment (MoM), the representative methods for the radiation analysis, and to compensate their disadvantages. The hybrid element method was introduced to analyze the ECE radiation by using EMAP5. In this analysis, the plasma was considered as dielectrics, and the source currents were from the plasma parameters.

DIFFUSION ASSOCIATED NEOCLASSICAL

INDEGENOUS SYSTEM OF HALL ASSEMBLY (DANISHA): A HALL THRUSTER

DIFFUSION ASSOCIATED NEOCLASSICAL

INDEGINOUS SYSTEM OF HALL ASSEMBLY (DANISHA) FOR HALL EFFECT THRUSTER AND

SUPPRESSION OF FLR & SHEARED AXIAL FLOW ON RTI

The present study is related different geometry of the Hall thrusters in which I have tried to get better results than the simple Hall thrusters available at present with the future next generation device Duo Triad Tokomak collider (DTTC) hub by the using new type of code Diffusion Associated Neoclassical Indigenous Hall Assembly (DANISHA).Suppression of sheared axial flow and finite larmor radius (FLR) on Rayleigh-Taylor instability with Diffusion associated neoclassical indigenous system of Hall assembly (DANISHA) is studied in toroidal geometry coordinates for derived magneto hydrodynamic formulation for getting the thrust effect by using such magnetic device used for first time. The DANISHA hall thruster works for 56000(FIFTY- SIX THOUSNAD HOURS) instead of 8000 hrs in case of SPT-100. The sheared axial flow is introduced into MHD and FLR effect

via ( )iiikit

Ω+−→∂∂

⊥22ρω . The sheared axial flow with a


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lower peak velocity suppresses the RT instability. It is observed that the FLR suppress the RT instability strongly than the sheared axial flow. The results are same as in case of slab geometry. INTRODUCTION TO THE THEORY OF DANISHA

Earlier the classical transport phenomena is studied by Pfrisch and Schluter (1962) in which the Pfrish –Schluter regime and other constants given by them afterwards Pfrisch (1978) studied the collisional transport phenomena. Kerner (1978) computationally studied for MHD stability of tokomak class with fixed boundaries. Fluctuations are suppressed whereas the BE

rr×

shear is above a critical value with sheared velocity; external source term with finite conductivity is included for stabilization of RTI by Hazarika (1998, 2001) in BETA machine. A conceptual device for greater energy is being considered hypothetically i.e., Magnetic confinement Tokomak collider (MCTC) hub, Hazarika (2003, 2004) for RTI stabilization in Low-β plasma and for Fuzzy Differential Inclusion (FDI) simulation is done to get the diffusion phenomena as we get new regime (Hazarika’s regime) for skin depth is seen to be very sharp with new moon like crescent having advantage over Tokomak. It is shown that velocity drift is also very much greater than that of Tokomak and BETA machine. Hazarika (2005, 2007),Low-frequency is studied for thermal conductivity by Hazarika (2009a), Feedback stabilization is studied in DTC by Hazarika (2009b),Hazarika(2009c) studied the classical transport phenomena in Double Tokomak Collider (DTC).Magnetic confinement Tokomak collider (MCTC) Hub is studied for neo classical theory of transport phenomena by Hazarika (2009d).Bhatia and Hazarika(2007) showed the Hall effect and FLR on R-T instability where the hall effect enhances the instability and the FLR suppresses the instability this forms the


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aspect of the paper. Similarly same effect is shown by Yaun et al (2009), Gaungde et al (2005), Xiao-Ming et al (2002) It is based on DUO TRIAD TOKAMAK COLLIDER (DANISHA) HUB with Low- β plasma having low frequency fluctuation which is being stabilized for sheared velocity, finite conductivity and with other parameters. The induced RTI is suppressed by above mentioned parameters and as a whole the classical transport phenomena is taken into consideration. The heat conductivity is calculated, Banana (Hazarika’s) regime is calculated where an important result regime for DUO TRIAD TOKAMAK COLLIDER (DANISHA) HUB which is

[ ]26 h

psH sC

DD

+= i.e., the term in bracket is better off the

Pfirsch-Schluter regime. After the Bohm diffusion the Hazarika’s diffusion coefficient is calculated. Bohm diffusion also gets

changed as 2/3

⎥⎦⎤

⎢⎣⎡=rRC

DD hHB .Here we see that at first

comes the Bohm diffusion than classical plateau, Pfirsch-Schluter’s regime than comes the Hazarika’s regime for DUO TRIAD TOKAMAK COLLIDER (DANISHA) HUB for transport phenomena one new result is found as

[ ]hcl

sCvq

v+

=⊥ 6

2

. The above facts compel one to study the

classical phenomena along with collisional transport phenomena, Mirror effect decreases drastically. Toroidal and poloidal beta are calculated. Earlier Bhatia and Hazarika (1995) have studied the effect of self gravitating superposed plasma flowing past each other which of use in the DUO TRIAD TOKAMAK COLLIDER (DANISHA) Hub’s collider region. The two torii meets together at collider region which is the source region of collision or stability in DUO TRIAD TOKAMAK COLLIDER (DANISHA)


2


HUB .This may be considered of interest to particle Physicist for quantum theory researchers and so on. Schematic diagram of DANISHA

DANISHA


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Cross-sectional view of DANISHA Hall thruster

Lateral view of DANISHA Hall Thruster


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BASIC EQUATIONS for VASIMR (DANISHA) ©

(1.1)

++ −=

∂∂ Vn

ci

CcE

xBC e

hci

pih

πωω 42

(1.2)

( ) 1−+

+++ +−+=∂∂

ncihi

gLVCimeE

xVV ωω (1.3)

xB

CBV

xBC

BnCmeB

xV

V x

h

h

he

x

∂∂

−∂

∂=

∂∂

+

++

+

++

022

0

28π(1.4)

==+ jBnVBC xh

0

constant (1.5)

( ) tih

x

yx eC

BB

iEExE ω−

+

+

+= 2/1

0

(1.6)

Boundary conditions

( ) 0=∞−+V

hCBcxE

++ =

∂∂ ω


2


( ) 0=∞++E

( ) 0=−+ ωB (1.7)

14

2−+⎟⎟

⎠

⎞⎜⎜⎝

⎛= n

pi

h

x gLc

lClV ωω

γ is the growth rate for the

VASIMR DANISHA© with axial velocity in consideration. 4

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛=

cl

lCdVd pi

hx

ωγ , the derivative of growth rate with

respect to axial velocity is positive showing that the axial velocity stabilizes the system.

14

2−+⎟⎟

⎠

⎞⎜⎜⎝

⎛= n

pi

h

gLc

llC

ωνγ Is the growth rate for the VASIMR

DANISHA© with the FLR in consideration for the system.

4

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛=

cl

lCdd pi

h

ωνγ

, similarly the growth rate with respect to

the FLR is positive giving us the stabilizing effect for the system.

σγhpRC

P = (1.8)

RF power dissipation is given by


2


4

22

cI

Ej ce

e

pexx ν

ω≈ (1.9)

The power lost via gas excitation and subsequent line radiation can be estimated as

⎥⎦

⎤⎢⎣

⎡−⎟⎟⎠

⎞⎜⎜⎝

⎛≈

e

exe

exee

e

e

ered T

EETnenm

mT

P exp84

0

2/3

π (1.10)

(1.11)

Where

2/1

4

63308

exp ⎟⎟⎠

⎞⎜⎜⎝

⎛≈⎥

⎦

⎤⎢⎣

⎡−

exee

ii

e

exe

EmemLn

TE σπ

(1.12)

2/1

53103

0 32

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛ Λ≈

exee

hiicece ET

CLmecnI

ωσω

Which is square root

of Hazarika constant times the VASIMR. VASIMR DANISHA©

⎥⎦

⎤⎢⎣

⎡−⎟⎟⎠

⎞⎜⎜⎝

⎛ Λ≈

e

exe

exee

cehce T

ELc

ETenLC

LmecI exp

34

2/1402

ωωω


2


τγ 1=

This provides the confinement time for the VASIMR DANISHA© as

In secs(1.13) VASIMR DANISHA is 7 times the VASIMR gives us 7 X

8000 hrs=56000 hrs=2333.33 days=6.392 years For power of DANISHA©

73

3

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

pipiheDANISHA l

ccnCmPωω

ω

(1.14)

hC =Hazarika constant for DANISHA VASIMR First bracket term is velocity component; second bracket term is a constant non-dimensional quantity. Considering initially that the VASIMR is having 1400 N/m as the power we get for DANISHA© P (DANISHA©) = 18.525 times the VASIMR=18.525 X 1400 N/m = 25935 N/m (1.15)

1

14

2

1−

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛== n

pi

h

X gLcl

lCV ωωγ

τ


3


COMPARISION OF PARABOLIC AND PLANAR SYSTEM FOR SHEARED AXIAL

VELOCITY

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10

NORMALIZED WAVE NUMBER

NORM

ALI

ZED G

ROW

TH

RATE Series1

Series2

Fig.1.Series 1: Sheared axial velocity with Parabolic Coordinates, Series 2: Sheared Axial velocity with planar coordinates.

PLOT FOR SHEARED AXIAL VELOCITY VS GROWTH RATE IN

PARABOLIC COORDINATES

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5 6 7 8 9 10

WAVE NUMBER

GRO

WTH

RATE Series1

Series2Series3Series4

Fig2.For V=105, 2X105, 3X105, 4X105


3


PLOT FOR FLR IN PARABOLIC COORDINATES

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10

WAVE NUMBER

GRO

WTH

RAT

E

Series1Series2

Fig.3 Series 1: FLR=1.0, Series 2: FLR=2.0 We can observe that the sheared axial velocity suppress the instability in the parabolic coordinates more than the planar coordinates which is shown is in Fig.1.But for the parabolic coordinates with sheared axial velocity, V= 105, 2X105, 3X105, 4X105 it remains static for higher than V= 2X105 is shown in the Fig.2.FLR stabilizes the instability for the normalized value 2.0, whereas it shows some instability in the initial stage for FLR=1.0 then stabilizes for higher wave number is exhibited in Fig.3.The results are in affirmation to the results given by Qui et al(2002). For Hazarika’s constant derivation

The basic equations which governs the DANISHA are as follows

Bvc

EJ ×+=1η , pP ∇=∇

(1.16)


3


( )0,,0 EErr

≡ ( )φθ BBBrrr

,0,≡ (1.17)

( )0,0),(rpp ≡r ( )crr vvv ,0,⊥≡ (1.18) Here η ,finite conductivity, eT (electron temperature) ,E ( electric

field), iv⊥ (perpendicular ion velocity), χ (magnetic

diffusivity), µ (viscosity) , ep (electron pressure), Br

(magnetic

field), ip (ion pressure ) ,q(safety factor) .

According to the geometry of the considered device the magnetic field also changes. The magnetic field coils are arranged around the DANISHA hub in the toroidal way, the toroidal

magnetic field is θθ BBrr

6= and the poloidal magnetic field is given by

( )θφθφπφφ sin2sin2sin3sin41 −−++= BBrr

.The total

magnetic field is given by φφθθ BeBeBrrr

ˆˆ += , (1.19)

( )θφθφπφθ sin2sin2sin3sin416 −−+++= BBBrrr

(1.20) ( )]sin2sin2sin3sin416[ θφθφπθ −−++= sBB

(1.21) where s is the magnetic ratio. Therefore the beta parameter,

( )[ ]22 sin2sin2sin3sin4168

θφθφππβ

θ −−+++=

sBnT

for DANISHA hub, the toroidal;


3


( )[ ]22 sin2sin2sin3sin4168

θφθφππβ

θθ

−−+++=

sBnT

(1.22) Poloidal; where

( )[ ]22

2

sin2sin2sin3sin4168

θφθφππβ

φφ

−−+++=

sBnTs

is Hazarika’s factor for DANISHA hub Here we have for equilibrium condition

BJpr

×=∇ ` (1.23)

[ ]

[ ]φθ

φ

θ

φη

BCRcU

CRRC

B

CB

BCRCR

p

hh

h

h

hh

r×∇+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛++

∇−=∇

222222

22

22222

116

1

16211

Here (1.24)

( )θφθφπ sin2sin2sin3sin41 −−++=hC is Hazarika’s constant for DANISHA (1.25) This is Hazarika’s DANISHA formula for equilibrium, where U is the feedback loop voltage which considers here absent for the present study. The resistivity η can be expressed by electron-ion

collision frequency nem

ei 2νη = with this we get Hazarika’s


3


diffusion term as

[ ][ ] LhLei

h

eiH rsCr

sCBemTc

D ,66

22222

2−+=

+= ν

ν is the finite

ion larmor radius for DANISHA hub. π

η4

2cDm = is the

magnetic diffusion coefficient describing the skin effect. Magnetic diffusion for DANISHA is

[ ][ ] LhLei

h

eimH rsCr

sCBemTc

D ,66

22222

2−+=

+= ν

νis finite

larmor radius BANANA REGIME

If we do not consider collisions still all the particles in DANISHA plasma could move freely round the quad (four) tori along the field lines. Magnetic field differs and varies along the field lines a length of the order ( )θφθφπ sin2sin2sin3sin41 −−++qR , a particle sees magnetic mirrors at a distance of the

( )θφθφπ sin2sin2sin3sin41 −−++qR strength of

mirrors ⎟⎠⎞

⎜⎝⎛ ∆BB

ratio is given by the inverse aspect ratio.

⎟⎠⎞

⎜⎝⎛ ∆BB

( )θφθφπ sin2sin2sin3sin41 −−++≈R

r

(1.26) The term in the denominator within bracket is Hazarika’s constant for DANISHA


3


Particles trapped between such mirrors according to the law of

energy conservation is tconsmvB tan21 2 =+ cµ or

021 2 =∆+∆ cmvBµ it hold for

max

22

21

21

⎟⎠⎞

⎜⎝⎛=∆ cc mvmv Here 2

21

⊥= mvµ that gives us

magnetic moment

( ) 1sin2sin2sin3sin412

2

⟨⟨−−+

=−=∆

⊥ θφθφπRr

vv

BB c

(1.27) Drift is in the vertical direction with velocity as

[ ] [ ]hh

PA

hhdrift sCRC

vRCsCeB

mvv

+=

+= ⊥⊥

66

222 τ

WheremeB

PAθτ =−2 , cyclotron frequency. The time required to

fly particles from one mirror to another r mirror is the time

cvqRCh .The particles moves a distance which is given by skin

depth,δ out of a magnetic surface in the vertical direction. SKIN DEPTH

[ ] [ ]hLh

hdrift sC

qvv

rsCeBvqmv

vqRC

v+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

+== ⊥⊥

66

2

ccc

δ


3


[ ] 2/1

2/12/1

6 rsCCqR

rh

hL +

=δ is the Hazarika’s diffusion coefficient

(1.28) Where

[ ]hL sCeBmvr+

= ⊥

6, finite larmor radius (FLR) for DANISHA

hub .Here we see that skin depth is 2/12/1hCR factor more than

the Tokomak .This thickness of banana like orbits we may call the crescent of a moon .If we consider collisions than reversal of cv

occurs, ⊥⟨⟨vvc . This means that a part of a banana thickness therefore replaces the gyro radius in plane geometry then trapped

particles collision frequency is given by vrRC

vvvv h

t ≈=c

2

,the no. of trapped particles is proportional to the cv internal given by tapping condition i.e.,

ht RC

rnvnv

n == c

(1.29) HAZARIKA’S DIFFUSION COEFFICIENT

A stochastic process with δ as step size then yields the diffusion coefficient

2/3222

⎥⎦⎤

⎢⎣⎡==rRC

qrnn

vD htL

ttB νδ This is Bohm diffusion


3


22 qrD LH ν= , Hazarika’s diffusion coefficient

[ ]26 h

psH sC

DD

+= , Hazarika’s diffusion coefficient and is

equal to 12.63787, PSD is Pfrisch-Schluter diffusion coefficient, now the Bohm diffusion becomes

2/3

⎥⎦⎤

⎢⎣⎡=rRC

DD hHB

(1.30) HAZARIKA’S REGIME

This condition stands valid for trapping the particle inhibited by collision i.e.

1⟨cvqRCv ht (1.31)

2/32

22

3

2

ArqRC

rCRq

vv

D

hh

λν =

c

Where

2

⎟⎟⎠

⎞⎜⎜⎝

⎛=

cvvA

(1.32) Or hD qRCA 2/3⟩λ where Dλ is the mean free path thus, the left regime is

hDh qRCAqRC 2/3⟨⟨λ (1.33)

DPSHB DDD

λ1,, ≈

One has ( ) [ ]hDHhDB qRCDqRCAD === λλ 2/3 where

Bohm diffusion is BD , ( )qRD DPS =λ


3


Inner part is plateau regime (flat region), and then smooth transition from banana to Pfrisch-Schluter regime then to Hazarika’s regime. It culminates with two effects of importance (I) Bootstrap current (II) Ware effect BOOTSTRAP CURRENT

The induction effect of high diffusion velocity leading to a current density in toroidal direction

[ ]hh

BB qCRC

rdrdp

Bc

cv

BJ+⎥

⎦

⎤⎢⎣

⎡−==

41

44

2/1

θθη

(1. 34)

As poloidal current is absent we get terms with toroidal field only


3


[ ]hh sCRCr

drdp

BcrB

rdrd

+⎥⎦

⎤⎢⎣

⎡−=

614

2/1

θθ

π (1. 35)

The high diffusion velocity leading to a current density in the toroidal direction is gives toroidal beta as

[ ]222 68

8hsCB

pBp

+==

θφθ

π

π

β (1. 36)

Since the diffusion velocity should not exceed the magnetic field in plasma with finite resistivity. For banana regime

polAqqAβββ 2222/3

1,1=< which are in agreement with

earlier results. Pfrisch –Schluter diffusion is expressed by

clD vqv 2≈ , the classical diffusion velocity is given by

magcl vv β21

= with magnetic diffusion velocity as we know that

magD vv < we get the plasma beta as [ ] Dh

cl

vsCv

+<

62

β

=> [ ]hcl

D sCvq

v+

≈6

2

which is known as Hazarika’s diffusion

expression. And from this we get 1<θβ , therefore

[ ]hsCA+

<6

2

β is considerably different from earlier results that

are obtained by the other authors.


4


WARE EFFECT Here the usual E/B drift is replaced by

[ ]hD sCBcEv+

=6θ

for the ware effect in DANISHA hub.

DANISHA HALL Thruster

[ ]hd sCBcEv+

=6θ

(1.37)

Drift velocity

[ ]kTsCBcv

hd +=

6θ

φ (1.38)

Thrust = [ ]kTsCBmcmvF

hd +==

6θ

φ (1.39)

[ ]kTsCF

hc +=

6ωφ

in Newton units (1.40)

CONFINEMENT TIME

2/1Apol ⟨β For impurity transport as long as the

temperature profile is flatter than as given by 2Tn but it is

modified by Hazarika factor 2hC .If we put 1=hC in

2222hMHDthH CRqv

H⟩ττ we can get

222 Rqv MHDthH H⟩ττ this is given by Samain and Werkoff (1977)


4


DHτ is deflection time

MHτ is Maxwellian time for Hydrogen ions.

pe

heEe

IT

BRCrn2/1

23161097.0 φτ−×

= for experimental purpose

also. (1.41) In the present study it is shown that DANISHA hub is better than the tokomak case which is depicted in the Fig.1 and the Fig.2. In Fig.1 it is shown that how DANISHA hub is broader the tokomak case in particle trapping .In Fig.2 it is shown that it takes less confinement time than the tokomak case and is epicentric whereas the tokomak case takes more time to come to the stabilized condition as compared to DANISHA. Therefore the confinement will remain for longer period without any instability generated therein. PARTICLE TRAPPING IN HAZARIKA’S (BANANA) REGIME

Here we can observe that the particle trapped which is exhibited by the Hazarika’s regime (banana) is broader than the Tokomak case in Fig.1.

HAZARIKA'S REGIME(BANANA)

05

101

2345

678910

11121314

15

Series1


4


Fig.1. The particle are trapped in showed region Hazarika’s (banana) regime which calculated from skin depth eqn. (11), q=2.5, R/r=1.5, Lr =3.5, 2.0,1.0 == φθ in radians Series 1. Tokomak, Series 2.DANISHA (HUB) FIG.2.Comparision of Hazarika’s (banana) regime for DANISHA (HUB) and Tokomak is shown for 2.0,1.0 == φθ in radians=2.5, R=1.5 in eqn. (14). It is observed from the above graph that the confinement time required for the DANISHA (HUB) is much lesser than the Tokomak case.

COMPARISION OF TOKOMAK AND DUO TRIAD TOKOMAK COLLIDER(DTTC)

050

100150

12

345

678910

11

1213

1415

Series1

Series2

TOKOMAK

DTTC


4


Fig.3 Comparison of skin depth of tokomak and DANISHA for different FLR From Fig.3 one can see that the skin depth of tokomak and DANISHA for different FLR which is less for DANISHA case. Condition for particle trapping: The velocity should be less than equal to the centrifugal force rgv 22 ≤ , the motion of the particle is oscillatory and the particle never loses contact with the circular path. rgv 22 ⟩ , the particle leaves the circle and

then describes a parabolic path. If rgv 22 = , the motion of the particle becomes oscillatory and it goes unto it attains diametrical path by performing the banana (Hazarika’s) regime path.

The present study is in relevance to the earlier studies done by Pfrisch(1978)and Pfrisch and Schluter(1962),Samain and Werkoff(1977).If we substitutive in the major radius with

1=hC only R remains ,we get the same results of

PLOT OF FLR VS SKIN DEPTH

00.10.20.30.40.50.60.7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

FLR( x 0.1 )

SKI

N DE

PTH

Series1Series2DTTC

TOKOMAK


4


Pfrisch(1978).The present study contains enhancement in the skin depth ,banana regime, bootstrap current, ware effect, diffusion coefficient as Hazarika’s diffusion coefficient ,Hazarika’s factor for DANISHA hub .The DANISHA hall thruster provides us 2.646 more thrust than the SPT-100 thruster. The power is 18.5 times more than SPT-100. results are in agreement with Ning et al (2009). APPLICATIONS: In DANISHA one can observe two types of cases which govern the system as the polarity of the magnetic field changes. (I)For current generation, (II) for rockets and missiles, (III) Hybrid technology Case I: FOR ELECTRICITY GENERATION As the polarity of magnetic field changes the flow of plasma also changes say if in both of the torus for all the four torus the magnetic field is in clockwise direction there will be collisional effect in the collider region of DANISHA which will give rise to more heat and friction and resulting in slowing down motion of plasma in collider region .Afterwards the plasma becomes consistent in every cycle of flow, which can be observed in this region as well as in DANISHA as a whole. Bhatia and Hazarika (1995) showed that in space the self gravitating superposed plasma flow past each other stabilizes the system. It can be useful for generation and getting the current density in enormous quantity which is useful for generation of electricity. POWER LAW: Here the definition of power is used to derive the power law.

Power = Rate of change of work done =dtdWP = (1.42)

Work done = Force X Distance Force= Pressure per unit area


4


A

pFσ

= where p is pressure and Aσ is cross sectional area of

DANISHA

Where dtd

=γ is growth rate.

hA

CpRWσ

= , hence we get the power as

hA

CpRPσγ

= In MW (1.43)

Case II: ROCKET AND MISSILES When we have the change in polarity of magnetic field say in one torus it runs in anti-clockwise and in other clockwise direction in such case we observe that the flow of plasma is accelerated in the collider region of DANISHA and may or may not become turbulent flow which is useful for propulsion system for the use in rockets, missiles and spacecraft etc. It is observed that the velocity drift in such case is hC times that of Tokomak case. Here the plasma is acting as the superposed flowing one over the other hence enhancing the velocity of resultant plasma which is observed by several researchers in past Bhatia and Hazarika (1996). Case III: HYBRID TECHNOLOGY Like the case II here we use the same type of system resulting into the different type of technology which is prevalent in many places known as the Hybrid technology. The accelerated neutrons which can be extracted from the DUO TRIAD TOKAMAK COLLIDER (DANISHA) HUB can be used in Fission Chamber where we need the those neutrons as for the fusion purpose the fast neutrons are waste products leading to the heating of plasma chamber, so it can be used through neutrons collecting blackest used and can be


4


channelized to the Uranium or plutonium based nuclear/atomic reactors. Case IV: COMPUTERS AND TELEVISION The growth rate is measured in per second (Hz) which gives us the speed compiling or formation of plasma. If it is used in computer chips will give us the processing speed of the microprocessor. Similarly we can enhance the speed of the normally used microprocessor by 1.5 times say if the speed is 3.6GHz in the present condition the microprocessor speed becomes 5.9 GHz. The calculation speed of the microprocessor becomes 5.9 Giga flops (i.e. 5.9 Giga floating points per second). If it is used in super computer with calculation speed of 1.73 Teraflops, the resultant will be near about 150 Tera floating points per second (150X1012 floating points per second).We can enhance the resolution of the computer monitor screen as well as that of the plasma TVs confinement time can be reduced with better resolution. The resolution is 24.75% better than the present best available computer monitor or plasma TVs .One particular brand of plasma and LCD TVs are projecting that it can give 1:1000000 resolution , here in this particular case it will be 1:1500000 resolution . No blurred images rather only crystal clear screen can view from 172 degrees wide angle without any diminishing images from side view angle. This entire thing can be done by using the nanotechnology and peizo-electrononics. REFERENCES

1. Hazarika,A.B.R.: Submitted in Physics of Plasma (2009a)& 13th National symposium on plasma Science &Technology, Rajkot(1998); 16th National symposium on plasma Science &Technology, Guwahati(2001)

2. Hazarika,A.B.R.: Submitted in Physics of Plasma

(2009b)& 18th National symposium on plasma Science &Technology, Ranchi(2003);19th National symposium on plasma Science &Technology, Bhopal(2004)


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3. Hazarika,A.B.R.: Submitted in Plasma of Plasmas

(2009c)& Proceeding of 20th National symposium on plasma Science &Technology, Cochin Univ. of Sci. & Technology, Cochin(2005) ;

4. Hazarika, A.B.R.: Submitted in Physic of plasma

(2009d)& Proceeding of 3rd Technical meeting of International Atomic Energy Agency on Theory of Plasma Instabilities, Univ. of York, York, UK(2007),31pp

5. Pfirsch, D: Theoretical and computational plasma

physics (1978), IAEA-SMR-31/21, pp59. 6. Pfrisch, D., SCHLUTER, A.: Max-Planck-Institut fur

Physik und Astrophsik, Munich, Rep. MPI/PA/7/62(1962).

7. Kerner, W: Z. Naturforsch. 33a,792(1978) 8. Samain,A., Wekoff, F: Nuc. Fus. 17,53(1977) 9. Bhatia, P.K and Hazarika, A.B.Rajib :Phy Scr

53,57(1996) 10. Hazarika,A.B.R: Proceeding of National symposium

of Plasma Science and Technology(2009),Hamirpur(HP)

11. Bhatia, P.K. and Hazarika, A.B.Rajib : J Ind. Acad. Maths.29(1),141(2007)

12. Gaunge. J, Lin. H and Xiao -Ming. Q: Plasma Sci & Tech 7(3),2805(2005)

13. Xiao-Ming. Q, Lin .H, Guangde. J: Plasma Sci & Tech. 4(5),1429(2002)

14. Ning. Z, Yu. D, Li. H and Yan. G : Plasma Sci and Tech. Vol.11(2),194(2009)

15. Qui, X.M, Huang, L, Jian, G: Plasma Sci &Tech, 5, 1429(2002)

16. De Groot, J.S, Toor, A, Goldberg, S.M et al: Phys Plasmas 4, 1519(1997)


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17. Haines, M.G.: IEEE transaction on Plasma Sci.26, 1275(1998)

18. Shumlak, U and Hartman, C.W.: Phys Rev. Lett. 75, 3285(1995)

19. Arber, T.D,Coppins, M, Scheffel, J: Phys Rev. Lett. 77, 1766(1996)

20. Ganguly, G: Phys Plasmas 4, 2322(1997) 21. Qui, X,M ,Huang,L and Jian,G.D: Chin. Phys Lett.

19,217(2002) 22. Turchi, P.J and Baker,W.L: J. Appl. Phys,

44,4936(1973) 23. Morozov, A.I: Introduction to Plasma Kinetics,

Fizmat, Moscow(2006) 24. Choueiri, E Y: Physics of Plasmas, 8, 1411(2001)

Introduction to different types of Propulsion system 1. Electric Propulsion System More than three hundred electric propulsion thrusters have flown on over 100 spacecraft over the last thirty five years and a significant increase in usage is expected over the next decade. The 1990s have been described as the ‘era of application [27]’ because the benefits of electric propulsion are being realized on numerous commercial satellite missions and there has been an increase in flight activity for a broad spectrum of electric propulsion devices. Advancements in electric propulsion related technologies and thruster design 3 improvements, based on extensive ground and flight test results, have brought some electric propulsion devices to a high level of technological maturity. The risk of employing electric thrusters on spacecraft has diminished in recent years due to an increase in the number of successful electric thruster missions, improvements in thruster materials and designs, and an improved understanding of fundamental thruster operating principles and spacecraft integration issues. With the increasing emphasis on lowering the mass of spacecraft propulsion systems, increasing spacecraft orbiting lifetimes, and reducing overall


4


costs, together with greater amounts of electric power now available on-board spacecraft, the applications for electric propulsion systems will certainly continue to grow. Electric propulsion technology has matured to a point where its expanded use for select space missions is justified from both a technological and an economic standpoint. Electric thrusters can outperform conventional chemical (liquid and solid propellant) propulsion systems for certain space missions because of their generally higher specific impulse values. For select missions, replacing current chemical propulsion systems with high performance electric propulsion systems can provide substantial mass and cost savings, increased orbiting lifetimes, and increased mission capabilities. The current and likely near-term electric thruster missions include station keeping, drag compensation, attitude control, station repositioning, orbit raising or lowering, orbit repositioning, and maneuvering of interplanetary spacecraft [49]. Electric propulsion is the acceleration of propellant gases by any of electrical heating, electric or magnetic, or both of field forces to provide propulsive thrust to a vehicle. It involves the conversion of electrical energy into kinetic energy of the exhaust gases. There are numerous electric propulsion devices described in the literature, which can be grouped into at least one of three fundamental categories. Electro-thermal Propulsion - the propellant is heated using electrical energy, and the hot propellant gas is then thermodynamically expanded and accelerated through an exhaust nozzle, e.g. resistojet and arcjet thrusters. Electro-static Propulsion - the propellant atoms are ionized and accelerated out of the thruster by electrostatic field forces. The exhausted propellant ions are neutralized by electrons emitted from an external cathode, e.g. ion thruster and field emission electric propulsion thruster.


5


Electromagnetic Propulsion - the propellant is ionized and accelerated by the combined interaction of electric and magnetic field forces on the resultant propellant plasma, e.g. Hall thruster, pulsed plasma thruster, and magneto-plasma-dynamic thrusters. New electric propulsion technologies designed to operate at higher power (5 – 50 kW) for future long range planetary exploration and large velocity change maneuvers are under study. This effort has in part been a response to NASA’s Project Prometheus [42], a technology program to develop safe, efficient high power sources for solar system exploration. In primary propulsion on micro spacecraft or fine position control of conventional spacecraft has driven the interest in sub kilowatt thrusters [10]. 2. Resistojet A resistojet is a device that heats a propellant stream by passing it through an ohmically heated chamber before the propellant is expanded through a downstream nozzle. In resistojets, the propellant is fed into the thruster and heated while flowing over an immersed resistance heater or over thruster chamber surfaces heated by radiation from an isolated resistance heater [27, 38]. Resistojets (MR-501, MR-502A, HiPEHT, etc.) have accumulated a substantial flight history onboard at least 75 spacecraft since 1965 [27], mainly performing north-south station keeping (NSSK) and some attitude control, east-west station keeping (EWSK), on-orbit maneuvering, and limited on-orbit boosting. Future resistojet missions include station keeping, orbit insertion, and de-orbit functions. Resistojets have been used on Lockheed Martin Astro Space (LMAS) Series 4000 and 5000 satellites and recently on Iridium satellites. 3. Arcjet An arcjet is a device that heats a propellant stream by passing a high current electrical arc through it, before the propellant is expanded through a downstream nozzle [38]. In arc jets, an electrical arc discharge is initiated between a central cathode and


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a coaxial anode, which also acts as the thruster’s nozzle. The propellant is fed into the thruster and heated while flowing through and around the arc discharge. A research group from the Kharkov Aviation Institute (KhAI), which was established with Russian industrial companies and still keeps working relations with them, has presented an analytical study of gas acceleration in the supersonic nozzle of the arcjet thruster [68]. The heat transfer in supersonic flow under electrical discharge results in significant displacement of the critical throat comparing with classic adiabatic flow. Key parameters like an expansion angle and throat position were presented as functions of arc parameters. Since 1993, arc jets (MR-508, MR-509, and MR-510) have been used for NSSK on at least six LMAS Series 7000 and A-2100 satellites and are base lined for several future satellites. In 1997-1998, arc jets were used on both an experimental USAF orbit raising mission (26-kW ESEX arcjet) and an orbit insertion/maintenance mission (ATOS arcjet). 4. Ion Thruster An ion thruster is a device that accelerates propellant ions by an electrostatic field [38]. In ion thrusters, neutral propellant atoms are fed into a discharge chamber and ionized by bombardment with electrons emitted from a cathode in a low voltage electrical discharge. Since 1962, ion thrusters have flown on about eleven experimental spacecraft. Several ion thrusters (XIPS-13, XIPS-25, IES, and UK-10) and a radiofrequency ion thruster (RIT-10) were launched to provide NSSK for several operational satellites. Hughes used their XIPS-13 ion thruster on HS-601, PAS-5, and Galaxt 8-i satellites and their XIPS-25 ion thruster on HS-702 and Galaxy 10 satellites [27, 49]. Keldysh Research Center presented results of numerical simulation of a low-power Xe-ion thruster with an advanced, slit-type accelerating system. Experiments were carried out for the power range of 50-150 W and specific impulse values of 2500 – 3500 s were achieved. Highest values of thruster efficiency were about 65 % [68]. The NSTAR electron bombardment ion thruster was provided primary propulsion for


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the Deep Space-1 spacecraft on the first flight of NASA’s New Millennium program in 1998. The success of the Deep Space 1 technology demonstration has led to the planned use of three NSTAR ion thrusters for the DAWN mission to explore Ceres and Vesta, two protoplanets between the orbits of Mars and Jupiter [10]. DAWN, rescheduled for launch in September 2007, would be the first NASA space science mission to implement electric propulsion. Boeing Electron Dynamics Division (EDD) is developing the 30 cm ion thrusters for this Discovery-class mission. The NSTAR thruster extended life test ended this year after more than 30,300 hr of operation, having processed over 230 kg of xenon. The NSTAR program far exceeded its original goals of 8,000 hr of operation with a total xenon throughput of 83 kg. The NASA Evolutionary Xenon Thruster (NEXT) is designed to deliver a throttle able 7 kW, 40 cm ion thruster with a xenon throughput capability of over 400 kg, a specific impulse (Isp) of 2,200 – 4,120 sec, and a thrust of 50 – 210 mN. Two NASA-led teams continued work toward the development of a long-life engine system for power levels greater than 20 kW and Isp in the 6,000-8,000-sec range. The High Power Ion Propulsion team, led by NASA Glenn is developing an 8,000 sec, 25 kW girded ion thruster using a microwave ionization source and neutralizer in a rectangular geometry. The JPL-led team is developing the nuclear electric xenon ion system, which will include advanced carbon-carbon grids and a reservoir hollow cathode, in an effort to develop a 20 kW, 7,500 sec Isp thruster with high propellant throughput capability. On January 31, 2003, ESA’s latest telecommunication technology demonstration satellite, Artemis, reached its assigned geostationary orbit after an 18 month transfer. The spacecraft had used its experimental ion propulsion system, consisting of two RIT-10 and T5 thrusters, to complete the maneuver. 5. Field Emission Electric Propulsion In field emission electric propulsion (FEEP) thrusters, the liquid propellant is fed to the tip of a needle-like emitter and intense


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local electric fields cause charged liquid droplets to spontaneously form. The charged liquid droplets are extracted away from the liquid surface and accelerated by the electrostatic fields. 6. Electromagnetic Propulsion A magneto plasma dynamic thruster is a device that accelerates propellant plasma by internal or external magnetic field acting on an internal arc current [38]. Magneto plasma dynamic (MPD) thrusters frequently use similar electrode geometries as arc jets and also use an electrical arc discharge. However, the majority of thrust generated in MPDTs is due to electromagnetic forces exerted on the propellant plasma by interaction with the arc and the self-induced magnetic field. In pulsed plasma, a portion of the propellant feedstock (typically solid Teflon) is ablated and ionized by an electrical arc discharge sheet initiated between two electrodes by a discharging capacitor. The resultant propellant plasma is accelerated by interaction with the arc and the self-induced magnetic field.


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Table 1.1: Thrust systems and their specific impulse [75]

Engine EffectiveExhaust

Isp Thrust Duration

Velocity (m/s)

(s) (N)

Solid rocket 1,000 - 4,000 100 103 − 107 minutes Resistojet rocket 2,000 - 6,000 10−2 − 10 minutes Arcjet rocket 4,000 - 12,000 10−2 − 10 minutes Hall thruster 8,000 - 50,000 1,500 10−3 − 10 months Ion thruster 15,000 - 80,000 5,000 10−3 − 10 months

VASIMR 10,000 -300,000 30,000 40 - 1,200 days - months

7. Hall Thrusters The Hall thruster is a plasma propulsion device designed in the 1960s. The inventor is A. I. Morozov. They are mostly known as electric propulsion thrusters for spacecraft, and are also called stationary plasma thrusters (SPTs). The advantages (SPTs). The advantages of the Hall thruster are higher thrust densities and specific impulses between 1 and 2000 sec. These advantages promise to


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Figure 1.1: The Hall thruster diagram [9]. 1) Magnetic system; 2) insulator; 3) anode; 4) cathode; 5) gas inlet. increase operating lifetime and payload mass. Because of these advantages, the Hall thrusters are considered ideal for many on-orbit applications including station keeping, orbit re-phasing, and orbit transfer of geosynchronous communication satellites. It has become clear that the physical processes in the Hall thrusters are extremely complicated, despite the simple construction of the devices. The discharge in the Hall thrusters is unlike any other known discharge. It is characterized by the spatial separation of the ionization and acceleration zones. In the ionization zone, crossed electric and magnetic fields are present with the radial directional magnetic field crossing the wall while the axial directional electric field is tangential to them. A free path length of charged particles much higher than the size of system, and the drift of electrons is closed. Electrons emitted from an external hollow cathode are hindered from directly reaching


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the anode by the radial magnetic field increasing to the outlet of thruster and become magnetized and confined in an azimuthally ~E ?~B drift motion. The neutral propellant atoms are fed into the discharge chamber and ionized by bombardment with the electrons. The radial magnetic field is not strong enough to make the ions magnetized, because the Larmor radius of the ions is much bigger than the thruster size. The ions are accelerated axially by the electric field, and the thrust is produced by momentum imparted to the ions. Plasma is created with a very high electron temperature of up to 20 eV within the discharge [55]. 8. SPT Series Hall thrusters (SPT-50, SPT-70, SPT-100, etc.) have an extensive flight history on-board Russian spacecraft for NSSK, EWSK, attitude control, orbit injection and repositioning applications on more than 50 Russian satellite since 1971 [27, 55]. Hall thrusters have continued to accumulate flight time on Russian satellites. Since 1994, more than eight geostationary satellites equipped with SPT-100-type thrusters have been launched. The total number of SPT-100 thrusters operated onboard these satellites is more than 64. The maximum operation time on a single SPT-100 has exceeded 1,500 hr (on Express 11). Stationary plasma thrusters (SPT) were developed and qualified at DB Fakel. Main functional specifications of SPT thrusters are listed in Table 1.2. Thrust Power Isp Efficiency Life time mN kW sec % hrs

SPT-35a 1 - 10 0.2 1100 35 2000SPT-50a 20 0.35 1250 35 2250SPT-70a 40 0.65 1450 48 3100SPT-100a 83 1.35 1550 52 8000SPT-140b 290 4.5 1800 51 7000PPS-1350c 92 1.5 1800 52 8000


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Table 1.2: SPT specifications a [68], b [12], c [5] 9. BPT-4000 The Aerojet BPT-4000 Hall thruster underwent qualification tests [31, 43, 46, 83]. Thruster performance was verified for multimode operation at 3.0 and 4.5 kW (high thrust mode at a discharge voltage of 300 V and high Isp mode at 400 V). The target performance ranges for the thruster are Isp of 1,844 – 2,076 sec and thrust of 168 – 294 mN [10]. The flight qualification test program, including an approximately 6,000-hr life test, was completed by the end of 2004. 10. BHT-200 The BHT-200 Hall thruster [19, 40, 41, 50, 59] originally developed for the TechSat 21 mission by Busek, is undergoing life tests at the Air Force Research Lab. NASA-Glenn and Aerojet were selected to begin the Hi-Voltage Hall Accelerator program to develop a Hall thruster targeting the 6 – 8 kW power, 2,200 – 2,800 sec Isp performance range. Preliminary testing of the [14] NASA-457M Hall thruster operating on xenon propellant at power levels up to 96 kW demonstrated thrust, Isp, and efficiency of 3.3 N, 3,500 sec, and 58%, respectively. 11. SMART-1 Mission In September 2003, ESA launched its SMART-1 mission to explore the Moon. SMART stands for Small Missions for Advanced Research in Technology. SMART-1 is the first European spacecraft to travel to and orbit around the Moon. It traveled to the Moon using solar-electric propulsion with the PPS-1350 Hall thrusters developed at Snecma and carrying a battery of miniaturized instruments. Figure 1.2 shows PPS-1350. Its use of solar electric propulsion as its primary drive mechanism will be a first for Europe and is essential in paving the way for future ESA projects with large velocity requirements, such as the Mercury


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Cornerstone mission [82]. As well as testing new technology, SMART-1 is making the first comprehensive inventory of key chemical elements in the lunar surface [74]. Figure 1.2: The PPS-1350 thruster [62] Motivation Former investigators have carried out detailed measurements and indicated that oscillations play a major part in the closed-drift accelerators with an extended acceleration zone (CDAE) [69], and verified that high-frequency (Up to 20 MHz) azimuthally waves (electron drift waves) are exited in a Hall current plasma accelerator [26]. Two instabilities, ionization instability and transit-time instability have been found [77], and the relationship between the amplitude and spectrum of the high-frequency waves (20 - 400 MHz) on the discharge has been revealed [76]. In 2003, measurements of radiated electric fields from 10 kHz to 18 GHz on a BPT-4000 Hall thruster being qualified for flight identified many types of emission, including strong electromagnetic emission in the 1-5 GHz range [43]. The frequency is similar to satellite communication frequencies (1-20 GHz), so it is of significant concern. The BPT-4000 is a 4.5 kW


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class thruster. The BPT-4000 Hall thrusters were tested to see the effect of a plasma plume on reflector antennas [46, 83]. The purpose of this test was to gain quantitative information on the effects of the thruster on various spacecraft subsystems and to help mitigate the risk associated with the introduction of this new propulsion technology on future spacecraft. Several broad harmonic peaks have been observed as one can see in Figure 1.3 [43]. These emissions are more than 20 dB above MIL-STD 461E, and 40 dB above spacecraft designers limits. MIL-STD 416E is the requirements of the United States department of defense [1]. The requirements are for the control of electromagnetic interference characteristics of subsystems and equipment. Ground tests of SPT-140 Hall thrusters were presented in [30, 66]. The SPT-140 is a 4.5 kW class thruster, which is similar to BPT-4000. Performances of the thruster are 1800 sec of Isp, 51% of overall system efficiency, and 7200 hrs of lifetime. EMI tests found very little emission in the traditional RF communication bands [30], and the emission of the tests is shown in Figure 1.4. At the lowest frequencies (10 kHz to 20 MHz), E-field emission exceeded the MIL-STD-461C specification by up to 53 dB. The SPT-140 was found to emit aperiodic broadband emissions at levels above the detection threshold from 1 to 3 GHz. An engineering model SPT-140 Hall thruster was evaluated with respect to thrust and radiated electromagnetic interference [66], shown in Figure 1.5. The broadband electromagnetic emission spectra generated by the engine were measured for a range of frequencies from 10 kHz to 18 GHz. These results were also compared to the noise threshold of the measurement system and MILSTD- 461C.

The emissions at frequencies above 100 MHz were below MILSTD- 461C and approached the minimum detectable values at frequencies in excess of 1000 MHz. The different trend from the work at Beiting et al [43] was shown in the above two measurements, which demonstrates consistency. Another


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intensive measurement of emission is reported [16]. Space Systems/ Loral (SS/L) characterized the emissions of SPT-100 thrusters developed by Design Bureau Fakel, and they are shown in Figure 1.6. The parameters characterized include emissions polarization, directivity, magnitude, burst ness, and coherency. In this paper, strong radiation was shown again in high frequency range (1 – 7 GHz). About 30 dB higher emission was shown at the peak around 1.4 – 2 GHz. This trend is similar to the trend of BPT-4000. To confirm that the measured radiation is indeed ECE, a simple 2D model was developed for the radiation of a Hall thruster [32]. The analysis of ECE radiation is performed with the magnetic field, plasma density, and plasma electron temperature distributions in a typical Hall thruster. Parameters for the models were obtained from the literature [21, 65].


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Chapter 2 Grad B Drifts Assume the magnetic field lines are straight, in the z direction, but their density increases in the y direction. The gradient in |B| causes the Larmor radius to be larger at the bottom of the orbit than at the top. This leads to a drift, in opposite directions for ions and electrons, perpendicular to both ~B and .B [20]. The drift velocity is proportional to rc/L and v., where L is the scale length. Consider the Lorentz force , averaged over a gyration. Since the particle spends as much time moving up as down Fx is clearly equal to 0. Taylor expansion of the magnetic field about the point x0 = 0 is taken into consideration 2.1: Drift of a particle in a non-uniform magnetic field [20]. 2.2 Electron Cyclotron Emission A plasma immersed in a magnetic field radiates as the result of the acceleration of the charges in their orbit motions around the magnetic lines of force. The frequency and angular distribution of the radiation undergoes dramatic changes as the electron energy is increased from non-relativistic to extreme relativistic energies [6]. In thermal equilibrium the emission can not exceed black-body radiation. The peak intensity is independent of the electron temperature. The intensity emitted in the backward direction is almost the same as that in the forward direction. The radiation is distributed over wide angular cones. 2.2.4 Optical Depth Consider a plasma sphere of radius a. The larger the a, the larger the re-absorption, until a point is reached at which the volume emission is just balanced by the black-body radiation from the surface.The emission at a given frequency has three characteristic


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regimes, depending on the value of t0 [6]. When t0 ?1, the radiation seen by the observer suffers negligible self-absorption in its passage through the medium, and the observer sees essentially the contribution from each individual volume element along the ray, that is, the intensity I! = R j! ds. The medium is said to be optically transparent to the radiation. When t0 ?1, the intensity is a direct measure of the source function. The medium is said to be opaque to the radiation. If, at the same time, the medium is in thermal equilibrium, the medium is said to emit as a black body. Finally, when t0 is neither very small nor very large compared with unity, the medium is said to be semitransparent or gray. Therefore, plasmas in this study are said to be optically transparent or optically thin. Reabsorption or self-absorption is negligible. Chapter 3 Numerical Method Three approaches for the electron cyclotron emission analysis of the Hall thrusters are developed. The first one employs the lumped plasma parameters from the simple plasma parameter models of a Hall thruster. The plasma parameter distributions are from the literature. The second method is the microscopic point of view. This analysis employs the Monte Carlo (MC) method to select electrons thoroughly, and the Particle-in-cell (PIC) method to obtain the acceleration data of the electrons for the cyclotron emissions. Their trajectories are followed as they move within sampling period. ECE radiation is calculated with the acceleration data. The fast Fourier transform is taken to obtain the radiation in the frequency domain. The last method is the macroscopic point of view. This analysis employs the hybrid finite element and moment methods (hybrid element method) to consider the plasma as inhomogeneous dielectric


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media. The cyclotron motion of the electrons is modeled with two dipoles with 90. phase difference. The plasma parameters and magnetic field in the thruster channel region are considered for the current sources of the dipoles. 3.1 Plasma Parameter Modeling for BPT-4000 class Hall thrusters ]To analyze the ECE radiation, the magnetic field, electron temperature, and electron density distributions are important parameters. We assume that the plasma fills an annular region of width, w, inner radius, rI , and length, L. The configuration of the Hall thruster considered in this study is shown in Figure 3.1. We note two critical points along the axial axis: za, a point in the throat, and zb, the exit point. In distance normalized to L we assume za = 0.5 (3.1) zb = 0.8 (3.2) 3.1.1 1D Modeling In the 1D modeling, we assume that all quantities are independent of the azimuthal and radial directions, and depend only on position in the axial direction. To analyze the ECE radiation, the magnetic field, electron temperature, and electron density distributions are important parameters. First, a 1D magnetic model is considered. In a typical Hall thruster, the radial field is dominant compared to the axial field [65]. Thus a 1D radial magnetic field might be adequate to approximate the ECE radiation. A shifted Gaussian (bell-shaped) magnetic field is assumed and the maximum value is at the exit plane [9]. The 1D magnetic field model is given by Br(z) = B0 + (Bmax - B0) exp[-(z - zb)/Lb2] (3.3) where B0 = 0.2Bmax and Bmax = 0.05 T and Lb = 0.6. This trend is reported in the literature [54]. Most of the plasma in the channel of the Hall thruster is quasi-neutral.Therefore the electron density


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is the same as the ion density in the channel. For the 1D model the acceleration channel. In this region, the radial magnetic field is maximum and thus a large number of electrons are inhibited from moving in the axial direction, resulting in the high probability of plasma production [9]. Our 1D electron density model is given by n = _ na + (nb - na)z/zb z < zb nb z > zb (3.5) where na = 2.8×1017 m.3 and nb = 1.6×1018 m.3. 3.1.2 2D Modeling In the 2D plasma modeling, We assume that all quantities are independent of the azimuthal angle, which is axisymmetric, and depend on position in the axial and the radial directions. The two critical points along the axial direction are used in this modeling. Additionally some new parameters are introduced. 3.1.3 Magnetic Field Model For a typical Hall thruster, the magnetic field density at the inner and outer walls of the channel is higher than at the center line of the channel. A shifted Gaussian (bell-shaped) radial magnetic field at center line is assumed and the maximum value is at the exit plane [9, 69]. The radial and axial magnetic field profiles at the inner wall, outer wall, and center line of the channel are based on the data given in [60]. 3.1.4 Electron Temperature Model The electron temperature is not uniform in the channel, and the maximum temperature appears at the acceleration region but not at the exit plane. The electron temperature at the exit plane is actually equal to or lowers than the maximum temperature. This trend is reported in the literature [54]. 3.1.5 Electron Density Model


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Most of the plasma in the channel of the Hall thruster is quasi-neutral. Therefore the electron density is the same as the ion density in the channel. Experimental results show that the plasma density reaches its peak value inside the acceleration channel. Electron density model at the center line is given by nc = _ na + (nb - na)z/zb z < zb nb z > zb (3.10) where na = 2.8 ?1017 m.3 and nb = 1.6 ?1018 m.3. In order to model the 2D electron density profile, we use the ion density measurement data given in [21, 29]. The axial electron density profile for the 2D model is the same as the 1D model, (3.10). 3.2.1 Electron Density and Electron Temperature The electron density and electron temperature distributions [9, 21, 65] are reconstructed and used again in this study. Electron density distributions from the literature . 3.2.2 Magnetic Field As mentioned before, not only radial but also axial magnetic field information is required for 2D analysis. Unfortunately, we could not obtain the structures and currents information to perform magnetic field analysis, so an alternate way to obtain the magnetic field distribution was tried. Many, but limited, information about magnetic field distributions of Hall thrusters are in literature. Generally, equipotent contours and radial distributions of the magnetic fields can be easily obtained. Equipotent contours of the magnetic fields are from [9, 60] and are shown in Figure 3.14. Radial magnetic field distributions at the center lines are from [9, 11] and are shown in Figure 3.15. If we can generate a similar contour pattern to the measurement and can obtain the radial magnetic field distribution from the generated contour pattern, then the generated contour pattern is weighted according to the scale between the generated radial field distribution and the


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measurement. The radial field distribution also shows good agreement at the exit plane. The exit region is more important for this analysis than the inside of channel. This is because the exit region has dominant values of plasma parameters: magnetic fields, electron density, and electron temperature. However, half of the channel from the anode side is different. It has a stronger magnetic field at the center line in our simulation than in the references. In the references, it also shows much less density than that of exit plane region. The magnetic field profiles from the literature are for optimized Hall thrusters, but the generated distribution is from simplified conventional structure and arbitrary currents. Consequently, generated field has wider low density region of magnetic field. This is a low frequency region, so the region is relatively less important than the exit plane region. This difference of magnetic field distribution can affect the results. 3.3 The Monte Carlo Method Statistical simulation methods may be contrasted to conventional numerical discretization methods, which typically are applied to ordinary or partial differential equations that describe some underlying physical or mathematical system. In many applications of Monte Carlo, the physical process is simulated directly, and there is no need to even write down the differential equations that describe the behavior of the system. The only requirement for the Monte Carlo simulation is the physical or mathematical system described by probability density functions (PDFs). For now, we will assume that the behavior of a system can be described by PDFs. Once the PDFs are known, the Monte Carlo simulation can proceed by random sampling from the PDFs. The outcomes of these random samplings must be accumulated in an appropriate manner to produce the desired result, but the essential characteristic of Monte Carlo is the use of random sampling techniques to arrive at a solution of the physical problem. In many practical applications, we can predict the statistical error, the


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variance, in this average result, and hence estimate of the number of Monte Carlo trials that are needed to achieve a given error. The Monte Carlo sampling result with the Maxwell-Boltzmann distribution of speeds is shown in Figure 3.20. This result also has the same trend as before. According to our results from the normal to the Maxwell-Boltzmann distributions, we can say that taking over 100 samples has good agreement with the CDF, and taking over 1000 samples shows fairly good matchs to both the PDFs and the CDFs. Consequently, if more than 1000 samples are selected, then it is enough to represent the distribution. 3.4.Particle-In-Cell There are many ways to analyze radiation. Two approaches are suggested in this study. By definition, the radiation is from charge acceleration [6, 7, 33]. In the first approach, we solve for the charge acceleration from the Lorentz equation. We then use the solution to simulate the radiation. The radiation is ultimately shown in the frequency domain. We will now discuss electron-neutral collisions in this particle-in-cell code. 3.4.1 Selecting Electrons We select electrons for the first step of this analysis. One electron represents a certain number of electrons in this analysis. Generally, electrons are in the position and velocity coordinates. Electrons in this analysis have the position, velocity and acceleration coordinates. We randomly select the initial positions for the electrons with the uniform distribution. The velocities of the electrons are also selected stochastically. Velocities have two components, speed and direction. Let us consider the two components separately. 3.4.1.1 Maxwell-Boltzmann Distribution of Speed


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The speed of electrons in the Hall thrusters is well represented by the Maxwell-Boltzmann distribution in many cases [13, 17, 21]. In this numerical approach, the distribution is embodied with the Monte Carlo method shown in section 3.3.1, and only this distribution is tried. However, we can easily expand this to other distributions. 3.4.1.2 Isotropic Velocity After a collision, not only the speed, but also the direction of the electrons is random. It is called isotropic velocity. Therefore, the unit vector of the velocity is uniformly distributed on the surface of a unit sphere. First, we try a simple linear relationship with uniformly distributed random variables on the interval [0,1]. 3.4.2 Time Scale The electron motions are calculated from the Lorentz force equation with a sampling time. Deciding the sampling time and total sampling period is very important for the PIC method. Shorter sampling time and a longer time period are, of course, better for the computational accuracy, but it requires a higher performance of computing. On the other hand, bigger sampling time and a shorter time period are better for computational load. We need to find compromising values to achieve both higher accuracy and acceptable computational load. The time scale is considered from these two points of view. 3.4.2.1 Fourier Transform Point of view The electric field from the accelerated electron is calculated and the Fourier transform is taken to obtain the electric field in the frequency domain. The sampling time and the total sampling period are decided from the maximum frequency and the resolution in the frequency domain, respectively. The frequency range of ECE is from 1 to 5 GHz. Analysis range up to 50 GHz is


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enough to cover the ECE radiation, and the resolution of 100 MHz is also detailed enough to check the results. The sampling time is given by 1/(2 ·50GHz) = 1×10-11s, and the total sampling period is written by 1/100 MHz = 1 ?10-8s. 3.4.2.2 Magnetic field Point of view In a numerical simulation, the motion of one particle is stable for ._t < 2, and accurate for ._t = 0.2 [8, 22]. In this analysis, . is .ce and the maximum magnetic field in the channel region is 1550 G. For the maximum field, 1550 G, _t is less than 7.3 ?10-12s For the sampling time, 7.3 ?10-12s is chosen from the magnetic field point of view, and 1 ?10-8s is chosen for the total sampling period from the Fourier transform point of view. If we consider a little margin for the sampling time, then 5×10-12s is good enough. During the sampling period of 1×10-8s, 2000 samples are needed with the sampling time of 5 ?10-12s. The resulting range in the frequency domain is up to 100 GHz from 1/(2 ?5 ?10-12) with the resolution of 100 MHz from 1/(2000 ?5 ?10-12). 2048 samples, instead of 2000, can be taken to use the fast Fourier transform. Then, the frequency range of the result is same as the range of the 2000 sample case. The resolution is 97.7 MHz from 1/(2048 ?5 ?10-12]). If 4096 samples are chosen, the frequency range is same as previous cases, but the resolution is half of the 2048 case, 48.8 MHz, 1/(4096 ?5 ?10-12). 3.5 Numerical Modeling of Electromagnetic Radiation 3.5.1 Hybrid Element Method A hybrid element method [47] has been devised where finite elements are coupled to boundary elements. The basic technique is to apply the equivalence principle to transform the original problem into interior and exterior problems, which are coupled on the exterior dielectric body surface through the continuities of the tangential electric field and magnetic field.


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The interior problem involving the inhomogeneous medium is solved by the finite element method, and the exterior problem involving unbounded region is solved by the moment method [88]. A detailed formulation of the hybrid moment and finite element method is described in [47]. A hybrid method code named EMAP5 was announced from the electromagnetic compatibility laboratory of the university of Missouri-Rolla [34, 39, 86]. EMAP5 is a full-wave electromagnetic field solver that combines the method of moments with a vector finite element method [25]. The FEM is employed to handle the interior domain of inhomogeneous dielectric bodies and the method of moments is used to develop surface integrals that relate the field quantities on boundary surfaces with the equivalent surface currents. These integral equations are then coupled to the finite element equations through the continuity of the tangential magnetic fields [34]. EMAP5 is designed primarily to simulate electromagnetic interference sources at the printed circuit board level [2]. They tried many other examples with EMAP5 [25, 81, 85]. The EMAP5 code can be freely downloaded from the website [25]. We use EMAP5 to analyze the radiation of the plasma as inhomogeneous media. 3..5.2 Near & Far Fields The space surrounding an antenna is usually subdivided into three regions: reactive near field, radiating near field (Fresnel) and far field (Fraunhofer) regions [4]. The outer boundary of reactive near field region is commonly taken to exit at a distance R < 0.62pD3/ from the antenna surface, where . is the wavelength and D is the largest dimension of the antenna. The inner boundary of the Fresnel region is taken to be the distance R = 0.62pD3/ and the outer boundary the distance R < 2D2/. D must also be large compared to the wavelength (D > ). For a very short dipole, a distance R < /2p from the antenna surface is commonly used. This criterion is based on a maximum phase


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error of p/8. The Fraunhofer region is commonly taken to exit at distances greater than 2D/ from the antenna. For a very short dipole, the region of distances R > /2p is referred to as the intermediate field region while that for R » ./2p is referred to as the Fraunhofer region or the far field region. In this study, the length of antennas is about 1 mm with frequency of 1 GHz. ./2p = 30 cm / 6.28 = 4.8 cm. Observation distance in this study is 1 m. The distance is more than ten times bigger than the criterion. Therefore, radiation regime in this study is the far field or Fraunhofer region.


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Chapter 4 Code Validation Before discussing the results of this study, we show the validation and/or verification of the numerical codes with examples. Two numerical codes are being used in this study. First one is the PIC code to analyze radiation with the electron motion information, and the other is hybrid element method code to solve the radiation problems with inhomogeneous dielectrics. The most important thing for the PIC code is the accuracy of particle motions including positions, velocities and acceleration. We consider ions in the plasma are stationary in the time scale mentioned in previous section. 3.4.2. Only electron motions are considered. Various compositions of electric and magnetic fields are tried to check the accuracy of the motions compared to analytic values. For the hybrid element method code, some examples are already presented in the literature [34, 85]. We here try various two dipole cases to check the possibilities of adopting this code for this study. The results of this validation are compared to analytic solutions. 4.1 Particle-In-Cell Analysis This PIC code uses the Lorentz force equation (2.1) to take the information of the charged particle motions. We test three cases with electric and magnetic fields to check the accuracy of the code and compare the result to the analytic calculations. 4.1.1 Constant Magnetic Field First, constant magnetic fields are tried for electron trajectories. Electrons in constant magnetic fields have gyration motions with


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Larmor radii. The electron trajectories are compared to analytically calculated values. 100, 500, and 1550 G magnetic fields are used for magnetic fields, and 1 and 10 eV for velocities. From (2.16) the Lamor radius is proportional to the ratio of the magnetic field and perpendicular speed. 4.1.2 .E X B Drifts Now let us include electric fields in our analysis. Charged particles have drift motions in crossed electric and magnetic fields. This drift motion is called the EXB drift or the guiding center drift. An electron is launched in the space with constant magnetic and electric fields. The electron has zero initial velocity. The electric fields considered in this case are 1 and 10 kV/m in +z direction, and the same magnetic fields as in the previous case are used in +y direction. From (2.22) the magnitude of the EXB drift is the ratio of ~E to ~B, and the direction is perpendicular to both of ~E and ~B. In this case, the drift has to have -vx direction, and the electron can have only x and z components of velocity due to the +y directional magnetic fields. The drift velocities of 100, 500, and 1550 G magnetic field cases with 1 kV/m electric field will be 1×105, 2×104, 6.45×103 m/s, respectively, and those with 10 kV/m electric field will be 10 times bigger. 4.1.3 . Grad B Drifts Last, the gradient of magnetic fields are considered. Charged particles have drift motions in magnetic fields with gradient. This draft is called the . B Drift,We launch an electron at the center of the near exit plane region. There are constant magnetic and electric fields in the channel. The electric field considered in this case is 10 kV/m in +z direction. The same magnetic fields as previous case ones are used as the maximum magnetic field.


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4.2 Hybrid Moment Method EMAP5 is a full-wave electromagnetic field solver that combines the method of moments with a vector finite element method [25]. The FEM is employed to handle the interior domain of inhomogeneous dielectric bodies. The method of moments is used to develop surface integrals that relate the field quantities on boundary surfaces with the equivalent surface currents. These integral equations are then coupled to the finite element equations through the continuity of the tangential magnetic fields [34]. EMAP5 allows only for the Cartesian coordinates. The code validity of EMAP5 is already shown in many papers [2, 34, 39, 81, 85, 86]. Here, the validity of EMAP5 for this study is checked with several cases. 4.2.1 Two Dipoles The cyclotron motion of charged particles can be modeled with two dipoles 90. out of phase. Two in phase dipoles make another tilted dipole. Two sets of the code run are used for the case of 90. phase difference. 4.2.2 Modified Length of Infinitesimal Dipoles The radiation of an infinitesimal dipole is proportional to the current on and the length of the dipole. The multiplication of the current and length acts as a constant not only in the far field range but also in the intermediate range. If it is possible to trade o_ between the amount of current on the dipole and the length of the dipole, then we can reduce the number of elements and the calculation time in this analysis with EMA.In satellite communications, the space loss is about 200 dB. Assume that the earth station transmitter and satellite receiver gains are 50 dB and 40 dB, respectively, and the transmitting power is 100 kW, 50


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dBW, which are typical. The receiving signal power with these condition is 1 Watt. The ECE radiation power is about 10% of the receiving signal power, which is significant.Hz increases to about 87 dB V/m with a strong peak. Radiation also now occurs at frequencies from 2 GHz to 4 GHz. In the 1D case the maximum frequency of the radiated field is 1.4 GHz. The increased frequency range of the radiation is due to the magnetic field density distribution. The 2D model has a higher magnetic field density profile near the walls. The higher magnetic field causes the radiation frequency range to broaden. Thus a more sophisticated magnetic field analysis of the Hall thruster is necessary to obtain the more accurate radiation frequency range.


7


Bibliography [1] Department of Defense interface standard, 1999. [2] Y. Ji M. Ali and T. H. Hubing. EMC applications of the EMAP5 hybrid FEM/MOM code. In Proc. 1998 IEEE International Symposium on Electromagnetic Compatibility, pages 543–546, Denver, CO, Aug 1998. [3] Constantine A. Balanis. Advanced engineering electromagnetics. John Wiley & Sons, Inc., New York, 1989. [4] Constantine A. Balanis. Antenna theory: analysis and design. John Wiley & Sons, Inc., New York, 1997. [5] Stephan Barensky. Electric propulsion in space is smart! Snecma magagine, pages 20–21, June 1998. [6] G. Bekefi. Radiation Processes In Plasma. John Wiley & Sons, Inc., New York, 1966. [7] G. Bekefi and A. H. Barrett. Electromagnetic Vibrations, Waves, And Radiation. The MIT Press, Cambridge, 1977. [8] C. K. Birdsall. Particle-In-Cell charged-particles simulations, plus Monte Carlo collitions with neutral atoms, MCC. IEEE Trans. Plasma Sci., 19(2):65–85, April 1991. 179 [9] A. M. Bishaev and V. Kim. Local plasma properties in a Hall-current accelerator with an extended acceleratioon zone. Sov. Phys. Tech. Phys., 23(9):1055–1057, September 1978.


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[10] John Blandino. Electric propulsion. Aerospace America, pages 60–61, December 2003. [11] L. Garrigues I. D. Boyd J. P. Boeuf. Computation of Hall thruster performance. In 26th International Electric Propulsion Conference, number IEPC-99-098, Kitakyushu, Japan, October 1999. [12] M. Touzeau M. Prioul S. Roche N Gascon C. Perot F. Darnon S. Bechu C. Philippe-Kadlec L. Magne P. Lasgorceix D. Pagnon A. Bouchoule and M. Dudeck. Plasma diagnostic systems for Hall-e_ect plasma thrusters. Plasma Phys. Control. Fusion, 42:B323–B339, 2000. [13] J. P. Bouef and L. Garigues. Low frequency oscillations in a stationary plasma thruster. J. Appl. Phys., 84(7):3541–3554, October 1998. [14] I. D. Boyd. Hall thruster far field plume modeling and comparison to Express flight data. In 40th AIAA Aerospace Science Meeting & Exhibit, number AIAA 2002-487, Reno, NV, January 2002. [15] S. I. Braginskii. In Reviews of plasma physics, volume 1, New York, 1965. Consultants Bureau. [16] W. Hreha R. Singh S. L. Liang D. Burr and M. Day. SPT interference assessment in communication satellites. In 22nd International Communi- 180 cations Satellite Systems Conference & Exhibit, number AIAA 2004-3216, Monterey, California, May 2004. [17] F. Taccogna S. Longo M. Capitelli. Very-near-field plume simulation of a stationary plasma thruster. Eur. Phys. J. Appl. Phys., 28:113–122,


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2004. [18] S. R. Hunter J. G. Carter and L. G. Christophorou. Low-energy electron drift and scatering in krypton and xenon. Phys. Rev. A, 38(11):5539– 5551, December 1988. [19] W. A Hargus Jr. C. S. Charles. Near exit plane velocity field of 200W Hall thruster. In 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2003-5154, Huntville, Alabama, July 2003. [20] F. F. Chen. Introduction to Plasma Physics and Controlled Fusion Vol.1: Plasma Physics. Plenum Press, New York, 1984. [21] E. Y. Choueiri. Plasma oscillations in Hall thruster. Phys. Plasma, 8(4):1411–1426, April 2001. [22] V. Latocha L. Garrigues P. Degond and J. P. Boeuf. Numerical simulation of electron tansport in the channel region of a stationary plasma thrusters. Plasma Sources Sci. Technol., 11:104–114, 2002. [23] I. D. Boyd R. A. Dressler. Far field modeling of the plasma plume of a Hall thruster. J. Appl. Phys., 92(4):1764–1774, August 2002. 181 [24] Roger Eckhardt. Stan Ulam, John Von Neumann, and the Monte Carlo method. Technical Report 15, Los Alamos Science, 1987. [25] http://www.emclab.umr.edu/emap5/. [26] Y. V. Esipchuk and G. N. Tilinin. Drift instability in a Hall-current plasma accelerator. Sov. Phys. Tech. Phys., 21(4):417–423, April 1976. [27] Je_ D. Filliben. Electric thruster systems. Technical Report CPTR 97-65, CPIA Technology Reviews, 1997.


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[28] Joseph W. Goodman. Introduction to Fourier optics. McGraw-Hill, New York, 1996. [29] J. M. Haas and A. D. Gallimore. Considerations on the role of the Hall current in a laboratory-model thruster. IEEE Trans. Plasma Sci., 30(2):687–697, April 2002. [30] J. M. Fife W. A. Hargus Jr. D. A. Jaworske C. Sarmiento L. Mason R. Jankovsky J. Haas and A. Gallimore. Spacecraft interaction test results of the high performance Hall system SPT-140. In 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2000-3521, Huntville, Alabama, July 2003. [31] J. T. Loane J. W. Meyer G. A. Hallock and J. C. Wiley. Analysis of communication signal modulation induced by periodic Hall thruster plume instabilities. In 27th International Electric Propulsion Conference, number IEPC-01-058, Pasadena, CA, October 2001. 182 [32] M. Kim G. A. Hallock and J. C. Wiley. ECE radiation analysis of the Hall thruster. In 45th Annual Meeting of the Division of Plasma Physics, Albuquerque, NM, October 2003. [33] M. A. Heald and C. B. Wharton. Plasma Diagnostics with Microwaves. John Wiley & Sons, Inc., New York, 1965. [34] M. Ali T. H. Hubing and J. Drewniak. A hybrid FEM/MOM technique for electromagnetic scattering and radiation from dielectric objects with attached wires. IEEE Trans. Electromagn. Compat., EMC-39(4):304–


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314, November 1997. [35] E. C. Ifeachor and B. W. Jervis. Digital Signal Processing. John Wiley & Sons, Inc., New York, 1973. [36] C. Nickel K. Imre D. F. Register J and S. Trajmar. Total electron scattering cross section: I. He, Ne, Ar, Xe. J. Phys. B: At. Mol. Phys., 18:125–133, 1985. [37] D. T. Jacobson and D. H. Manzella. 50 kW class krypton Hall thruster performance. In 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2003-4550, Huntville, Alabama, July 2003. [38] Robert G. Jahn and Edgar Y. Choueiri. Encyclopedia of Physical Science and Technology, volume 5. Academic Press, 3rd edition, 2002. [39] Y. Ji and T. Hubing. EMAP5: A 3d hybrid FEM/MOM code. J. Appl. Computational Electromagn. Society, 15(1):1–12, March 2000. 183 [40] B. E. Beal A. D. Gallimore W. A. Hargus Jr. Preliminary plume characterization of a low-power Hall thruster cluster. In 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2002-4251, Indianapolis, IN, July 2002. [41] B. E. Beal A. D. Gallimore W. A. Hargus Jr. The effects of cathode configuration on Hall thruster cluster plume properties. In 41th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2005-3678, Tucson, AZ, July 2005. [42] S. Oleson I. Katz. Electric propulsion for project Prometheus. In 39th


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AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2003-5279, Huntville, Alabama, July 2003. [43] E. J. Beiting J. E. Pollard V. Khayms and L.Werthman. Electromagnetic emissions to 60Ghz from a BPT-4000 EMD Hall thruster. In 28th International Electric Propulsion Conference, number IEPC-03-129, Toulouse, France, March 2003. [44] M. A. Lieberman and A. J. Lichtenberg. Principle of Plasma Discharges and Materials Processing. John Wiley & Sons, Inc., New York, 1994. [45] V Vahedi G Dipeso C K Birdsall M A Lieberman and T D Rognlien. Capacitive RF discharges modelled by paricle-in-cell Monte Carlo simulation. i: analysis of numerical techniques. Plasma Source Sci. Technol., 2:261–272, 1993. 184 [46] G. A. Hallock J. C. Wiley A. Khanna E. A. Spencer J. W. Meyer J. T. Loane. Impact analysis of Hall thruster on satellite communication. J. Spacecraft and Rockets, 39(1):115–124, January 2002. [47] K. D. Paulsen D. R. Lynch and J. W. Strohbehn. Three-dimensional finite, boundary, and hybrid element solutions of the Maxwells equations for lossy dielectric media. IEEE Trans. on Microwave Theory and Tech., 36(4):682–693, April 1988. [48] H. C. Kim O. Manuilenko and J. K. Lee. Particle-In-Cell Monte-Carlo simulation of capacitive RF discharges: Comparison with experimental data. Japanese J. Appl. Phys., 44(4A):1957–1958, 2005.


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[49] M. Martinez-Sanchez and J. E. Pollard. Spacecraft electric propulsion – an overview. J. Propulsion Power, 14(5):688–699, September-October 1998. [50] S. Y. Cheng M. Martinez-Sanchez. Simulations for a shuttle-based Hall thruster plume experiment. In 27th International Electric Propulsion Conference, number IEPC-01-054, Pasadena, CA, October 2001. [51] Lee S. Mason and Steven R. Oleson. Spacecraft impacts with advanced power and electric propulsion. Technical Report NASA/TM-2000-209912, NASA Technical Memorandum, 2000. [52] R. P. McEachran and A. D. Stau_er. Relative low-energy elastic and momentum transfer cross section for electron scattering from xenon. J. 185 Phys. B: At. Mol. Phys., 20:3483–3486, 1988. [53] N Metropolis. The beginning of the Monte Carlo method. Technical Report 15, Los Alamos Science, 1987. [54] M. Mitchner and C. H. Kruger. Partially Ionized Gases. John Wiley & Sons, Inc., New York, 1973. [55] A. I. Morozov and V. V. Savelyev. Fundamentals of stationary plasma thruster theory. In Reviews of plasma physics, volume 21, New York, 2000. Consultants Bureau. [56] A. I. Morozov and L. S. Solov’ev. Steady-state plasma flow in a magnetic field. In Reviews of plasma physics, volume 8, New York, 1980. Consultants Bureau.


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[57] A. I. Morozov Y. V. Esipchuk A. M. Kapulkin V. A. Nevrovskii and V. A. Smirnov. E_ect of the magnetic field on a closed-electron-drift accelerator. Sov. Phys. Tech. Phys., 17(3):482–487, September 1972. [58] W. K. H. Panofsky and M. Phillips. Classical Electricity and Magnetism. Addison-Wesley Publishing Company, Inc., Cambridge, MA, 1955. [59] M. Celik M. Santi S. Y. Cheng M. Martinez-Sanchez J. Peraire. Hybrid- PIC simulation of a Hall thruster plume on an unstructured grid with dsmc collisions. In 28th International Electric Propulsion Conference, number IEPC-03-134, Toulouse, France, March 2003. 186 [60] R. R. Hofer P. Y. Peterson and A. D. Gallimore. A high specific impulse two-stage Hall thruster with plasma lens focusing. In 27th International Electric Propulsion Conference, number IEPC-01-036, Pasadena, CA, October 2001. [61] N. Sitnikova D. Volkov I. Maximov V. Petrusevich and D. Allen. Hall effect thruster interactions data from the Russian Express-A2 and Express- A3 satellites. Technical Report NASA/CR-2003-212005, NASA Contractor Report, 2003. [62] http://commons.wikipedia.org/wiki/Image:SNECMA PPS 1350 Ion Rocket engine.jpg. [63] Von C. Ramsauer. Über den wirkungsquerschnitt der gasmolek üle


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gegenüber langsamen elektronen. ii. fortsetzung und schluß. Ann. Phys., 72:345–352, 1923. [64] Von C. Ramsauer and R. Kollath. Über den wirkungsquerschnitt der edelgasmoleküle gegenüber elektronen unterhalb 1 volt. Ann. Phys., 3:536–564, 1929. [65] S. Roy and B. P. Pandey. Numerical investigation of a Hall thruster plasma. Phys. Plasma, 9(9):4052–4060, September 2002. [66] D. Manzella C. Sarmiento J. Sankovic and T. Haag. Performance evaluation of the SPT-140. Technical Report NASA/TM-97-206301, NASA Technical Memorandum, 1997. 187 [67] I V Schweigert V A Schweigert. Combined PIC-MCC approach for fast simulation of a radio frequency discharge at a low gas pressure. Plasma Source Sci. Technol., 12:315–320, 2004. [68] S.Galitsky. Electric propulsion in Russia. News from Moscow, (26):9–13, 2000. [69] A. I. Morozov Y. V. Esipchuk G. N. Tilinin A. V. Trofimov Y. A. Sharov and G. A. Shchepkin. Plasma accelerator with closed electron drift and extended acceleration zone. Sov. Phys. Tech. Phys., 17(1):38–45, July 1972. [70] T. Koizumi E. Shiragawa and I. Ogawa. Momentum transfer cross section for low-energy electrons in krypton xenon from characteristic energies. J. Phys. B: At. Mol. Phys., 19:2331–2342, 1986.


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[71] L. T. Sinfailam. Relativistic effects in electron scattering by atoms iii. elastic scattering by krypton, xenon and radon. J. Phys. B: At. Mol. Phys., 15:119–142, 1982. [72] M. S. Dababneh W. E. Kauppila J. P. Downing F. Larerrier V. Pol J. H. Smart and T. S. Stein. Measurents of total scattering cross sections for low-energy positrons and electrons colliding with krypton and xenon. Phys. Rev. A, 22(5):1872–1877, Nobember 1980. [73] M. S. Dababneh Y. F. Hsieh W. E. Kauppila V. Pol J. H. Smart and T. S. Stein. Total-scattering cross-section measurements for intermediate- 188 energy positrons and electrons colliding with Kr and Xe. Phys. Rev. A, 26(3):1252–1259, September 1982. [74] http://www.esa.int/esaMI/SMART-1/. [75] http://encyclopedia.thefreedictionary.com. [76] G. N. Tilinin. High-frequency plasma waves in a hall accelerator with an extended acceleration zone. Sov. Phys. Tech. Phys., 22(8):974–978, August 1977. [77] Y. V. Esipchuk A. I. Morozov G. N. Tilinin and A. V. Trofimov. Plasma oscillations in closed-drift accelerators with an extended acceleration zone. Sov. Phys. Tech. Phys., 18(7):928–932, January 1974. [78] W. H. Press S. A. Teukolsky W. T. Vetterling and B. P. Flannery. Numerical Recipes in C. Cambridge University press, Cambridge, MA, 1992. [79] D. F. Register L. Vuskovic and S. Trajmar. Elastic electron scattering


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cross section for xe in the 1-1000 eV impact energy region. J. Phys. B: At. Mol. Phys., 19:1685–1697, 1986. [80] R. W. Wagenaar and F. J. de Heer. Total cross section for electron scattering from Ar, Kr and Xe. J. Phys. B: At. Mol. Phys., 18:2021– 2036, 1985. [81] M. Xu H. Wang and T. H. Hubing. Application of the cavity model to lossy power-return plane structures in printed circuit boards. IEEE Trans. Adv. Packag., 26(1):73–80, February 2003. 189 [82] G. D. Racca G. P. Whitcomb and B. H. Foing. The SMART-1 mission. ESA Bulletin, 95:72–81, August 1998. [83] G. A. Hallock J. C. Wiley and E. A. Spencer. Development and application of the beamserver code for plume impact analysis on satellite communication. In 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2001-3354, Salt Lake City, UT, July 2001. [84] A. V. Oppenheim A. S. Willsky and S. Hamid. Signals and Systems 2ed. Prentice-Hall, Englewood Cli_s, N.J., 1997. [85] M. Xu and T. H. Hubing. The development of a closed-form expression for the input impedance of power-return plane structures. IEEE Trans. Electromagn. Compat., 45(3):478–485, August 2003. [86] T. Hubing Y. Ji and H. Wang. Techniques for optimizing FEM/MOM codes. In Proc. 16th Annual Review of Progress in Applied Computational Electromagnetics, pages 444–451, Monterey, CA, March 2000.


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[87] D. Manzella J. Yim and I. Boyd. Predicting Hall thruster operational lifetime. In 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, number AIAA 2004-3953, Fort Lauderdale, Florida, July 2004. [88] X. Yuan. Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method. IEEE Trans. on Microwave Theory and Tech., 38(4):1053–1058, August 1990.

F I E L D E M I S S I O N C A T H O D E S

Busek’s Field Emission Cathodes use in-house synthesized multi-

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For over 12 years, Busek has been developing the next generation of high performance electric propulsion systems. Our family of U.S.-designed Hall Effect thruster spans the power spectrum from 200 W to 20 kW and produces 5 mN to 1 N of thrust with specific impulse values varying between 1000 and 3000 seconds. Our designs embody patent features, combined with precise control of the magnetic field distribution and a short acceleration zone that result in thrusters with high propulsive efficiency and high total impulse.

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B H T - 2 0 0 Discharge Input Power: 200 W Discharge Voltage: 250 V Discharge Current: 800 mA Propellant Mass Flowrate: 0.94 mg/sec Thrust: 12.8 mN Specific Impulse: 1390 sec Propulsive Efficiency: 43.5 %

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BHT-200

B H T - 6 0 0 Discharge Input Power: 600 W Discharge Voltage: 300 V Discharge Current: 2.05 A Propellant Mass Flowrate: 2.6 mg/sec Thrust: 42 mN Specific Impulse: 1650 sec Propulsive Efficiency: 55.0 %

The BHT-600 Hall Effect Thruster is an ideal size for primary

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BHT-600

B H T - 1 0 0 0 Discharge Input Power: 1000 W Discharge Voltage: 350 V Discharge Current: 2.85 A Propellant Mass Flowrate: 3.4 mg/sec Thrust: 58.5 mN Specific Impulse: 1750 sec Propulsive Efficiency: 50.3 %

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While optimized for lifetime at 1.7 kW input power, the BHT-

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BHT-1500

B H T - 8 0 0 0 Discharge Input Power: 8 kW Discharge Voltage: 300 V Discharge Current: 26.7 A Propellant Mass Flowrate: 27.4 mg/sec Thrust: 512 mN Specific Impulse: 1900 sec Propulsive Efficiency: 60.0 %

The BHT-8000 is an ideal size for orbit insertion and transfer of

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BHT-8000

B H T - 2 0 K Discharge Input Power: 20.25 kW Discharge Voltage: 500 V Discharge Current: 40.5 A Propellant Mass Flowrate: 40.0 mg/sec Thrust: 1.08 N Specific Impulse: 2750 sec Propulsive Efficiency: 72 %

The largest Hall Effect thruster in the family is the BHT-20K, a

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1


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Pumping Speed: 90,000 liters/sec for Xe Up to 6.0 kW HET Power

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HOME PROPULSION MATERIALS FACILITIES

ABOUT CONTACT DOWNLOADS NEWS A 2 kW Hall thruster in operation as part of the Hall Thruster Experiment at the Princeton Plasma Physics Laboratory.

In spacecraft propulsion, a Hall thruster is a type of ion thruster in which the propellant is accelerated by an electric field. Hall thrusters trap electrons in a magnetic field and then use the electrons to ionize propellant, efficiently accelerate the ions to produce thrust, and neutralize the ions in the plume. Hall thrusters are sometimes referred to as Hall Effect Thrusters or Hall Current Thrusters.

Hall thrusters are able to accelerate their exhaust to speeds of around 15–30 km/s, and can produce thrusts of about one newton.


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Applications

The solar electric propulsion system of the European Space Agency's SMART-1 spacecraft used a Hall thruster (Snecma PPS-1350-G). Over the course of 13 months and 289 engine pulses it had consumed about 58.8 kg of xenon and produced a delta-v of 2737 m/s (46.5 m/s per kg xenon).

Current research on Hall thrusters is ongoing and focuses mainly on

1. Scaling the typically 1 kW Hall thruster to higher powers (50 to 100 kW) and lower powers (50 to 100 W)

2. Resolving spacecraft integration issues regarding the large plume divergence

3. Enabling operation at higher specific impulse and variable specific impulse

4. Flight validating thrusters for use on western spacecraft 5. Extending the operational lifetimes to enable use on deep

space science missions

A Hall thruster typically operates at around 50–60% thrust efficiency and provides specific impulse from 1,200 to 1,800 seconds (12 to 18 kN·s/kg), and thrust-to-power ratios of 50–70 mN/kW.

• Space Systems/Loral - Western Satellite Manufacturer Offering SPT's


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Views

The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 1 Hall Thruster Electron Mobility Investigation using Full 3D Monte Carlo Trajectory Simulations IEPC-2007-291 Presented at the 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 Darren A. Alman,* Joshua L. Rovey,† Robert A. Stubbers,‡ and Brian E. Jurczyk§ Starfire Industries LLC, Champaign, IL. 61820 Abstract: Axial electron transport represents a loss in efficiency for crossed field devices, such as Hall-effect thrusters (HETs). Previous experimental and computational investigations have revealed an anomalous axial mobility that cannot be explained with classical theory. This work describes the development of a computational model that calculates electron mobility in HETs using known electric and magnetic fields. Specifically, a full 3D Monte Carlo trajectory simulation code is developed to simulate HET internal electron dynamics. Simulations were completed using the AFRL/University of Michigan P5 HET. The magnetic field for this thruster is known from magneto static simulations and the electric field present during thruster operation has been experimentally measured by Haas. Comparison of the axial mobility from our code and the mobility calculated by Koo for the P5 shows agreement. Nomenclature B = magnetic field vector E = electric field vector


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r = radial coordinate, with zero being the thruster centerline v = electron velocity vector z = axial coordinate, with zero being the anode location µ = electron mobility I. Introduction HALL-EFFECT thrusters (HETs) are a type of space propulsion device that use electric fields to accelerate and expel ionized propellant to generate thrust. A schematic of an HET is shown in Figure 1. A HET is a coaxial device that utilizes a radial magnetic field crossed with an axial electric field. Electrons emitted by the cathode drift in the E×B direction, forming an azimuthal Hall current. Neutral xenon atoms injected through the anode collide with these electrons producing xenon ions that are subsequently accelerated by the electric field to produce thrust. The magnitude of the magnetic field is designed such that only the electrons are magnetized. A mixture of electrons and ions in the acceleration zone creates a quasi-neutral plasma and thus the operation of the HET is not space charge limited in ion current density as is the case with girded ion thrusters. * Research Engineer, 60 Hazelwood Drive, Suite 143/203A, AIAA Member. † Propulsion Research Engineer, 60 Hazelwood Drive, Suite 143/203A, AIAA Member. ‡ Vice President, 60 Hazelwood Drive, Suite 143/203A, AIAA Member. § President, 60 Hazelwood Drive, Suite 143/203A, AIAA Member. H The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 2 Transverse electron mobility represents a loss in efficiency of the device, so ideally electrons would be confined to drift in the Hall current indefinitely. Unfortunately this is not realizable in practice


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and electrons do migrate to the anode. Furthermore, axial mobility can not be characterized by a purely classical collisional diffusion model. In fact, experimental measurements in the SPT-100 have shown that the electron collision frequency is on the order of 107-108 Hz.3 Calculations from both internal and global measurements have shown that the collision frequency based off classical theory is 1,000 times lower.4 Because of this discrepancy, the term “anomalous” mobility has been used to describe the increased axial mobility present in cross-field devices such as HETs.5 Explanations of the “anomalous” mobility have been suggested and two main candidates are plasma turbulence4,6 and wall-effects.7-9 More efficient HETs that better confine Hall current electrons may be possible if a clearer understanding of the mobility in these devices is developed. With this in mind, Starfire Industries LLC is using both numerical modeling and experiment to investigate and study mobility in HETs. II. Full 3D Monte Carlo Trajectory Simulations Star fire Industries has developed a 3D Monte Carlo trajectory simulation code to investigate electron transport in HETs. The simulations are carried out by rigorously simulating the electron trajectory over a series of very small time steps, ~10-13 seconds. The forces on the electron due to magnetic and electric fields are calculated at each time step and the particle is moved and its velocity is adjusted. The possibility of a collision occurring is checked at a somewhat larger interval (because the probability over one .t is extremely low), and if necessary the electron’s velocity (energy and direction) is modified according to the tabulated collision data. If the electron leaves the simulation volume it either collides with a wall, and is handled appropriately, or escapes and finishes its flight depending on the properties of the wall object that it strikes. Tallies of desired properties are output to data files both periodically throughout the run and at the completion of all electron flights. Data for each individual electron history (coordinates, velocities, local properties, forces, collision probabilities, etc.) can be saved after each flight. Due to


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the abundance of data collected, much can be learned from the simulations and most of the interesting properties or occurrences can be studied in detail after the simulations are completed. Three electron-neutral collisions with xenon are sampled - elastic scattering, excitation, and ionization. Data on electron collision cross sections were taken from the literature10 and the Evaluated Electron Data Library11 from Lawrence Livermore National Laboratory. The values used by the code for elastic scattering over one example electron flight are shown in Figure 2. Again, elastic collisions play a dominant role in the electron transport process since the scattering of the Hall drifting electrons results in a change in electron direction and subsequent orbit-center motion along the z-axis. Wall collisions are treated with a varying level of detail, with initial simulations simply returning the incident electron back into the thruster channel with a cosine angular distribution and a Maxwellian energy distribution sampled from the wall temperature. This simplified wall treatment can be expanded to account for improved energy of incidence, angle of incidence, and surface roughness effects to potentially improve code accuracy. Figure 2. Electron elastic scattering cross section values used in the Monte Carlo code during one electron flight The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 To get good statistics, typically tens or hundreds of thousands of electron flights are run for a given set of conditions. Electrons start with a Maxwellian energy distribution with a low initial temperature and a random direction in three dimensions. Electrons were simulated for up to one to ten microseconds (user definable) or until they reach the anode, whichever comes first. A time limit must exist, because some electrons were found to be very well trapped, and these flights would otherwise never come to a conclusion. The trade-off is between increased accuracy and simulation time requirements.


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The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 4 III. Simulation Results for the P5 Hall thruster Simulations using the code described above were performed on the AFRL/University Michigan P5 HET. A calculated magnetic field and experimental measurements of the electric potential1,2 were used as input to the code. The geometry of the simulation and a contour plot of the electric potential and magnetic field are shown in Figure 3. In this and subsequent plots, the x-axis and z-axis are the thruster radial and axial dimensions, respectively. A small, greatly magnified portion of a single electron trajectory, output from the Monte Carlo code, is shown in Figure 4b. The electron displays the traditional orbit in crossed electric and magnetic fields. Of course, the electrons do not always perfectly follow such an archetypical Hall orbit. There are many forces that tend to complicate the electron path, including slight variations in electric and magnetic field directions, varying strengths of these fields, and collisions with the background gas. An example of the latter is given in Figure 4c, where the electron has a collision, changes direction, and is forced by the fields to resume the Hall drift. Any additional velocity that the electron keeps beyond what the Hall drift requires results in extra features in the trajectory, for example, an extra loop at the top of the orbit like that shown in such as spatial and velocity history throughout the thruster computational domain. . Total time that electrons spent at each (r,z) location, totaled over 10,000 flights. The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 5 The most important output for investigating the electron mobility is the average velocity that electrons have at each (r, z) location because velocity is directly related to electron mobility.


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However, there are small pockets of axial velocity directed downstream away from the anode, due to variations in the magnetic field direction ,etc. The average velocities toward the anode are largest in the low-magnetic field region near the anode, and to a lesser extent downstream of the thruster exit plane. Average axial velocities are low in the high-field acceleration region of the thruster. From these calculated velocities and the electric field in each cell, the electron mobility can be calculated in each cell. The mobility and velocity are related through E v µ = , where v is the velocity vector, µ is the electron mobility, and E is the electric field vector. This relationship becomes somewhat more complicated in the case of crossed electric and magnetic fields, where an electric field in one direction can lead to a velocity in a perpendicular direction (e.g.; an axial electric field giving rise to an azimuthal electron velocity and Hall current). In this case the mobility is a tensor. The Monte Carlo electron transport code calculates the full 3D electron mobility tensors for a given thruster and set of initial conditions. For comparison purposes however, these detailed tensor mobilities were collapsed into an effective 1D axial mobility, as shown in Figure 7. These results can be compared to the best fit mobility to experimental data that was previously plotted by Koo,12-14. There is agreement between the shape of the code output and the previous fit to experiment, indicating that the major relevant physics are indeed included in the simulations. In both cases, the axial mobility is highest near the anode, drops to a minimum further downstream toward the high-magnetic field region of the thruster, and then rises again as you move beyond the exit plane – but not to the near-anode levels. A full 3D Monte Carlo trajectory simulation code has been developed to simulate HET internal electron dynamics. Electron transport is important to thruster performance, because electron current reaching the anode represents a loss in efficiency. Previous experimental and computational investigations have revealed an anomalous axial mobility that cannot be explained


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with classical theory. This makes predictive modeling of HETs difficult because the electron mobility values are not known without performing measurements on existing hardware. The goal of the transport code is to enable calculation of the mobility directly from the knowledge of electric and magnetic fields. Simulations were completed using data from the AFRL/University of Michigan P5 HET. The magnetic field for this thruster is known from magnetostatic simulations and the electric field present during thruster operation has been experimentally measured by Haas. Key outputs from the Monte Carlo code include information on where electrons spend their time, and how they move throughout the thruster. The latter output, the average velocity of electrons versus position in the thruster, allows calculation of the full 3D electron mobility tensor. The 30th International Electric Propulsion Conference, Florence, Italy September 17-20, 2007 6 Mobility can be defined that takes the mobility tensor and expresses it in terms of axial velocity and axial electric field. Comparison of the 1D axial mobility from our code and the mobility calculated by Koo for the P5 shows agreement, indicating that the transport code is correctly simulating the major relevant physics. Improvements to the model can be made, e.g. in the level of detail for wall interactions. The code can be used to calculate electron mobilities for known fields, without the need for experimental measurements of mobility from each thruster and set of conditions. This represents a major improvement to Hall thruster modeling, allowing predictive modeling to be performed. References 1Haas, J. M., "Low-Perturbation Interrogation of the Internal and Near-field Plasma Structure of a Hall thruster using a High- Speed Probe Positioning System," Doctoral Thesis, Dept. of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 2001.


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2Haas, J. M., Gallimore, A. D., "Internal Plasma Potential profiles in a Laboratory-model Hall thruster," Physics of Plasmas, Vol. 8, No. 2, pp. 652-660, February 2001. 3Ahedo, E., Gallardo, J. M., Martinez-Sanchez, M., "Effects of the radial plasma-wall interaction on the Hall thruster discharge," Physics of Plasmas, Vol. 10, No. 8, pp. 3397-3409, 2003. 4Meezan, N. B., Hargus, W. A., Cappelli, M. A., "Anomalous electron mobility in a coaxial Hall discharge plasma," Physical Review E, Vol. 63, No. 2, Feb. 2001. 5Janes, G. S., Lowder, R. S., "Anomalous Electron Diffusion and Ion Acceleration in a Low-Density Plasma," Physics of Fluids, Vol. 9, No. 6, pp. 1115-1123, June 1966. 6Knoll, A., Thomas, C., Gascon, N., Cappelli, M., "Experimental Investigation of High-Frequency Oscillations within Hall Thrusters," AIAA-2006-5171, 42nd Joint Propulsion Conference, Sacramento, CA, July 9-12, 2006. 7Keidar, M., Beilis, I. I., "Electron Transport Phenomena in Plasma Devices with ExB Drift," IEEE Transactions on Plasma Science, Vol. 34, No. 3, pp. 804-814, June 2006. 8Raitses, Y., Staack, D., Keidar, M., Fisch, N. J., "Electron-wall interaction in Hall thrusters," Physics of Plasmas, Vol. 12, No. 5, May 2005. 9Raitses, Y., Smirnov, A., Staack, D., Fisch, N. J., "Measurements of secondary electron emission effects in the Hall thruster discharge," Physics of Plasmas, Vol. 13, No. 1, Jan. 2006. 10Date, H., Ishimaru, Y., Shimozuma, M., "Electron collision processes in gaseous xenon," Nucl. Instr. and Meth. in Phys. Res. B, Vol. 207, No. 4, pp. 373-380, August 2003. 11Perkins, S. T., Cullen, D. E., Seltzer, S. M., "Tables and Graphs of Electron-Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Electron Data Library (EEDL)," UCRL-50400, LLNL, Livermore, CA, November 1991. 12Koo, J. W., "Hybrid PIC-MCC Computational Modeling of Hall Thrusters," Doctoral Thesis, Dept. of Aerospace Engineering, University of Michigan, Ann Arbor, 2005.


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13Boyd, I. D., "Modeling a Hall Thruster from Anode to Plume Far Field," Air Force Office of Scientific Research: Space Propulsion and Power Contractors Meeting, Annapolis, MD., Sept. 25-29, 2006. 14Koo, J. W., Boyd, I. D., "Modeling of anomalous electron mobility in Hall thrusters," Physics of Plasmas, Vol. 13, No. 3, March 2006. Pulsed Plasma Thruster (PPT) is an electromagnetic propulsion device. It uses the electrical energy of a capacitor to form a high current arc discharge across a solid propellant surface (typically Te.on). The energy of the arc ablates the surface of the propellant creating an ionized gas. This ionized gas is accelerated out of the channel at high velocities by electromagnetic forces creating thrust. The electromagnetic force is called the Lorentz force, which describes the interaction between the current vector and the self induced magnetic .eld vector of the arc discharge. A PPT is a pulsed device that is capable of very precise impulse bits. This capability allows for low jitter precision maneuvers of small satellites that can not be match by traditional ACS systems. Busek began commercial development of a micro version of a PPT in 2002 based on technology originally developed at AFRL. A 3-axis version of the MicroPPT (µPPT) is lying on the US Air Force Academy’s FalconSat-3 mission under the acronym MPACS. MPACS stands for Micro Propulsion Attitude Control System. Four clusters of MPACS thrusters will be .own for propulsive ACS demonstration. Each cluster is a stand-alone unit containing all necessary electronics, requiring only power and commands from the spacecraft. The Leading Source Micro Pulsed Plasma Thrusters (µPPTs) MPACS Performance Discharge Energy 1.96 Joules Impulse Bit (avg) 80 µN-sec Speci.c Impulse (avg) 827 sec Propellant Consumption 19.7 µg/pulse


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Ef.ciency (avg) 16 % Speci.c Thrust (avg) 40.8 µN/W Plasma Thrust Spark Plug Teflon Fuel Bar Electrodes Capacitor Spacecraft Bus PPU Spring B Fuel Retainer BUSEK S P A C E P R O P U L S I O N Four MPACS are lying on FalconSat-3, launched February 2007. The Busek micro propulsion effort spans several technologies and capabilities intended for a variety of missions. The thrusters in various stages of development include: 1) 0.01 mN class colloid thrusters suitable for low thrust noise (<0.0001 mN) and highly accurate (~10 nm) satellite position control for interferometeric missions such as LISA (Laser Interferometer Space Antenna). First demonstration of these thrusters will be on the JPL New Millennium, Space Technology 7 mission called DRS which will .y on ESA spacecraft. 2) 0.01 to 1 mN-sec class microPPTs suitable for low deltaV nanosat missions or for ACS on larger satellites. The .rst of this class µPPTs will .y on the U.S. Air Force Academy satellite FalconSat3. 3) 5 mN class micro-resistojets for nanosats (<100 kg) with limited power on board (<20 W) and low deltaV (~100 m/sec) missions. The resistojet uses ammonia or methanol as propellant. Methanol is a green propellant that achieves nearly the same performance as ammonia. Both are a far less toxic alternative to hydrazine.


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4) 1 mN class RF Ion thrusters intended for accurate position control required by IR interferometeric missions such as the Terrestrial Planet Finder. The RF thruster eliminates the internal discharge cathode and the neutralizer and allows broad adjustability/wide dynamic range of thrust. These features make this thruster ideal for multiple satellite coordinated formation lying missions. 5) 0.1 to 1 mN class simpli.ed colloid thrusters intended for missions with less demanding position accuracy. This class of micro thrusters is also ideal for drag make-up or coordinated formation .ying of multiple satellites. Micropropulsion Across Technologies The Leading Source BUSEK S P A C E P R O P U L S I O N

Challenges

Hall Thruster Channel Wall Erosion

Overview

The main life-limiting factor for Hall thrusters is the erosion of the channel walls. As Hall thrusters are beginning to be used on more extended missions (10000 hours+), lifetime issues become a priority. Characterizing this erosion experimentally in ground based vacuum chambers is prohibitively long and expensive. Thus there is a need for quick and cheap, yet accurate, simulations and this is the main motivation behind this research.


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Modeling the erosion rates along the channel walls incorporates two major parts. First, the ion current to the walls needs to be determined. Then the sputter yields need to be found in order to obtain the erosion rates. Two ion flux models are examined. One is based on scattering collisions while the other focuses more on a hydrodynamic description of the plasma. The sputter yields are obtained from an empirical model based on curve fits to experimental data.

Models

Scattering collisions model

Experimental data of the total volumetric erosion rate of the SPT-100 as a function of time is shown below. There is a rapid decrease in the erosion early on, but levels off after about 1000 hours. Explanations have ranged from a two-mechanism process to a logarithmic one. A possible physical underpinning behind a logarithmic decrease in the erosion rate may be explained by scattering collisions as the channel width increases due to erosion.

The scattering collisions model assumes that most of the ion flux to the walls is due to collisions of the ions with the neutral atoms in the channel. The ions are diverted from their trajectory and possibly into the walls.

Hydrodynamic model

The hydrodyanmic model uses a fluid description of the plasma to calculate the ion flux to the walls. The ion continuity and momentum equations are solved in an iterative manner. The electron momentum and energy equations are also solved to determine the electron temperature and the components of the


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electric field. The neutral flow is modeled as one-dimensional with a constant axial velocity.

The near-wall processes are also modeled, as they are important in determining the erosion rates. The boundary conditions are set by those on the edge of the plasma sheath. The Bohm condition is not assumed a priori, but rather, a smooth presheath-sheath matching technique is applied to find the electric field and entrance velocity at the sheath edge. The effects of secondary electron emission are also included. This affects, among other things, the potential drop across the sheath, which in turn influences the ion impact parameters and thus the erosion rate.

Sputtering model

The above ion flux models are coupled with a sputtering model to calculate the erosion rates. Sputter yields are primarily a function of wall material, ion species, angle of incidence, and ion energy. We have used experimental data of xenon ions striking boron nitride samples at various angles and energies [1]. For our purposes, we have applied a curve fit to model the sputter yield for xenon ions on boron nitride.


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Results

The results using the scattering model are shown below. Overall, the model shows fairly good comparison with the experimental data [2].


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The hydrodynamic model results are shown below. Again the model compares fairly well to the data. However, there are some deficiencies, such as underpredicted erosion in the later stages of thruster life. The erosion at the exit plane (figure on the far right below), however, matches quite well with experimental data [2,3].


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Since this is usually the location of greatest erosion, and thus the location under most concern, the results are promising.


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Overall, the two models here show fairly good comparison with existing experimental data. The models are also computationally inexpensive, running on the order of minutes, making them attractive for future design and prediction purposes. However, there remains much work to be done in improving the models, making sure they capture all of the necessary physics and are applicable over a variety of thruster types and operating conditions.


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References

1. Garnier, Y., Viel, V., Roussel, J.-F., and Bernard, J., "Low-Energy Xenon Ion Sputtering of Ceramics Investigated for Stationary Plasma Thrusters," Journal of Vacuum Science and Technology A, Vol. 17, No. 6, Nov/Dec 1999, pp. 3246-3254.

2. Absalamov, S. K., et al., "Measurement of Plasma Parameters in the Stationary Plasma Thruster (SPT-100) Plume and Its Effect on Spacecraft Components," 28th AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit, 1992, AIAA-92-3156.

3. Garner, C. E., Brophy, J. R., Polk, J. E., and Pless, L. C., "Cyclic Endurance Test of a SPT-100 Stationary Plasma Thruster," 30th AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit, 1994, AIAA-94-2856.

Recent Publications

• Yim, J. T., Keidar, M., and Boyd, I. D. An Investigation of Factors Involved in Hall Thruster Wall Erosion Modeling AIAA-2006-4657, Presented at the 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 2006, Sacramento, CA.

• Yim, J. T., Keidar, M., and Boyd, I. D. A Hydrodynamic-Based Erosion Model for Hall Thrusters IEPC-2005-013, Presented at the 29th International Electric Propulsion Conference, October 2005, Princeton, NJ.

• Yim, J. T., Keidar, M., and Boyd, I. D. An Evaluation of Sources of Erosion in Hall Thrusters. AIAA-2005-3530, Presented at the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 2005, Tucson, AZ.


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Future applications

Hypersonics

NASA's new vision for space exploration aims to take humans back to the Moon, and eventually to Mars and beyond. Achieving this goal will involve many missions over the coming years. Perhaps the most dangerous and challenging aspect of any mission is a spacecraft's hypersonic entry into a planet's atmosphere. The physical processes occurring around the spacecraft are quite complex and involve the synthesis of chemical kinetics, quantum mechanics, radiation physics, and ablation effects with fluid dynamics. To further complicate matters, the atmosphere is often rarefied and conventional fluid dynamic analysis is no longer applicable. Such high energy, high speed, rarefied conditions are very expensive and often impossible to reproduce in wind tunnels here on Earth. Actual flight tests are even more expensive and measured data is limited to that collected during the 1960's Mercury, Gemini, and Apollo programs. If numerical simulation can reproduce the experimental data that is available, it can then be used with confidence as a fast and inexpensive design tool for new spacecraft flying new missions.

At low altitudes (below ~80km for Earth) the atmosphere is sufficiently dense such that molecules undergo a vast number of collisions as they move over the spacecraft. Under these conditions the gas can accurately be assumed to behave as a continuum and the Navier-Stokes equations can be solved using methods from Computational Fluid Dynamics (CFD). CFD methods are very mature and are capable of incorporating advanced physical models such as chemical and thermal non-


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equilibrium, radiation, and even ablation. For very high altitudes (above ~100km for Earth) the atmosphere is rarefied to the point where molecules undergo far fewer collisions invalidating the continuum assumptions inherent in the Navier-Stokes equations. In this regime the most mature numerical method is the direct simulation Monte Carlo (DSMC) method which is also capable of incorporating advanced physical models. Since the DSMC method simulates the gas on the molecular scale it provides accurate results in all regimes, however under continuum conditions, large numbers of particles and collisions demand impractical computational resources. Thus, in general, the DSMC method is used to simulate atmospheric entry at high altitudes and CFD is used at lower altitudes. Of course there is a large overlap regime in which the flow around the spacecraft exhibits regions of both continuum flow and non-equilibrium or rarefied flow. For this reason current research is not only focused on using CFD and DSMC to simulate the aerothermodynamics of atmospheric entry, but also focuses on incorporating these methods into a hybrid particle-continuum code.

• Current Work o Particle Simulations of Continuum/Rarefied

Flows o Development of a Hybrid Particle-Continuum

Method o Plasma-Based Flow Control at Hypersonic

Speeds o ReEntry and Hypersonic Vehicle Plasma

Communications System

Direct Simulation Monte Carlo Modeling of Weakly Ionized Flows


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Efficiency Analysis of a Low Discharge Voltage Hall Thruster was done by Jerry L. Ross,Jason D. Sommerville , Lyon B. King on power loss mechanisms for a 2 kW (nominal) Hall thruster operating at low discharge voltages were examined through thrust stand measurements and probe studies. Operating conditions included discharge voltages ranging from 100 V to 300 V and mass flow rates of 3 to 5 mg/s of xenon. Thrust stand measurements indicate a minimum thrust efficiency of 15% at 100 V at 3 mg/s and a maximum of 59% at 300 V and 5 mg/s. Retarding potential analyzer, emissive and Faraday probes were utilized to quantify multiple sources of inefficiency. The ratio of exhausted ion current to discharge current was found to be the dominant loss mechanism at low discharge voltage. Nomenclature T= trip time, s !V= velocity increment, m/s2 Ÿ= m flow rate of propellant as determined by the mass flow controller, kg/s e =elementary charge, C fi =ionization mass fraction of the propellant Id =discharge current, A Ii =exhausted ion current, A Isp= specific impulse, s j(!) =ion current density, A/m2 M =spacecraft mass, kg m =mass of a xenon atom/ion, kg P =kinetic power delivered to the spacecraft, W Ps =supply output power IdVd, W Q =average charge state of the ionized propellant q =charge number T =thrust, N Ue =ion velocity, m/s2 Vd =discharge voltage (anode potential), V Vaccel= acceleration potential for a given ion, V Symbols


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" average o"-axis ion trajectory angle "B =beam divergence as an efficiency "c =current efficiency "probe the product of all probe-measured efficiencies "E= energy efficiency "p =propellant efficiency "T =thrust efficiency "vdf= velocity distribution efficiency "v =voltage utilization efficiency "ctg= cathode to ground potential, V "plasma plasma to ground potential, V # angle from thruster axis I. Introduction The Hall thruster belongs to a class of electric propulsion that uses electric and magnetic fields to ionize and accelerate propellant. Electric spacecraft thrusters, such as the Hall thruster, can greatly decrease the propellant mass required to perform a desired mission #V because of their high exhaust velocities.1 However, because the power available on spacecraft is limited to, at present, tens of kW, electric propulsion (EP) devices are limited in thrust to hundreds of mN. This implies that, while EP can save propellant mass, it is sometimes accompanied by increased trip time for near-Earth missions. The trip time is related to the required velocity change, spacecraft mass, and thrust by #t = M#V T . (1) The spacecraft mass, M, and mission #V are fixed quantities and hence, when the trip time is of greatest concern, a high-thrust device is required. For an electric thruster, the relation between thrust, power, and specific impulse can be expressed as T = 2"TPs Ue


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(2) While greater thrust can be obtained by increasing Ps, spacecraft power is limited by the on-board energy source and greater spacecraft power comes at the price of increased vehicle mass. To increase the thrust at fixed power, Ue must be decreased while maintaining a high level of "T . The exit velocity of the ionized propellant relates to the accelerating potential according to 1 2mU2 e = qVaccel. (3) The acceleration potential, through which the ions fall, is approximately the discharge potential (Vaccel ! Vd). Therefore, the discharge voltage (nominally 300-500 V for a Hall thruster) must be reduced to reduce the exit velocity. The difficulty of high thrust-to-power operation is maintaining high levels of thrust efficiency when the propellant mass flow rate increases and the discharge voltage decreases. Under high thrust-to-power operation, desired power levels are in excess of 1 kW. Most of the research in the field of low voltage Hall thrusters, however, focuses on reduced power operation (low voltage and low current). For example, space qualified Hall thrusters, such as the Busek BHT-200, operate at relatively low voltages (250 V) but nominally at 200 Wa. Alta created the XHT-100 Hall thruster at American Institute of Aeronautics and Astronautics by scaling their 1 kW thruster to design the main propulsion system for a micro or mini-satellite that operates nominally at 180 V and 100 W but with only 22% efficiency.2 The Mitsubishi Electric Corporation (MELCO) reported performance results on their 200 mN-class Hall thruster of !30% total thrust efficiency at !200 V and !1 kW.3 In 2005 TsNIIMASH reported ! 45% efficiency for a TAL thruster operating at 200 V and 3.5 mg/s flow of xenon. They further demonstrated that the power and thrust can be linearly scaled with thruster arrays or clusters.4 Clusters, however, add mass and complexity to the system that could be


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alleviated by a single thruster with identical capabilities. Literature is sparse for high powered Hall thrusters operating at low anode voltages (voltages < 200 V and currents > 3 A). It is known that Hall thrusters do not perform well in this regime, however, the physics of the inefficiency and instability are unknown. In 2003, Manzella experimented on the NASA-120M and NASA-457M Hall thrusters and identified voltage utilization efficiency as the leading loss mechanism of low voltage operation. The devices in the aforementioned study were operated as low as 100 V on the anode at < 25% efficiency.5 Ashkenazy’s work found limited improvements by extending the discharge chamber channel length.6 These improvements, however, were only reported at low power operation. Research in alternative propellants such as bismuth has been shown to lower the cost of ionization, a power loss aggravated at low discharge voltages.7, 8 Additionally, as a heavier atom than xenon, bismuth would also decrease the exit velocity for a given discharge voltage according to Eq. 3. Performance data for bismuth Hall thrusters, however, are not yet available. Using alternative propellants will benefit high thrust-to-power operation but it does not address the physics inhibiting high efficiency. This is a parametric study of an Aerojet BPT-2000 Hall thruster operated at low voltages. By implementing a variety of thrust stand and probe studies the goal of this work was to better understand the underlying physics and diagnose as many loss mechanisms as possible. The probe study includes Faraday, emissive and retarding potential analyzer (RPA) probes to diagnose beam divergence, current efficiency, and voltage utilization efficiency. II. Apparatus All measurements were taken on an Aerojet BPT-2000 Hall thruster designed to operate nominally between 300 V and 500 V.9 The xenon testing facility is a 2-m diameter and 4-m long vacuum chamber, where the thruster is mounted at the radial center 1 m from the end of the tank (see


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figure 1). Rough vacuum is reached by a 400-cfm two-stage rotary oil-sealed pump. High vacuum is reached and maintained by two 48-inch cryopumps that operate at 120,000 L/s (N2). Chamber base pressure was 1 10-6 Torr and the pressure did not exceed 4

10-5 Torr (corrected for xenon) during thruster operation. Thrust measurements were taken by the use of an inverted-pendulum thrust stand.10 The thrust stand is water cooled to alleviate thermal drifts and its level is monitored by a tilt sensor accurate to one half an arc second. Anode and cathode propellant lines are controlled by thermal mass flow controllers. The thrust stand was calibrated before each change in mass flow rate. At each operating condition the magnets were adjusted to obtain the maximum thrust efficiency as calculated by thrust stand diagnostics. A laboratory-grade LaB6 cathode was used for testing at a constant flow of 0.3 mg/s xenon. All efficiency values, both referenced and presented, exclude cathode flow and heater power. Plume diagnostics were taken by three probes mounted on a three-axis motion table (rotational stage mounted upon two perpendicular linear slides. The Hall thruster was rigidly mounted in the tank (not on the thrust stand) for this portion of the tests and the probes were swept through the plume by the motion table. Voltage utilization e!ciencies were obtained by a 4-grid RPA probe placed 0.55 m downstream 3 of 15 American Institute of Aeronautics and Astronautics .. ........... Figure 1. A top down view of the inside of the xenon Hall thruster testing facility


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from the thruster faceplate at 0", 15", and 30" to the thruster centerline. The RPA probe uses a series of biased grids to repel ions of low energy. Sweeping the retarding potential on the grids yields an ion energy-per-charge distribution of the plume of the Hall thruster. The RPA grid wires are 0.114 mm in diameter with 0.140 mm spacing resulting in a 30% open area. Each grid is 0.254 cm from each other with the exception of the front floating grid which is 0.508 cm from the first electron repeller. The outer diameter of the grids is 1.235 cm and the outer diameter of the body of the probe is 3.170 cm. The electron repellers were biased 15 V below cathode. The ion repeller grid was swept from 0 V to 450 V for each trace. The current collected by the probe was then passed through a current amplifier and recorded by an oscilloscope. The anode and RPA were both referenced to cathode during data acquisition. In calculating the voltage utilization efficiency the repelling voltages were adjusted to be relative to ground potential and to account for the plasma potential. Faraday probe sweeps yield ion current density measurements. Current density as a function of o$-axis angle can then be used to compute beam divergence. The Faraday probe is enclosed in an alumina sheath with an outer diameter of 4.75 mm. A steel guard ring with a diameter of 10 mm was included to reduce edge e$ects on the potential structure in front of the probe face. The gap between the the guard ring and collector face is 1.25 mm. Probe data were taken at 25 cm radius from the front plate of the thruster through a half-angle of 53" with an angular resolution of 2". Plasma potentials were recorded by an emissive probe constructed from a 1.27 10-4 mm


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diameter thoriated tungsten wire encased in an alumina sheath and referenced to cathode potential. The potentials were recorded at 0", 15", and 30" 0.55 m downstream from thruster centerline (same as the RPA probe). Plasma potentials were extracted from the emissive probe traces using the intersection method discussed by Kemp11 in 1965 and first introduced by Langmuir in 1923. III. Efficiency Analysis There are various loss mechanisms that degrade Hall thruster operation. As we will show, reducing the discharge voltage further aggravates many of these ine!ciencies. Measurements from the thrust stand, mass-flow controllers, and discharge power supplies can be combined in real-time 4 of 15 American Institute of Aeronautics and Astronautics to produce thrust efficiency "T = T2 2 ÿ mPs . (4) Thrust efficiency is a measure of the discharge power conversion into net thrust of the system. A recast of the thrust efficiency equation breaks it into the product of energy efficiency, the measure of total energy in the ion beam, and propellant efficiency, the measure of the velocity distribution function and beam divergence efficiency.12 "T = 1 2 ÿ m"V#2 Ps = "V#2 "V2# 1 2 ÿ m"V2# Ps


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= "p"E (5) Energy efficiency can further be separated into voltage utilization efficiency and current efficiency where the voltage utilization efficiency is the percentage of the anode-cathode potential that the ions are accelerated through and the current efficiency is the ratio of exhausted current to discharge current. Voltage utilization efficiency is expressed as "v = 1 2m"V2# eVd 1 fiQ (6) where 1 2m"V2# = "!ion# and current efficiency is "c = ÿ me mId (fiQ) = Ii Id (7) where Q equals Q = 1 fi !f1 + 2f2 + 3f3". The variable fi is the ionization mass fraction of the propellant fi = f1 + f2 + f3... f0 + fi = 1 where f0, f1, f2, f3 are the exit mass fractions of Xe, Xe+, Xe2+, Xe3+. Thus, thrust efficiency is the product of propellant, voltage utilization and current e!ciencies "T = "v"c"p. (8) Voltage utilization efficiency can be measured with an RPA probe and the current efficiency can


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be obtained with Faraday probe data. An in depth derivation of equations 6 and 7 can be found in Larson’s work.12 The propellant efficiency is the product of the velocity distribution efficiency and the beam divergence efficiency13 "p = "|V |#2 "|V |2#"cos $#2 = "vdf "B (9) where $ is the current-weighted average o$-axis ion trajectory angle as determined by the Faraday probe, defined later in Eq. 11. The velocity distribution function can be measured with an ExB probe. Finally, we can recast the thrust efficiency equation as the product of all four loss mechanisms "T = "v"c"vdf "B. (10) The term Thrust Efficiency has been used by Kim1 but also appears under the name anode e!- ciency14 and discharge efficiency5 and refers to a benchmark for anode performance that excludes the magnets and cathode operation. 5 of 15 American Institute of Aeronautics and Astronautics IV. Results A. Thrust Stand Figure 2 shows the thruster operated at above 50% thrust efficiency for all three mass flow rates at 300 V. The data here is comparable with the data from reference 9 after the cathode operation is accounted for.b The discharge supply was current limited to 6 A eliminating the possibility of testing data for 4 mg/s discharge voltages below 140 V and below 180 V for 5 mg/s. At Vd = 100 V, maximum thrust efficiency was 15% for 3 mg/s. T Figure 2. Thrust efficiency as determined by thrust measurements. Error bars are calculated based


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on the reproducibility of calibration measurements both during operation and when the thruster is turned o". The discharge current is the current that accumulates at the anode from ionization, secondary electron emission, and “recycled” electrons originating from the cathode. The discharge current is plotted against the discharge voltage in Figure 3. The current levels were nearly constant for each mass flow rate until the discharge voltage dropped below 200 V where the current increased rapidly; again, this increase in current is the result of the magnetic field being optimized for maximum "T . Figure 3. Discharge current at max !T . Uncertainty is ±0.05 A based on manufacturer’s specified uncertainty for the discharge power supply. bFor the 300 V data. Data for discharge voltage lower than 300 V was not available for comparision. 6 of 15 American Institute of Aeronautics and Astronautics B. Raw Probe Data Figure 4 shows the current density as a function of angle for a flow rate of 3 mg/s. The measurements reflect the raw data as collected by the Faraday probe. As the discharge voltage is decreased the beam magnitude decreased at the center peak and increased in the higher o$-axis angles. Facility limitations prohibited sweeps past 53". Figure 4. Faraday probe sweeps 250 mm downstream for 3 mg/s flow rate at five di"erent discharge voltages C. Derived E!ciencies The beam divergence efficiency, "B in Figure 5, was calculated using Faraday probe data and with the assumption that the plume was axisymmetric. The current values, j(#), obtained by each trace


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create a weighted distribution function of the ion trajectory o$-axis angles used to calculated the beam divergence efficiency "B = "cos $#2 = !# cos #j(#)r2 sin #d# # j(#)r2 sin #d# "2 . (11) Beam divergence efficiency is subject to underestimation based on the positioning of the Faraday probe and the assumption of axisymmetry in the integral of Eq.11. An accurate sweep would be positioned directly over the apex of the beam profile. If the probe is positioned o$ apex center it will result in a sweep that displays an artificially low beam current. By assuming a maximum vertical probe misalignment of dx =3 cm, the maximum error in the calculation of "B was estimated to be 3.5%. There is an unaccounted error due to the hemispherical integration of charge exchange ions at high angles, common to Faraday probe results.12 Figures 6 - 8 display the integrated ion-energy per charge distributions for three o$-axis angles. The greatest change in efficiency occurred in the 3 mg/s experiments where the voltage utilization efficiency dropped from 76% at 300 V to 54% at 100 V when the probe was positioned 30" o$- axis. As seen with other Hall thrusters, the voltage utilization efficiency decreases with increasing o$ axis angle.15 The traces in figures 6 - 8 are referenced to cathode potential. Overall voltage utilization efficiency requires a reference correction with respect to ground and plasma potentials. Additionally, since the ion energy is function of o$-axis angle, the calculation of a total voltage utilization efficiency must be properly weighted according to the current distribution function as 7 of 15 American Institute of Aeronautics and Astronautics


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B Figure 5. Beam divergence efficiency as calculated by Eq. 11 from Faraday probe sweeps 250 mm downstream obtained with the Faraday probe. These adjustments are outlined in section V and are visible in figures 10 to 12. The dominant error in figures 6 to 8 came from the uncertainty in the integrated ion-energy per charge distributions due to noise in the recorded %I/%V trace. V Figure 6. ¯"/eVd as calculated from RPA data 0! o" axis and 550 mm downstream The ion-energy per charge distribution is dependent on the local plasma potential at the position of the probe. Even though the retarding grid is referenced to cathode, the energy the ions have acquired is equal to the potential drop between the discharge potential and the local plasma potential. In the absence of the probe, the ions will continue to accelerate until they reach their terminal potential, which, in the case of ground testing, is the tank wall (ground) potential. Hence, RPA measurements are sensitive to the location of the probe. Thus, to remove the positional dependence of the RPA, knowledge of both the local plasma potential and cathode to ground potential is necessary. Assuming that the RPA grids are referenced to ground the energy values can be corrected by $!ion q %= $!rpa q %- "ctg +"plasma (12) where the charge number is assumed to be unity and the left hand side is the ion energy to be used 8 of 15 American Institute of Aeronautics and Astronautics V


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Figure 7. ¯"/eVd as calculated from RPA data 15! o" axis and 550 mm downstream V Figure 8. ¯"/eVd as calculated from RPA data 30! o" axis and 550 mm downstream 9 of 15 American Institute of Aeronautics and Astronautics in the correct calculation of Eq. 6. RPA traces were taken at 0", 15", and 30" and average ion energy values were linearly interpolated for angles in between 0" and 15" and in between 15" and 30". The energy values from 30" out to 53" were assumed to be constant. While the validity of this extrapolation is admittedly unknown, past studies indicate the approach is resonable. King’s RPA results on a 1.5 kW-class Hall thruster showed that measured probe values varied less than 5% from 30" to 60".15 An assumption of 5% error in our high-angle extrapolated probe values propagates through the integral as 2% uncertainty in the calculation of Eq. 13. Finally, the traces are weighted against the current distribution function from the Faraday data and integrated to obtain the overall voltage utilization efficiency. Thus, by equation 13 the final values for "V are obtained and are shown in figures 10 to 12. "V = # !ion(#)j(#)r2 sin #d# qeVd # j(#)r2 sin #d# (13) Current efficiency, "c, is seen in figure 9 where Id is measured directly from the discharge supply. The beam current, Ii, is obtained from an integration of j(#) as measured by the Faraday probe. Current in the beam outside the probe’s maximum o$-axis angle of 53" was not collected


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and, therefore, Ii is a lower bound. By using a linear extrapolation of the probe sweeps from 53" to 90"(assuming 0 A/m2 at 90") we estimate the amount of current that is omitted from our integration. This technique indicates our "c calculations to have a maximum underestimation error of 12% due to the uncollected portions of the beam. Previous studies have shown, however, that the beam dies o$ faster much faster than linearly and therefore our error is a conservative estimate. The efficiency decays linearly from 300 V - 160 V and then begins to decline more rapidly. C Figure 9. Current efficiency as a function of discharge voltage V. Discussion Figures 10 -12 depict the various efficiency terms for each mass flow rate as measured using probe techniques. The current efficiency becomes the dominant loss mechanism for all operation below 200 V. The voltage utilization efficiency increases with increasing mass flow rate and with decreasing discharge potentials. Current and beam divergence efficiency, however, monotonically decay with decreasing discharge voltage. Experimentally, it is well known that "c can be increased by adjusting the magnets to minimize the discharge current.12 In doing so, however, the thrust efficiency as a whole declined in spite of reduced discharge current. This implies that one of the remaining losses 10 of 15 American Institute of Aeronautics and Astronautics begins to penalize efficiency at a faster rate than the reduced anode current increased efficiency. Most unusual is the fact that the voltage utilization efficiency begins to increase at the lowest of discharge potentials. It may be that maximum thrust efficiency is obtained by maximizing voltage


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utilization and not current efficiency during operation at low discharge voltages. Table 1 displays the final values for all calculated and experimentally determined loss mechanisms. Plasma-to-cathode values are displayed as determined by the emissive probe at 0.55 m downstream 0" o$ axis. The probe studies measured three of the four loss mechanisms comprising thrust efficiency. The velocity distribution was not obtained, and therefore the the ’probe efficiency’ is an upper bound on the thrust efficiency. Probe efficiency is defined as "probe = "v"c"B = "T "vdf . (14) Figures 13 - 15 plot thrust and probe e!ciencies as determined by the thrust stand and probe studies. The discrepancy between the probe and thrust stand values can be attributed to several things: overestimation of the beam divergence, inflated thrust measurements due to background neutrals, inflated thrust measurements due to cathode propellant ingestion, and underestimation of the current efficiency. The last of which is because the current fraction at high angles was not recorded. At low discharge voltages where the beam divergence is greater this omission has a larger e$ect on the calculation of current efficiency. The two benchmarks are in closest alignment at low discharge voltages for the 4 and 5 mg/s trials, and in the highest of discharge voltages for the 3 mg/s trial. V B C 3 mg/s


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Figure 10. ! values for 3 mg/s VI. Conclusions Probe studies and thrust stand measurements were performed on an Aerojet BPT-2000 Hall thruster at discharge voltage from 100 V to 300 V for 3 to 5 mg/s flow of xenon. The Hall thruster was unable to run stably at discharge voltages below 180 V at 5 mg/s. Thrust e!ciencies determined by the thrust stand measurements reached as low as 15% and the probe studies recorded 11 of 15 American Institute of Aeronautics and Astronautics V B C 4 mg/s Figure 11. ! values for 4 mg/s V B C 5 mg/s Figure 12. ! values for 5 mg/s probe T 3 mg/s Figure 13. Thrust efficiency from the thrust stand and probe efficiency from the probe studies for 3 mg/s 12 of 15 American Institute of Aeronautics and Astronautics probe T 4 mg/s


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Figure 14. Thrust efficiency from the thrust stand and probe efficiency from the probe studies for 4 mg/s probe T 5 mg/s Figure 15. Thrust efficiency from the thrust stand and probe efficiency from the probe studies for 5 mg/s 13 of 15 American Institute of Aeronautics and Astronautics Anode to Cathode (V) Current (A) Mass Flow (mg/s) Thrust (mN) Cathode to Ground (V) Plasma to Cathode (V) !V !B !C !probe !T 300 2.85 3 65.63 -27.00 46.10 0.78 0.80 0.78 0.49 0.50 250 2.84 3 57.12 -26.30 41.85 0.74 0.78 0.78 0.45 0.46 200 2.89 3 45.62 -22.50 35.07 0.72 0.77 0.77 0.43 0.36 140 3.59 3 31.96 -13.90 18.53 0.70 0.73 0.62 0.31 0.20 100 4.81 3 26.77 -9.70 12.61 0.72 0.69 0.46 0.23 0.15 300 3.92 4 73.60 -28.10 49.88 0.79 0.81 0.76 0.48 0.58 250 3.90 4 63.82 -25.90 44.29 0.76 0.80 0.76 0.46 0.52 200 3.99 4 51.40 -24.60 37.65 0.71 0.77 0.74 0.41 0.41 140 6.26 4 43.44 -11.10 17.88 0.80 0.71 0.47 0.27 0.27 300 4.96 5 72.63 -28.70 54.32 0.80 0.82 0.75 0.49 0.59 250 5.01 5 64.71 -210 45.39 0.79 0.81 0.74 0.47 0.56 200 5.15 5 53.21 -23.90 41.28 0.74 0.78 0.72 0.42 0.46 65.633 300 2.849 300 45.6158 200 2.843 250


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0 0 26.7655 100 2.89 200 Table 1. Comprehensive summary of all ! values as low as 23%. The dominant loss mechanism at the lowest discharge potentials was the current efficiency, whereas the voltage utilization efficiency increased in value; the only loss mechanism to do so across all operating conditions. While the current efficiency can be increased by adjusting the magnet current, overall thrust efficiency su$ers, indicating a coupled e$ect with one of the other loss mechanisms. References 1Kim, V., “Main Physical Features and Processes Determining the Performace of Stationary Plasma Thrusters,” Journal of Propulsion and Power, Vol. 14, No. 5, 1998, pp. 736–743. 2Andrenucci, M., Berti, M., Biagioni, L., and Cesari, U., “Characteristics of the XHT-100 Low Power Hall Thruster Prototype,” 4th International Spacecraft Propulsion Conference, Vol. ESA SP-555, Chia Laguna, Sardinia, Italy, October 2004. 3Ozaki, T., Inanaga, Y., Nakagawa, T., and Osuga, H., “Development Status of 200mN Class Xenon Hall Thruster of MELCO,” 29th International Electric Propulsion Conference, Vol. IEPC-2005-064, Princeton, NJ, October 31 - November 4 2005. 4Zakharenkov, L. E., Semenkin, A. V., and Garkusha, V. I., “Study of the 3-TAL Thruster Assembly Operation,” 29th International Electric Propulsion Conference, Vol. IEPC-2005-185, Princeton, NJ, October 31 - November 4 2005. 5Manzella, D. and Jacobson, D., “Investigation of Low-Voltage/High-Thrust Hall Thruster Operation,” 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Vol. AIAA-2003-5004, Huntsville, Alabama, July 20-23 2003. 6Ashkenazy, J., Shitrit, S., and Appelbaum, G., “Hall Thruster Modifications for Reduced Power Operation,”


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29th International Electric Propulsion Conference, Vol. IEPC-2005-080, Princeton, NJ, October 31 - November 4 2005. 7Massey, D. R., King, L. B., and Makela, J. M., “Progress on the Development of a Direct Evaporation Bismuth Hall Thruster,” 29th International Electric Propulsion Conference, Vol. IEPC-2005-256, Princeton, New Jersey, October 31 - November 4 2005. 8Kieckhafer, A. and King, L. B., “Energetics of Propellant Options for High-Power Hall Thrusters,” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Vol. AIAA-2005-4228, Tucson, Arizona, July 10-13 2005. 9King, D., Tilley, D., Aadland, R., Nottingham, K., Smith, R., Roberts, C., Hruby, V., Pote, B., and Monheiser, J., “Development of the BPT family of U.S.-designed Hall current thrusters for commercial LEO and GEO applications,” 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Vol. AIAA-1998-3338, Cleveland, Ohio, July 13-15 1998. 14 of 15 American Institute of Aeronautics and Astronautics 10Haag, T. W., “Design of a thrust stand for high power electric propulsion devices,” 25th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Vol. AIAA-1989-2829, Monterey, CA, July 10-13 1989. 11Kemp, R. F. and Jr., J. M. S., “Plasma Potential Measurements by Electron Emissive Probes,” Review of Scientific Instruments, Vol. 37, No. 4, 1966, pp. 455–461. 12Larson, C. W., Brown, D. L., and Hargus, W. A., “Thrust E"ciency, Energy E"ciency, and the Role of the VDF in Hall Thruster Performance Analysis,” 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Vol. AIAA 2007-5270, Cincinnati, Ohio, July 8-11 2007. 13Bugrova, A. I., Kim, V., Maslennikov, N. A., and Morozov, A. I., “Physical Processes and Characteristics


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of Stationary Plasma Thrusters With Closed Electrons Drift,” AIDAA/AIAA/DGLR/JSASS 22nd International Electric Propulsion Conference, Viareggio, Italy, October 14-17 1991. 14Hofer, R. R. and Gallimore, A. D., “E"ciency Analysis of a High-Specific Impulse Hall Thruster,” 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Vol. AIAA-2004-3602, Ft. Lauderdale, Florida, July 11-14 2004. 15King, L. B., Transport-Property and Mass Spectral Measurements in the Plasma Exhaust Plume of a Hall-E!ect Space Propulsion System, Ph.D. thesis, University of Michigan, 1998. 15 of 15 American Institute of Aeronautics and Astronautics


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Variable Specific Impulse Magneto plasma Rocket

Artist's impression of several VASIMR engines propelling a craft through space

The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an electro-magnetic thruster for spacecraft propulsion. It uses radio waves to ionize and heat a propellant and magnetic fields to accelerate the resulting plasma to generate thrust. It is one of several types of spacecraft electric propulsion systems.


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The method of heating plasma used in VASIMR was originally developed as a result of research into nuclear fusion. VASIMR is intended to bridge the gap between high-thrust, low-specific impulse propulsion systems and low-thrust, high-specific impulse systems. VASIMR is capable of functioning in either mode. Costa Rican scientist and former astronaut Franklin Chang-Diaz created the VASIMR concept and has been working on its development since 1977.[1]

The Variable Specific Impulse Magneto plasma Rocket, sometimes referred to as the Electro-thermal Plasma Thruster or Electro-thermal Magneto plasma Rocket, uses radio waves [2] to ionize and heat propellant and magnetic fields, accelerating the resulting plasma which generates thrust. This type of


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engine is electrode less and as such belongs to the same electric propulsion family (while differing in the method of plasma acceleration) as the electrodeless plasma thruster, the microwave arcjet, or the pulsed inductive thruster class. It can also be seen as an electrodeless version of an arcjet, able to reach higher propellant temperature by limiting the heat flux from the plasma to the structure. Neither type of engine has any electrodes. The main advantage of such designs is elimination of problems with electrode erosion that cause rival designs of ion thrusters which use electrodes to have a short life expectancy. Furthermore, since every part of a VASIMR engine is magnetically shielded and does not come into direct contact with plasma, the potential durability of this engine design is greater than other ion/plasma engine designs.[1]

The engine design encompasses three parts: turning gas into plasma via helicon RF antennas; energizing plasma via further RF heating in an ion cyclotron resonance frequency (ICRF) booster; and using electromagnets to create a magnetic nozzle to convert the plasma's built-up thermal energy into kinetic force. By varying the amount of energy dedicated to RF heating and the amount of propellant delivered for plasma generation VASIMR is capable of either generating low-thrust, high-specific impulse exhaust or relatively high-thrust, low-specific impulse exhaust.[3]


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In contrast with usual cyclotron resonance heating processes, in VASIMR ions are immediately ejected through the magnetic nozzle before they have time to achieve thermalized distribution. Based on novel theoretical work in 2004 by Arefiev and Breizman of UT-Austin, virtually all of the energy in the ion cyclotron wave is uniformly transferred to ionized plasma in a single-pass cyclotron absorption process. This allows for ions to leave the magnetic nozzle with a very narrow energy distribution and for significantly simplified and compact magnet arrangement in the engine.[3]

VASIMR does not use electrodes and magnetically shields plasma from all the hardware parts, thus eliminating electrode erosion, a major source of wear and tear in ion engines. Compared to traditional rocket engines with very complex plumbing, high performance valves, actuators and turbo pumps, VASIMR eliminates practically all moving parts from its design (apart from minor ones like gas valves), maximizing its long term durability .

However, some new problems emerge like interaction with strong magnetic fields and thermal management. The relatively large power at which VASIMR operates generates a lot of waste heat which needs to be channeled away without creating thermal overload and undue thermal stress on materials used. Powerful superconducting electromagnets, employed to contain hot plasma, generate tesla-range magnetic fields.[4]


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They can present problems with other on board devices and also can adversely interact with Earth magnetosphere. To counter this latter effect the VF-200 will consist of two 100 kW thruster units packaged together with the magnetic field of each thruster oriented in opposite directions in order to make a zero-torque Quadra pole.

A view of 50kW VASIMR

SA, Franklin Chang-Diaz set up the Ad Astra Rocket Company in January 2005 to begin development of the VASIMR engine. Later that year, the company signed a Space Act Agreement with NASA, and were granted control of the Advanced Space Propulsion Laboratory.[5] In this lab, a 50 kW prototype was constructed, and underwent testing in a vacuum


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chamber. Later, a 100 kW version was developed, and this was followed by a 200 kW prototype. After a long period of rigorous testing in a 150 m3 vacuum chamber, the latest configuration was deemed space-worthy, and it was announced that the company had entered into an agreement to test the engine on the International Space Station, in or before 2013.

The first VASIMR engine model VX50 proved to be capable of 0.5 newtons (0.1 lbf) thrust. According to company's data, current VASIMR efficiency was then at 67%. Published data on the VX50 engine, capable of processing 50 kW of total radio frequency power, showed efficiency to be 59% calculated as: 90% NA ion generation efficiency × 65% NB ion speed boosting efficiency. It was hoped that the overall efficiency of the engine could be increased by scaling up power levels.

Model VX100 was expected to have an overall efficiency of 72% by improving the NB ion speed boosting efficiency to 80%.[6][7] There were, however, additional (smaller) efficiency losses related to the conversion of DC electric current to radio frequency power and also to the superconducting magnets' energy consumption. By comparison, 2009 state-of-the-art, proven ion engine designs such as NASA's HiPEP operated at 80% total thruster/PPU energy efficiency.[8].


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Development of the 200 kW engine

On October 24, 2008 the company announced that the plasma generation aspect of the VX-200 engine: helicon first stage or solid-state high frequency power transmitter, has reached operational status. The key enabling technology, solid-state DC-RF power-processing, has become very efficient reaching up to 98% efficiency. The helicon discharge uses 30 kWe of radio waves to turn argon gas into plasma. The remaining 170 kWe of power is allocated for passing energy to, and acceleration of, plasma in the second part of the engine via ion cyclotron resonance heating.[9]

Based on data released from previous VX-100 testing,[4] it was expected that the VX-200 engine would have a system efficiency of 60-65% and thrust level of 5N. Optimal specific impulse appeared to be around 5000s using low cost argon propellant. The specific power estimated at 1.5 kg/kW meant that this version of the VASIMR engine would weigh only about 300 kg. One of the remaining untested issues was potential vs actual thrust; that is, whether the hot plasma actually got detached from the rocket. Another issue was waste heat management (60% efficiency means about 80 kW of unnecessary heat) critical to allowing for continuous operation of VASIMR engine.]


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Between April and September 2009, tests were performed on the VX-200 prototype with fully integrated 2 Tesla superconducting magnets. They successfully expanded the power range of the VASIMR up to its full operational capability of 200 kW.[10]

Testing on the space station

On December 10, 2008, Ad Astra Company signed an agreement with NASA to arrange the placement and testing of a flight version of the VASIMR, the VF-200, on the International Space Station (ISS). Its launch is anticipated to be in 2011 or 2012,[11][12] though it may be later.[5] Since the available power from the ISS is less than 200 kW, the ISS VASIMR will include a trickle-charged battery system allowing for 15 min pulses of thrust.

The ISS orbits at a relatively low altitude, so as to make it easily accessible from Earth. The downside of this, however, is that the ISS experiences fairly high levels of atmospheric drag, making periodic boosts of altitude necessary. Currently, altitude reboosting by chemical rockets fulfills this requirement. If the tests of VASIMR reboosting of the ISS goes according to plan, the increase in specific impulse could mean that the cost of fuel for altitude reboosting will be one-twentieth of the current $210 million annual cost.[5] Hydrogen is generated by the ISS as a by-product, which is currently vented into space.


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Potential future applications

VASIMR magnetic field

VASIMR is not suitable to launch payloads from the surface of the Earth due to its low thrust to weight ratio and its need of a vacuum to operate. Instead, it would function as an upper stage for cargo, reducing the fuel requirements for in-space transportation. The engine is expected to perform the following functions at a fraction of the cost of chemical technologies:

• drag compensation for space stations • lunar cargo delivery • satellite repositioning • satellite refueling, maintenance and repair • in space resource recovery • ultra fast deep space robotic missions

Other applications for VASIMR such as the rapid transportation of people to Mars would require a very


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high power, low mass energy source, such as a nuclear reactor (see nuclear electric rocket). NASA Administrator Charles Bolden said that VASIMR technology could be the breakthrough technology that would reduce the travel time on a Mars mission from months to days.[13]

In August 2008, Tim Glover, Ad Astra director of development, publicly stated that the first expected application of VASIMR engine is "hauling things [non-human cargo] from low-Earth orbit to low-lunar orbit" supporting NASA's return to Moon efforts.[11]

Use as a "space tug" and orbital transfer vehicle

The most important near-future application of VASIMR-powered spacecraft is transportation of cargo. Numerous studies have shown that, despite longer transit times, VASIMR-powered spacecraft will be much more efficient than traditional integrated chemical rockets at moving goods through space. An orbital transfer vehicle (OTV) — essentially a "space tug" — powered by a single VF-200 engine would be capable of transporting about 7 metric tons of cargo from low Earth orbit (LEO) to low Lunar orbit (LLO) with about a six month long transit time. NASA envisages delivering about 34 metric tons of useful cargo to LLO in a single flight with a chemically propelled vehicle. To make that trip, about 60 metric tons of LOX-LH2 propellant would be burned. A


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comparable OTV would need to employ 5 VF-200 engines powered by a 1 MW solar array. To do the same job, such OTV would need to expend only about 8 metric tons of argon propellant. Total mass of such electric OTV would be in the range of 49 t (outbound & return fuel: 9 t, hardware: 6 t, cargo 34 t). The OTV transit times can be reduced by carrying lighter loads and/or expending more argon propellant with VASIMR throttled down to lower Isp. For instance, an empty OTV on the return trip to Earth covers the distance in about 23 days at optimal specific impulse of 5,000 s (50 kN·s/kg) or in about 14 days at Isp of 3,000 s (30 kN·s/kg). The total mass of the NASA specs' OTV (including structure, solar array, fuel tank, avionics, propellant and cargo) was assumed to be 100 metric tons (98.4 long tons; 110 short tons)[14] allowing almost double the cargo capacity compared to chemically propelled vehicle but requiring even bigger solar arrays (or other source of power) capable of providing 2 MW.

As of October 2010, Ad Astra Rocket Company is working toward utilizing VASIMIR technology for space tug missions to help "clean up the ever-growing problem of space trash." They hope to have a first-generation commercial offering by 2014.[15]

Dr.A.B.Rajib Hazarika provides with new type of VASIMR named VASIMR DANISHA to give more thrust to travel up to 56000 hours.

Documents

VASIMR DANISHA:A Hall Thruster Space Odyssey