Study of Laser Plasmas Dynamics Through Real and Virtual Langmuir Probes

3048 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 10, OCTOBER 2013

Study of Laser Plasmas Dynamics ThroughReal and Virtual Langmuir Probes

Nadia Gambino, David Mascali, Salvatore Tudisco, Antonello Anzalone, Santo Gammino,Franco Musumeci, and Alessia Spitaleri

Abstract— A novel technique for laser produced plasmas(LPPs) investigation is proposed. It combines high time resolvedmeasurements using a compact Langmuir probe (LP) withsimulated data obtained with a numerical model designated ashybrid laser ablation simulations (HYBLAS). The code simulatescharged particle collection with what we will refer to as a virtualLP. With the use of an appropriate experimental setup and witha MATLAB software, which analyzes the experimental I − Vcurves, LPPs can be investigated properly even if the probeis placed very close to the target surface. The method permitsto study the plume expansion with a high temporal resolutionand to correctly estimate the self-generated Coulomb electricfield inside the plume. It permits to detect the inner structureof the first upcoming expanding plasma. HYBLAS is able todescribe the plume expansion at relatively low power densitiesif the initial conditions are set properly. A direct comparisonof the theoretical data with the experimental ones realized ondifferent metal targets shows that this method is able to predictproperly the overall plasma expansion in the nanosecond laserpulse duration regime. The virtual probe method was moreovertested by comparing the numerical results with the numericalcode called MULTI.

Index Terms— Ablation, Langmuir probe (LP), lasers,plasmas, simulation.

I. INTRODUCTION

LANGMUIR probes (LPs) are widely used for charac-terizing plasmas in different conditions of density and

temperature, going from fusion to lower temperature plasmassuch as discharge and laser produced plasmas (LPPs). For aLPP, the high non equilibrium regime requires to review theclassical way of data acquisition technique. At laser powerdensities in the order of 1010–1012 W/cm2 the plasma evolvessupersonically. High time and spatial resolved diagnosticstools are required to deduce the information about the plasmadynamic that expires within few microseconds. Electrostaticprobes such as ion collectors, ion energy analyzers (IEAs),and LPs are well-know experimental techniques used for thispurpose. They are able to provide time of flights (TOFs)spectra, which help to reconstruct the overall plasma dynamic.

Manuscript received November 20, 2012; revised April 28, 2013 andJune 29, 2013; accepted August 6, 2013. Date of publication September 23,2013; date of current version October 7, 2013.

N. Gambino is with the LEC Department, ETH, Zürich 8092, Switzerland(e-mail: [email protected]).

D. Mascali, S. Tudisco, A. Anzalone, S. Gammino, F. Musumeci,and A. Spitaleri are with the Laboratori Nazionali del Sud, IstitutoNazionale di Fisica Nucleare, Catania 95125, Italy (e-mail: [email protected]; [email protected]; [email protected]; [email protected];[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPS.2013.2281115

LPs permit to estimate the plasma parameters, such as theelectron and ion density, the electron temperature and theself-generated plasma potential. To avoid damage and signaldistortions, these devices are usually placed far away from thelaser–plasma interaction area. Most of the results reported inthe literature refer to the experiments where the probe is placedvery far from the target surface. These traditional experimentalconditions, however, allow investigating the plume dynamiconly at later expansion stages, when the plasma undergoesto free-streaming expansion and information about the earlydynamics are missed.

In this paper, it will be shown that using an appropriate read-out circuit, the real current signals can be acquired with verylow electrical noise and the probe can be placed very close tothe target surface (few millimeters). We have developed a the-oretical model, hybrid laser ablation simulations (HYBLAS)able to simulate a LP, which we will refer to as a virtual LP.It is obtained using and revising the numerical model proposedin [1]. This model solves the gas dynamical equations underthe hypothesis that the plasma evolves adiabatically. The codewas implemented in MATLAB and solves the equations ofplasma plume front evolution using a fourth- and fifth-orderRunge–Kutta routine [2].

The analysis method consists in the strict comparisonbetween the model predictions (virtual probe) and the experi-mental data (real probe). It has been applied for the determi-nation of a laser generated plasma structure in the nanosecondpulse duration regime [3], [4]. The reliability of the HYBLASmodel was also tested by comparing the numerical results withthe simulated data obtained with the MULTI code. MULTIalso considers the radiative transport [5]. Comparisons withthis code and with the experimental data show that HYBLASis able to describe the plasma bulk expansion at power densityin the order of 1011 W/cm2 with low CPU time consumptionand at expansion stages in the order of microseconds.

II. EXPERIMENTAL SET-UP

An Nd:Yag laser operating in single-shot mode at a powerirradiance of 3 × 1011 W/cm2 with 6 ns of pulse durationand emission wavelength of 1.064 μm was focused on flatAl targets through a 250-mm focal length lens. The vacuumchamber is a compact cylindrical stainless steel chamber witha diameter of 250 and 240 mm of height.

The LP is an analytical ESPion advanced LP, consistingof a tungsten tip of cylindrical area of 2.43 mm2 connectedto 300-mm long coaxial cable, having a diameter of 3 mm.

0093-3813 © 2013 IEEE

GAMBINO et al.: STUDY OF LASER PLASMAS DYNAMICS 3049

Fig. 1. Experimental set-up showing the vacuum chamber-LP configuration.(a) and (b) RC circuit used to read out the current signal.

The tip protrudes from an alumina sheath, which covers thecoaxial cable. A motor moves the probe with a total rangeof 300 mm. The probe was biased with a HP power supplyfrom generally −90 V to +90 V with steps of few volts foreach laser shot and placed at different distances from the targetsurface (from 2 to 50 mm with steps of 2–3 mm), parallel tothe plasma expansion direction. The TOF signals obtained atdifferent voltages are then send through a particular RC circuitconfiguration and read out through the oscilloscope having asampling rate of 2.5 GS/s. The experimental setup is shownin Fig. 1.

It is important to use the appropriate read-out circuit for LPmeasurements since the input impedance affects the interpre-tation of the LP current signals [6]. In our case, the read-out scheme resulted in a high signal-to-noise ratio for theLP current signals. Only one BNC vacuum feedthrough isassociated with the probe thus reducing the plasma noiseeffects.

The RC circuit observed in Fig. 1 allows one to exactlyevaluate the amount of current (in the order of several ofhundred milliamperes) flowing through the LP and to obtainlow noise current signals, even if the LP is placed at fewmillimeters from the target. The power supply G is used to biasthe probe. A capacitor C1 is placed in parallel with the powersupply. It forms a RC circuit with the resistor R1. The R1C1circuit allows stabilization of the power supply (G) voltage.The capacitor C1 can have a value in the order of hundredof nanofarads. The resistor R1 needs, at least, tens of � (orin general R1 > R2). With a high value for the resistor R1most of the current read out by the probe flows through thebranch containing the R2C2 circuit. The R2C2 circuit is henceused to read out the entire probe current signal then sent tothe oscilloscope. The values of R2 and C2 are chosen to havea RC time constant τ = R2C2 comparable with the durationof the signal (that is in the order of few μs). According tothe absolute current values obtained from the probe, R2 musthave values (general in the order of few �) to fit the currentvalues into the scale of the oscilloscope. R0 is a 50 � resistorfor ensuring impedance matching between the circuit and theoscilloscope.

Data are then processed through a MATLAB code, whichanalyzes the TOF signals to obtain the current values with theformula

I = Vp

Req(1)

Fig. 2. Experimental TOF signals obtained for four different probe voltages.(a) and (b) Construction of the I−V curves. (b) Four different time expansionswhen the probe was placed at 14.5 mm from the target, parallel to theexpansion direction.

where the equivalent resistor Req is given by

Req = Ro

Ro + R2·(

1

R1+ 1

Ro + R2

)−1

. (2)

Since LPPs expand rapidly in time with velocities in theorder of 104 m/s, a different method needs to be used toreconstruct the I–V curves with respect to the one used forquasi-stationary plasmas. In Fig. 2(a), an example of differentexperimental TOF current signals are reported, at four differentprobe voltages of −50, 0, 30, and 60 V. The intersectionbetween the black line and the TOF signals gives the currentversus voltage plot values in Fig. 2(b), thus obtaining thewell-known I–V curves (current I versus probe potential V )at different expansion times. Note that the current values arechanged in sign and then plotted as shown in the figure.

The current signals versus probe potential I (V ) are analyzedfor different expansion times to estimate the time-dependentplasma parameters, i.e., the electron density, the electrontemperature, and the plasma potential.

In principle, every 400 ps an I–V curves can be recon-structed and analyzed. However, considering the general goalof this paper (which aims to reconstruct the overall plasmaplume expansion dynamics) we analyzed each I–V curves witha temporal resolution of about 500 ns.

To monitor the shot-to-shot reproducibility, the Al planartarget was fixed on a micrometric linear stage to guaranteefresh surface for each laser irradiance exposure. A Faradaycup (FC) placed at 120 cm from the target surface was alwaysbiased with a fixed voltage of −30 V . In this way, the shot-to-shot reproducibility could be monitored although the voltageon the LP and the target surface ablated by the laser, wherechanging each time. Effectively, the FC acts as a referenceprobe. The signals obtained by the FC were reproducible,being mostly identical in shape and time when moving theAl target to a new surface.

III. THEORETICAL MODELS

The equations describing extensively the laser–matter inter-action are numerous: many physical phenomena, such asthe hydrodynamics motion, the radiation transport, the heattransfer, and particles collisions, must be considered to com-pletely describe the Laser–target interaction and the subse-quent plasma evolution.

The radiation field is coupled to the fluid motion throughemission and absorption phenomena. In the general form, the


transport equation is expressed as(1

t∂c + �n · ∇

)I (�r , �n, ν, t)

= η(�r , �n, ν, t) − χ(�r , �n, ν, t)I (�r , �n, ν, t) (3)

where I (�r , �n, ν, t) is the specific intensity of radiation offrequency ν at a position �r traveling in direction �n at timet , η is the total emissivity, and χ is the total opacity [5]. Theright term is the effective rate of energy emission by the matterper unit of volume, frequency, and solid angle. Integrating overall frequencies and directions, the total emission rate per unitvolume of energy Q and the radiated momentum �R, can beobtained. Their expressions are described by

Q =∫ ∞

0

∫4π

(η − χ I )d �ndν (4)

�R =∫ ∞

0

∫4π

(η − χ I )

c�nd �ndν. (5)

The fluido-dynamical motion of the plasma can be describedby the hydrodynamics equations given by

Dtρ = −ρ∇ · �v (6)

ρDt �v = −∇ �P − �R (7)

ρDt e = −P∇ · �v − ∇ · �q − Q + S (8)

where Dt = ∂t + �v · ∇ and ρ, �v , P , q are, respectively,the density, the velocity, the pressure, and the thermal flux.S includes other energy sources like laser or ion beam energydeposition. The heat flux q (carried mostly by electrons) canbe calculated through the Spizter formula. However, since theSpitzer formula overestimates the thermal flux in fluids char-acterized by strong temperature gradients, like laser plasmas,the collisional term must be corrected as in [5].

Apart from the plasma expansion, some additional equationscan be solved together with the equation of motion, to considerthe laser–plasma interaction during the laser pulse duration.In this case, the isothermal regime is established, and the Singand Narayan equations hold [7]. The laser light is mainlyabsorbed for photoionization and Inverse Bremmstrahlung(IB); the latter process is the principal absorption mechanismin the laser energy regime discussed in this paper.

The total amount of absorbed laser energy will be α I+,where α is the absorption coefficient for IB which expressioncan be found in the literature [8], [9], and I+(xc, t) is theabsorbed laser light intensity at the critical density in the 1-Dplane. The reflected laser light intensity will then be equal toI−(xc, t) = (1 − α)I+(xc, t). Once I+ and I− are known, thelaser deposition rate at the target surface can be calculatedby [5]

S = ∂x I+ − ∂x I−. (9)

One of the codes available in the literature that considersthe radiation transport, the hydrodynamics motion, the heatflux, and laser energy deposition is the MULTI code. It wasdeveloped by Ramis et al. and is a reference for laser–matterinteraction in the high power density regime. MULTI is usedespecially for inertial fusion confinement calculations. It isable to simulate layered targets (up to ten layers) and up to

three different materials can be considered. The model com-bines hydrodynamics equations in the Lagrangian coordinatesto radiation transport and considers both opacities that non-LTE equilibrium. Laser energy deposition is modeled by IB,so that the model can be also used in the power densityregime of 1010–1012 W/cm2. The MULTI approach consistsin a discretization of the radiation transfer equation, which isconsistently simplified by neglecting scattering processes, andassuming that the plume velocity is much smaller than thespeed of light. In this way, opacity and the source function(the ratio between η and χ) can be considered isotropic. Thehydrodynamics equations are then combined with a multigroup(finite number of domains called groups) method for theradiation transport. A finite number of differential equationsare solved with a finite time splitting scheme. The completetreatment can be found in [5].

Our theoretical model HYBLAS consists in a revised ver-sion of the Anisimov model. The Anisimov model solves thegas dynamical equations, under the basic hypothesis that theplasma expands self-similarly, adiabatically, and isoentropi-cally in vacuum: a special solution of the Eulero’s equationsgives out the plasma density and temperature profiles versustime. The density is described by [1]

ρ(x, y, z, t)th = M

I1 X (t)Y (t)Z(t)

×(

1 − x2

X (t)2 − y2

Y (t)2 − z2

Z(t)2

) 1γ−1

(10)

where M is the plume mass, X (t), Y (t), Z(t) are the spatialcoordinates, and γ is the adiabatic index. HYBLAS solvesthe equations of motion by adding two additional input para-meters, to include the effect of the accelerating Coulombianfield and the difference between the ion and the electrontemperatures. The plasma evolution is strongly influenced bythe charge separation of electrons and ions. The differentmobility makes typically the electrons faster than the ions.In the separation layer a self-generated electric field arises tocompensate the charge discrepancy. In a free-flowing plasma(i.e., when the effect of the background medium can beneglected), the electric field boosts the plasma mobility. Theelectric field must be included in the plasma plume equationsof motion. These improvements permitted us to successfullycompare the numerical results with the real ones in differentexperimental conditions [2]–[4].

The adimensional equations of motion of the plasma frontare expressed in the form

ξ ξ̈ = ηη̈ =[

σ

ξ2η

]γ−1

(11)

where τ = t/t0; ξ(τ ) = X (t)/R0; η(τ) = Y (t)/R0;σ(τ) = Z(t)/R0 represent, respectively, the time expansionand the three spatial coordinates. R0 is the crater spot diameter.

Equation (11) is then corrected by inserting an additionaldrift velocity term vc, which considers the effect of the self-generated electric field [4]

ξshifted = ξ + vc = ξ +√

2 < q > eVp

Mi

R0

t0(12)


where vc = 2〈q〉eVp/M is the contribution of the Coulombshift to the velocity term, 〈q〉 is the mean charge state,Vp is the plasma potential, and Mi is the ion plume mass.The estimation of the inner electric field was done as inthe stationary case: electrons are typically absorbed by thechamber walls where plasmas are formed. The expansion invacuum virtually reproduces the absorption of fast electronsin the plume front by a virtual wall placed close to the plasmaat each time step.

Equation (12) has been solved numerically using a fourth-and fifth-order Runge–Kutta Nyström routine implemented ina MATLAB code developed in [2].

Vp can be roughly estimated by the electron temperature,according to the formula Vp = ckB Te, where c has a value ina range between 0.12 and 2.9 for the simulations performedin this paper, kB is the Boltzmann’s constant and Te is theelectron temperature. From thermodynamic considerations, thevelocity of the adiabatic expansion can be expressed by [10]

vγ =√

γ kB Te

Mi�⇒ Te = Miv

2γ

γ kB. (13)

Once γ is fixed, we can calculate the adiabatic velocityterm vγ (not including the term vc used to correct (11), andextrapolate from (13) the initial electron temperature Te(0).Consequently also Ti (0) can be calculated since the electron-ion thermalization times are in the order of τei 100 ps, henceTe(0) Ti (0).

Due to the mass difference, during the expansion, electronand ions will evolve with a different kinetic energy andalso with a different temperature. The high collisional ratedetermines that ions share the ordered, forward peaked energychanging it into disordered, thermal energy. The ion velocitywill be in the same order of magnitude of the expansionvelocity vexp so that the ion temperature can be estimated as

3

2kB Ti ≈ 1

2Mv2

exp. (14)

By considering (13) and (14) the ion to electron temperatureratio will be

kB Ti

kTe= 1

3

[√γ + √

2 < q >]2

(15)

where vexp = ξshifted + vγ .This relation can also be observed as the temperature ratio

dependence on a given charge state inside a single plume [4].It predicts not only that the ion temperature is consistentlyhigher than the electron one, but also that the ratio growswith the charge state, that is in qualitative agreement withexperimental results [11]. Using (14), the Anisimov model hasbeen further improved by introducing the discrepancy betweenthe ion and electron temperatures. Two γ factors have beenalso introduced, one for electrons (γe) and the other one forions (γi ) [4]. The adiabatic index lies generally in the range1.1–1.4, since excitation and recombination processes or clus-ter formation, can reduce the plasma degrees of freedom andhence the γ value [12]. Cluster formation can also affect the γvalue. With this approach, most of the simulation parametersare evaluated self-consistently: only the laser energy, the crater

Fig. 3. 2-D simulation of the density resolved Al plume at 20 ns. (a) Activearea contains a certain number of cells in the probe domain. (b) Real CCDimage obtained at 20 ns of time expansion.

TABLE I

SIMULATION PARAMETERS

depth, and crater spot size must be set externally as inputvalues.

IV. VIRTUAL LP

The virtualization of the LP consists in the definition of a2-D domain in the x–z plasma expanding plane (the activecollection area of charged particles), where the probe charac-teristics can be tuned in relation to the experimental conditions,i.e., by considering the probe dimension, its orientation withrespect to the plasma expansion direction and its distancefrom the target. The probe domain D is defined with acertain number of unitary cells c each of A = 100 μmof dimension. Once the domain is defined, considering theprobe characteristics mentioned above, the current density onthe probe is calculated from an overlapping between D andthe plasma density mapping coming from the resolution of thefluid equation. A mesh routine interpolates the density value ineach numerical cell with the nearest cell at the plasma ellipticalisosurfaces.

Fig. 3 schematically shows the interaction between theplasma plume and the virtual probe placed parallel to theexpansion direction at a fixed time of 20 ns of expansion cal-culated with the HYBLAS code. The plasma density definedin (10), was simulated in the y = 0 plane; the horizontalaxis represents the forward expansion direction z, and thevertical axis represents the lateral expansion direction x (orequivalently y, due to assumed axial symmetry). Fig. 3(b)shows a real charge-coupled device (CCD) image obtainedat 20 ns of time expansion: a first qualitative comparisonwith the simulation, shows a good agreement between thenumerical and the experimental data. Simulation parametersare shown in Table I.


Fig. 4. Density maps obtained with the HYBLAS (top) and with the MULTI (bottom) code at four different expansion times: t1 = 10 ns, t2 = 30 ns,t3 = 50 ns, and t4 = 70 ns. The initial input parameters (laser energy, laser wavelength, and crater spot size) are the same in both simulations. Note that thedensity is normalized to the initial Al solid target density.

The current density at the probe surface Jpr is calculatedwith the following:

Jpr = Ji + Je (16)

where Ji and Je are, respectively, the ion and the electroncurrent densities defined by

Ji = eρprvB〈q〉 (17)

Je = eρpr

(vth

4

)exp

[e(Vpr − Vp)

kB Te

](18)

where ρpr = D×ρth is the plasma density on the virtual probedomain calculated from (10), vB = (kB Te + γ kB Ti/Mi )

1/2

is the Bohm velocity, 〈q〉 is the mean charge state,vth = (2kB Te/me)

1/2 is the electron thermal velocity, and Vpris the applied probe voltage. The total current is the obtained

I = Jpr Apr (19)

where the probe area is equal to Apr = cA. It must be notedthat when the probe is placed parallel to the plasma expansiondirection, the ion current contribution does not include the partaccounting for the drift motion of the plasma flow.

With the method of the virtual probe, not only the currentdensity obtained from HYBLAS can be used to simulatethe plume expansion, but also the ones from any other hydro-dynamic code able to simulate the plasma expansion versustime, giving 2-D arrays of density and temperature as outputdata.

V. VALIDATION OF THE VIRTUAL PROBE METHOD

This section reports the numerical simulations realized withHYBLAS and MULTI to test the validity of the virtualprobe method. Starting from the same initial conditions, adirect comparison of the bidimensional 2-D density mappingobtained with the two codes at different expansion times wascarried out. The density mappings were then used to reproducenumerically the current signals.

A. Plasma Density Mappings

As observed in Fig. 3, the plasma can be simulated in the(x, z) plane in terms of density mapping. 2-D plots are helpfulto compare the theoretical data with the experimental imagesthat can be obtained for example, with ICCDs, interferometry,and so on. [13].

The simulation parameters for HYBLAS are the ones shownin Table I. In addition, MULTI requires the laser wavelength(1.064 μm) and the laser pulse duration and does not requiresthe crater depth, the constant c and the γ values. Density mapsobtained in the 2-D space are shown in Fig. 4. Comparisonswere done for four fixed plasma expansion times: 10, 30, 50,and 70 ns.

The plasma maps obtained with the two codes are compara-ble in the region of interest of LP measurements (i.e., for probedistances from the target higher than 0.5 cm). The densitiesobtained with MULTI (ρM ) and with HYBLAS (ρH ) canreasonably be compared in terms in the order of magnitudefor all expansion times. However, the maps obtained with


Fig. 5. Comparisons between ρM and ρH in the y = 0 plane obtained at t1 = 10 ns, t2 = 30 ns, t3 = 50 ns, and t4 = 70 ns.

MULTI display a higher density in regions close to the targetsurface. The front plume dimensions along the x-axis arecomparable for t = 10 ns and t = 70 ns. For t = 30 nsand t = 50 ns, MULTI gives a front plume size, respectively,of 1.7 and 2.1 cm (not visible in Fig. 4); these values arestill comparable with those obtained with HYBLAS. The maindifference between the two dynamics is revealed along thelateral expansion dimensions. MULTI has a more leaf shapedstructure, while HYBLAS gives a more elongated shape. Thiswas expected since in this last case the special solution of (12)gives an elliptically shaped density distribution; in addition,the presence of the Coulomb shifted velocity term accountsfor an additional contribution to the plasma elongation alongthe z-direction. It is in fact the electric field that boosts thevelocity of each charge state populating the expanding plume.In addition, radiative losses are not considered in HYBLAS,so that the density distribution can be different.

A more significant comparison is given by plotting thedensity profiles along the forward expansion axis for y = 0.Results are shown in Fig. 5. They show that the disagreementbetween the two densities ρM and ρH becomes less evidentat higher time steps. In the region of interest of LP measure-ments, the densities obtained with MULTI and with HYBLASare less than one order of magnitude different.

B. Comparison With Experiments

Previous versions of HYBLAS were already used to com-pare the numerical results with real TOF signals using dif-ferent types of metal targets: a good agreement between thenumerical and the experimental data was found [3], [14].Results concerning the ion current signals of this paper (com-parison between the experimental and theoretical trends) areshown in Fig. 6. The experimental ion signal was obtained

Fig. 6. Negative biased Langmuir probe LP signal (−50 V) detected at14.5 mm from the target compared with the simulated one.

when the probe was placed at 14.5 mm from the targetbiased with a negative voltage of −50 V. Obviously, thevirtual probe was placed in the same position. Simulationpredicts the width and the centroid position of the experimentalsignal, once the electron contribution tail is subtracted. A goodagreement comes from comparison with the experimental datawith the upgraded version HYBLAS. The fast peaks of thereal signal eventually present at the early stage of the plumeexpansion (especially when the probe is located closer tothe target surface), cannot be simulated with the HYBLASmodel since they do not obey fluid dynamics modeling. Theirformation mechanism is strongly different with respect to theremaining part of the plasma; these dynamics are discusseddetailed in [15]. In Fig. 7, the comparison between the virtualprobe current signal Je and the experimental electron current


Fig. 7. Positive biased Langmuir probe LP signal (+60 V) detected at14.5 mm from the target compared with the simulated one.

Fig. 8. Electron temperature Te and Te−9/2 trends versus time obtained

from the analysis of the I–V curves at 14.5 mm from the target surface.

signal is shown. A positive voltage of +50 V was considered.Initial conditions were the same as those used for the ions. Cal-culations show that the simulated signal is able to reproducethe temporal dynamic of the real signal, but not the overallexpansion.

This discrepancy can be explained with the presence of aslow hot electron tail produced by the recombination mech-anisms that are not considered in the HYBLAS model: in athree-body recombination, the extra energy obtained from therecombination of an ion and an electron is absorbed by a thirdelectron taking part to the process. This electron will survivelonger in the plasma for higher energy excess.

This is confirmed by the experimental electron temperaturetrends versus time shown in Fig. 8. The plasma tempera-ture obtained from the analysis of the I–V curves when theprobe was located at 14.5 mm from the target is in theorder of 2–5 eV when the corona plasma reaches the probe.The temperature then increases to 9 eV when the plasmabulk reaches the probe. When the late expansion stage isdetected by the LP, the plasma temperature decreases to afew electron volts with the typical decreasing trend observed

Fig. 9. Simulated ion density compared to with the experimental oneevaluated from the ion saturation current when the probe was placed at14.5 mm from the target; ρth was multiplied for the mean charge state 〈q〉 = 4.

for LPPs. Since three-body recombinations scale with T −9/2e ,

which trend is reported in the same figure, we observe thatthe contribution of hot electrons generated via recombinationprocesses becomes significant at later expansion stages.

Hot electrons also influence the evaluation of the experi-mental electron density ρexp, obtained by analyzing the I–Vcurves in the electron saturation current region I S

e [16].The trends like those shown in Fig. 9 are obtained by

comparing ρexp with ρth when the experimental density iscalculated from the ion saturation current I S

i (in Fig. 2 ionsaturation starts, depending on the expansion time, around−55 V for t = 0.41 μ, or already between −10 and −20 Vfor later expansion times). A better agreement with ρth isfound when the ion signals are used [16]. The experimentaldensity was evaluated with I S

i = 〈q〉nivtot, where 〈q〉 = 4 isthe mean charge state and vtot is the total experimental velocityevaluated from the peak position of the LP-TOF signal. Thevelocity term includes the adiabatic flow, the thermal, and thedrift velocity term. A mean charge state 〈q〉 = 4 was chosenaccording to the existing literature showing data collected withIEAs: at laser irradiances that are one order of magnitudelower than ours (1010 W/cm2), it is found that the meancharge state lies between 〈q〉 = 2 and 〈q〉 = 3 [3], [17].It is expected that for laser irradiances of this experiment(1011–1012 W/cm2), the mean charge state increases.

VI. DISCUSSION

The probe virtualization method introduced inside a moregeneral model able to simulate the plume expansion dynamic,could provide a valid technique of plasma characterizationand data analysis. HYBLAS assumptions are oversimplifiedwith respect to the MULTI code. This helps to easily handlethe code and to directly compare the simulated data withthe experimental data. Except for the energy content insidethe plasma, which is fixed inside the HYBLAS model, oncelaser proprieties are established, other parameters such asthe initial electron temperature, the plasma potential (i.e.,self-accelerating E field), and the electron-ion temperature


discrepancy can be calculated. The numerical values are inagreement with the real data. This in turn permits us to tune theremaining free parameters like γi , γe, thus finally describingthe overall plasma expansion dynamic. The reliability of theinitial input values can be controlled by evaluating otherparameters having a direct dependence from the input data,i.e.., the plasma velocity terms. The Bohm velocity and thethermal electron velocity were in this case, respectively, equalto 2.7 × 104 m/s (maximum value at 170 ns of the plasmaexpansion time) and to 9.37×105 m/s, in accordance with theexpected values in the laser energy regime of this paper.

The 1-D simulated density trend versus time, in a positioncoinciding with the real probe location, is in a reasonably goodagreement with the experimental data, especially for the ionbulk plasma. Once found the agreement with the simulatedparameters, the code gives the opportunity to evaluate theplasma parameters at the early stage expansion, i.e., close tothe target surface. The plasma expansion can be reconstructedbackward since the plasma signal at the probe position isknown. The backward reconstruction is made by the HYBLAScode. The code is calibrated on the experimental data bycomparing a virtual signal on a virtual probe with the realsignal collected, at a certain time and distance, by the realprobe. The calibration procedure requires that some parametersmust be included into the code as starting conditions (theseparameters are reassumed in Table I). Some of these conditionsare known ab initio, or can be independently estimated (forinstance, the crater depth), or can be argued on the basis ofphysical considerations. Other conditions can be deduced bythe virtual probe method. The initial plasma potential, forexample, must be varied to reproduce the correct expansionvelocity (it fixes the centroid position of the simulated signalshown in Fig. 6); the other parameters must be calibratedto give a virtual signal spread in Fig. 6 that is comparablewith the experimental one. Since we know the equation oftemperature variation included into the specific code, wecan thereby obtain the temperature at each plume expansionstage (the code runs for several expansion times, so that thedetailed temperature and density maps can be obtained foreach time). A similar procedure provides the density evolution.Once the temperature and the density trends are known, it ispossible to calculate the Debye length. This length gives, atfirst approximation, the length over which the self-producedpotential acts. By comparing it with the plasma potential, theelectric field driving the Coulomb expansion of the plasmacan be estimated. With this method was found that at 5 nsof the plume expansion the electron temperature Te has avalue of 350 eV and the electron density ne of 2 × 1025 m−3.The Debye length λD can then be calculated: it has a valueof 0.03 μm. The initial plasma potential is evaluated fromVp = ckBTe = 42 V with c = 0.12. It is hence possible toestimate the initial electric field of the expanding plasma fromE = Vp/λD . At a power irradiance of 3 × 1011 W/cm2 E isin the order of 1.4 × 107 V/cm2. This value is in agreementwith experimental electric field measurements reported in [18]at similar laser fluences.

In principle, once the experimental data are fitted with thevirtual probe signals, the trend of the main plasma parameters

can be estimated for each expansion stage, to obtain anexhaustive picture of the entire plume dynamic.

VII. CONCLUSION

In this paper, we demonstrated that it is possible to obtainthe time-resolved plasma parameters, up to expansion stages inthe order of microseconds, using a very simple and low-CPUtime-consuming numerical code named HYBLAS. Numericalresults were compared with the experimental ones collectedat a fixed expansion stage with the implementation of avirtual LP. For the ion bulk plasma, we obtained a goodagreement between the experimental and the simulated data.Once a good agreement between the numerical data and theexperimental data is obtained at a fixed LP position, theHYBLAS code was used to backward estimate the plasmaparameters at the early expansion stages. It is in fact notpossible to obtain these data experimentally, since the probeshould be located very close to the target surface and thiswould perturb consistently the plume propagation. To validateits reliability, HYBLAS was also compared with a moresophisticated software named MULTI. The codes agree withinsome restrictions, concerning a specific part of the expandingplasma signal related to the plasma core evolution. This is infact mostly governed by the hydrodynamics equations. It isclear that the HYBLAS code leads to some physical simplifi-cations in the simulation of the plasma dynamic: the first partof the probe’s detected signal (fast bumps of ions) and the longtail following the core are not treated in the HYBLAS scheme.To our knowledge, the fast component is also not treatedin the MULTI approach and requires alternative theoreticalstrategies to be correctly interpreted. The fast component isalso missing from hydrodynamics approaches and requireskinetic calculations like those ones performed in [15] basedon particles in cell strategies.

Future possible implementations of the HYBLAS code arefocused on the possibility to include in the numerical simula-tions the effect of three-body recombinations to reproduce thehot electron tail dominant at later expansion stages.

ACKNOWLEDGMENT

The authors would like to thank the technical and electronicstaff of the LNS-INFN of Catania for helping in the buildup ofthe experimental apparatus and R. Ramis from the UniversidadPolitécnica de Madrid, Spain, that gave assistance in the useof the MULTI code.

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Nadia Gambino was born in Baden, Switzerland, in1980. She received the “Laurea” degree in physicsfrom the University of Catania, Catania, Italy, in2007 and the Ph.D. degree in engineering physicsfrom the Department of Physics and ChemicalMetodologies for the Engineering of Catania, Cata-nia, in 2011. The Ph.D. work was mainly carriedout at the Laboratori Nazionali del Sud, IstitutoNazionale di Fisica Nucleare, Catania, and wasfocussed on the investigation of Laser ProducedPlasmas. Part of the Ph.D. research activities were

carried out at the Dublin City University, Dublin, Ireland, where the interactionof two colliding laser produced plasmas was studied.

She has experience on the optimization and characterization of laser pro-duced plasma sources and on plasma diagnostics. Since 2011, she has been aPost-Doctoral Research Assistant with the Laboratory for Energy Conversion,ETH-Zürich, Zürich, Switzerland. Her work is focused on the investigationof LPPs as a possible source of EUV radiation for the manufacture of next-generation integrated circuits, having node sizes below 32 nm. Her currentresearch interests include the investigation of microwave generated plasmasproduced by electron cyclotron resonance for environmental applications.

David Mascali was born in Catania, Italy, in 1981.He received the “Laurea” degree in physics fromUniversità degli Studi di Catania, Catania, in 2005,where he is currently pursuing the Ph.D. degree withDipartimento di Fisica e Astronomia.

He is working with the Ion Sources Researchand Development Team, Laboratori Nazionali delSud, Istituto Nazionale di Fisica Nucleare, Catania.His current research interests include microwave-plasma interaction in electron cyclotron resonanceion sources and it aims to increase the extracted

currents of HCIs through innovative schemes of wave to plasma coupling. Heworked on plasma diagnostics, microwave discharge ion sources, and laserproduced plasmas.

Mr. Mascali received the National Scholarship from the Istituto Nazionaledi Fisica Nucleare in 2004.

Salvatore Tudisco was born in Catania, Italy, in1970. He received the “Laurea” degree in physicsand the Ph.D. degree from Università degli Studi diCatania, Catania, in 1994 and 1999, respectively.

He is currently a Senior Researcher with NuclearAstrophysics Team, Laboratori Nazionali del Sud,Istituto Nazionale di Fisica Nucleare, Catania. Hiscurrent research interests include nuclear physicsand astrophysics, detectors, and instrumentationresearch and development of laser produced plasmas.

Antonello Anzalone was born in Randazzo, Italy.He received the “Laurea” degree in physics fromthe University of Catania, Catania, Italy, in 1976.

He was with the Faculty of Physics, Universityof Catania, between 1976 and 1977. Since 1977,he has been a Senior Researcher with LaboratoriNazionale del Sud, Istituto Nazionale di FisicaNucleare (INFN-LNS), Catania, and since 1993, hehas been a Principal Technologian Scientist.

Dr. Anzalone served as a member of the Compu-tational National Committee of INFN in Italy and is

the Head of the Computational Group of the INFN-LNS of Catania.

Santo Gammino was born in Riposto, Italy, in 1963.He received the “Laurea” degree in physics from theUniversity of Catania, Catania, Italy, in 1987.

He has been with Laboratori Nazionali del Sud,Istituto Nazionale di Fisica Nucleare (INFN-LNS),Catania, since 1988, where he became a ResearchPhysicist in 1990 and a Principal Research Physi-cist in 2002. His current research interests includethe production of monocharged and highly chargedbeams and their acceleration. He proposed differentinnovative concepts for the development of electron

cyclotron resonance (ECR) ion sources, and he actively worked on theconstruction of many different ECR ion sources. His project SERSE camein operation in 1997, and for many years, it was on the forefront for theproduction of HCIs. This activity has taken in the last years to the developmentof the so-called “third generation ECRIS,” as the MS-ECRIS source underconstruction at GSI, Darmstadt, Germany. He has designed and built othertypes of ion sources, as laser ion sources and the microwave discharge ionsources named MIDAS and TRIPS, for high efficiency ionization of recoilsand intense monocharged beam production. He worked during the nineties onthe development of the K-800 superconducting cyclotron and on the designand construction of the EXCYT radioactive beam facility at INFN-LNS.

Dr. Gammino served as a member of the National Committee of INFN forthe Technological Research from 1996 to 2002.


Francesco Musumeci was born in Catania, Italy, in1949.

He is a Full Professor of applied physics with theEngineering Faculty, University of Catania, Cata-nia. He is a Scientific Researcher with Labora-tori Nazionali del Sud, Istituto Nazionale di FisicaNucleare, Catania and a Visiting Professor with theUniversity of Washington, Seattle, WA, USA, andthe University of Kyoto, Kyoto, Japan. His researchactivities were focused in the field of solar energy, onthe interaction between electromagnetic waves and

rough metal surfaces, and on the dielectric properties of aqueous solutions. Hiscurrent research interests include the investigation of ultraweak luminescense,spontaneous and photo induced, and biological systems.

Alessia Spitaleri was born in Catania, Italy, in1979. She received the “Laurea” degree in computerengineering from the University of Catania, Catania,in 2006.

She has been with Laboratori Nazionali del Sud,Istituto Nazionale di Fisica Nucleare, Catania, sinceSeptember 2007, first with a two-year technologyscholarship and then with an annual scholarshipfrom the “Centro Siciliano di Fisica Nucleare eStruttura della Materia” of Catania, Catania. Hercurrent research interests include simulations of laser

produced plasmas.

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Study of Laser Plasmas Dynamics Through Real and Virtual Langmuir Probes