High-current ��1 kA�, relativistic ��200 keV� pulsedelectron beams with a duration of 10−7–10−5 s have foundextensive applications in scientific research and industry, forinstance, for pumping gaseous lasers, surface treatment,high-power microwave, and x-ray fluxes generation.1–3 Togenerate an electron beam with a moderate energy of severalhundreds of keV, electron diodes with active plasmacathodes2,4 �i.e., when the cathode plasma is produced priorto the application of the accelerating pulse� become prefer-able to diodes operating with either explosive emission5 orflashover6 plasmas. The application of an active plasma cath-ode allows one to control the plasma parameters �density andtemperature� and to generate electron beams with uniformcross-sectional electron current density distribution withouttime delay with respect to the beginning of the acceleratingpulse. The latter becomes a problematic issue in the case ofexplosive or flashover plasmas when the amplitude and risetime of the accelerating electric field are �50 kV /cm and�1012 V / �cm s�, respectively.6,7
A ferroelectric plasma source8,9 �FPS� assisted hollowanode �HA� can be considered as one of the advanced activeplasma electron sources, which can be used to generate elec-tron beams with a current density up to 30 A /cm2, pulseduration up to several milliseconds, and cross-sectional areaof several tens of cm2.4,10 The FPS-assisted HA does notrequire additional continuous electron sources for its opera-tion as do the plasma sources described in Refs. 4 and 11–13,where either thermionic cathode or magnetron or arc plasmasources were used to sustain hollow cathode and HA dis-charges.
Recent experiments4,10 have shown that FPS-assistedHA discharge allows reliable and reproducible plasma gen-
eration at a pressure in the range 10−5–10−4 Torr and a uni-form current density electron beam to be extracted by apply-ing a high-voltage pulse with an amplitude of �250 kV andpulse duration of �300 ns. It was shown that FPS-assistedHA high-current ��1 kA, �20 �s� discharge can be con-sidered as a self-sustaining discharge due to the continuousformation of the FPS surface plasma, which serves as analmost unlimited electron source. The HA discharge is initi-ated by the formation of the plasma at the front surface of theferroelectric sample due to incomplete surface dischargesinitiated at triple points of the ringlike front electrode when ananosecond time duration, high-voltage �several kilovolts�driving pulse is applied to the rear solid electrode. Spectro-scopic research showed that the density and electron tem-perature of the initial FPS plasma are, respectively,npl�1013 cm−3 and Te�6 eV in the vicinity of the ferro-electric surface. Thermal expansion of this plasma inside theHA leads to the beginning of the main HA high-current gasdischarge supplied by an �5 kV pulsed low-impedance gen-erator. This discharge occurring between the HA walls andFPS front electrode is initiated by the current flowingthrough the plasma. The time delay between the formation ofthe FPS initial plasma and the beginning of the HA plasmadischarge with a current amplitude of �1 kA was found tobe dependent on the background pressure and was varied inthe range of 1–8 �s for the range of pressure 5�10−4–5�10−5 Torr. Using spectroscopic and Thompson scatteringdiagnostics,14,15 it was found that the HA discharge initiationincreases significantly the density of the surface plasma, upto npl�5�1014 cm−3, probably due to the continuous bom-bardment of the FPS surface by the HA plasma ions. Here letus note that it was shown that the HA plasma obtains apositive potential of �10 V with respect to the HA walls
and �200 V with respect to the FPS.16 It was found alsothat the process of dense plasma expansion inside the HAcavity occurs with a typical velocity of �106 cm /s. Namely,plasma with a density of �1012 cm−3 appears in the vicinityof the HA output grid with a time delay of �15 �s withrespect to the beginning of the HA discharge with a currentamplitude of �1 kA. In addition, it was found that the HAdischarge current is sustained mostly by thermal electronswith an average temperature Te�6 eV. However, a fastcomponent ��20%� of electrons with energy �50�20 eVwas also obtained.10 The appearance and influence of theseelectrons on HA bulk plasma and discharge parameters re-quire additional research. Also, our understanding of the evo-lution of the HA discharge at a background pressure in therange 10−4–10−5 Torr is far from the clear yet.
In the present paper we characterize the FPS-assistedHA operation using time- and space-resolved laser inducedfluorescence �LIF� nonperturbing diagnostics. This sensitivespectroscopic technique allows one to determine the plasmaion velocity distribution function �VDF� and plasma densityevolution. The obtained results are compared with the modelof the FPS plasma diffusion inside the HA cavity.
II. EXPERIMENTAL SETUP AND DIAGNOSTICS
Experiments were carried out using the HA design �seeRefs. 10 and 15� at a background Ar�95%�+H2�5%� gaspressure of �2�10−4 Torr kept by two turbomolecularpumps. The HA was made of a hollow stainless-steel cylin-der 25 cm in diameter with seven identical FPSs placed atthe bottom of the HA cylinder on a cathode disk 10 cmin diameter �see Fig. 1�. Each FPS8,9 was made of a ferro-electric BaTi-based ceramic sample with ring-type frontand solid rear electrodes. Application of a driving pulse��8 kV, �200 ns� to FPSs causes plasma to form on theFPS front surfaces. Expansion of this plasma inside the HAcavity leads to the initiation of the HA discharge supplied bythe PFN generator ��5 kV, 20 �s�. The HA outside gridwas decoupled from the HA cavity by a low-inductance re-sistor of 50 � and 2 �F capacitor connected in parallel. Itwas shown that such decoupling allows one to decrease the
plasma penetration through the grid significantly, due tonegative autobias grid potential.10
A tunable �510–715 nm� dye laser Continuum ND6000�spectral line full width at half maximum �FWHM� of 0.0019nm at �=560 nm� pumped by a pulsed neodymium-dopedyttrium aluminum garnet SureLite laser ��=532 nm, pulseduration of 8 ns� was used to form a laser beam with energyof 2 mJ at the desired wavelength. An iris diaphragm and aset of calibrated neutral density filters were used to attenuatethe laser beam intensity and its spatial transformation. Thelaser beam ��6 mm in diameter�, after its propagationthrough the HA plasma, was absorbed by a graphite damperplaced at the bottom of vacuum chamber. A photomultipliertube �PMT, Hamamatsu R1104� with an achromatic lens, in-terference filter �spectral bandpass of 5 nm at �=461 nm�and a set of collimators was used to collect photons emittedfrom the intersection volume �5�10�6 mm3� of the laserbeam and plasma.
The LIF measurements were carried out using the threelevel Ar II scheme. A brief description of the LIF diagnostictechnique is as follows. The Ar ions from the 3d 2G9/2 meta-stable level �lifetime �20 �s� can be excited to the4p 2F7/2 upper electronic level by absorbing laser resonantphotons at �0=611.492 nm. The electrons from this upperlevel then spontaneously decay to the 4s 2D5/2 level by radi-ating fluorescence photons at 460.957 nm. By detuning thelaser from the resonance wavelength the Ar ions having ap-propriate velocity in the direction of the laser beam can stillundergo excitation to the upper level due to the Dopplereffect. Indeed, for a moving ion having velocity V, the reso-nant wavelength of transition �res in the laboratory frame,which is �0 in the rest frame of the moving ion, is Dopplershifted as �res=�0+k�V. Thus, neglecting the laser line-width and assuming that the number of fluorescence photonsis proportional to the population of Ar ions metastable state,one can obtain the VDF of Ar ions using the dependence ofthe LIF intensity on the laser wavelength, i.e., LIF excitationspectrum. If the Ar ions are in thermal equilibrium one candetermine the ion temperature as well.
In fact, the above assumptions should be checked accu-rately in order to obtain the actual VDF of the Ar ions. Let usconsider the first assumption, i.e., the effect of a finite laserbandwidth. Suppose that the population density of states 0�metastable� and 1 �upper� are n0 and n1, correspondingly.If the laser tuned at wavelength � has a bandwidth �,the velocities of absorbing ions should be in the rangeV=�� around V=���−�01�. Here �01= �E2−E1� /h is theresonant frequency of the transition 0→1, E1 and E2 are theenergy of atomic states 0 and 1, respectively, h is the Plankconstant, and � is the laser frequency. Thus the laser finitebandwidth leads to an additional change in the state popula-tion densities n0 and n1 for ions with velocities in the range����−�01�−�� /2; ���−�01�+�� /2�. For the laser used��=1.5 GHz� one obtains the limit in the temperature mea-surements of Ar species �0.11 eV.
In fact, LIF diagnostics is routinely used to determineparticle temperature in dc plasmas using tunable low-powerful dc lasers.17,18 However, for a short living �micro-second timescale� plasma one has to use a pulsed laser and
FIG. 1. �Color online� Experimental setup.
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adjust both the laser pulse duration and power for properdetection of LIF photons. An excess in the laser powercan lead to Stark broadening of the LIF spectrum by thelaser beam electric field.19 Estimates of the Starkbroadening20 of the Ar II 3s22p4�1D�4p�2F�-3s22p4�1D�3d�2G� ��=611.492 nm� showed that this effect becomes im-portant at electric field �50 kV /cm, which corresponds to apower density of �106 W /cm2.
The most important effect that leads to a significant errorin the ion temperature determination is related to large laserintensity, namely, the so-called saturation effect caused byartificial LIF spectrum broadening.21 This effect leads also toa nonlinear mode of LIF measurement, i.e., when the amountof fluorescence photons becomes not proportional to thepopulation of the pumped Ar state. This effect occurs whenthe absorption photon rate �electron transition from state 0 tostate 1� becomes almost equal to the stimulated absorptionrate �electron transition from state 1 to state 0� and signifi-cantly exceeds the spontaneous rate �electron transition fromstate 1 to lower state 2�. In this case, a further increase in thelaser intensity does not lead to an increase in the spontaneousemission. Moreover, when this effect occurs at the laserspectral line wings, i.e., at ���L, where �L is the centrallaser frequency, one obtains artificial LIF spectrum broaden-ing. The latter leads to the ion �atom� temperature beingsignificantly overestimated. In order to avoid this artificialbroadening, the laser intensity should be decreased. How-ever, this results in a weaker LIF signal, which becomescomparable with the noise signal. Thus, one has to find alaser intensity, which will supply a strong LIF signal, on theone hand, and on the other will not cause artificial LIF spec-trum broadening.
The optimization of the laser intensity, which allows oneto avoid the saturation effect, was considered in detail in thepaper by Goeckner and Goree.21 Using semiclassical treat-ment of collisionless plasma, the dependence of the FWHMof the LIF spectrum was obtained and three experimentalmethods were suggested to adjust the optimum laser inten-
sity. However, several misprints in Ref. 21 �for instance,there is a minus sign missing in the exponent’s argument forthe ion velocity distribution, and in Eq. �6� for the number ofcollected fluorescence photons, all powers � 1/2� should bepositive, otherwise a negative LIF signal is received� makethe application of the expressions presented in the paper forLIF modeling problematic. Thus, following the generalconcept of Ref. 21, we have solved the set of rate equationsfor the ion distribution functions f i�x ,V , t� of three ion states�0, 1, 2� involved in the LIF process mentioned above. Forconvenience we rewrite the set of rate equations for states 0,1 with the same definitions as in Ref. 21:
d
dtf0�x,V,t� = f1�x,V,t��A10 + B10��x,V��
− f0�x,v,t�� 1
0+ B01��x,V�� , �1�
d
dtf1�x,V,t� = f0�x,V,t�B01��x,V�
− f1�x,v,t�� 1
1+ B10��x,V�� , �2�
where ��x ,V�=1 /4��0+�d�L�� ,�ij ,V�I�x ,�� is the effective
isotropic laser intensity. Here L�� ,�ij ,V� is the ion ab-sorption spectrum, Aij is the Einstein spontaneous emis-sion coefficient, Bij is the Einstein absorption coefficient,i is the lifetime of the atomic state, and I�x ,��= I0�4 ln 2 /����2�1/2exp4 ln 2���−�l� / ����2 is the laserintensity spectrum assumed to be constant during the laserpulse duration and having a Gaussian frequency distributionwith a laser intensity I0 at �l and bandwidth �. Also, in Eqs.�1� and �2� it was assumed that the laser absorption �0–1�,induced �1–0�, and spontaneous �1–2� emission is the domi-nant process which determines the ion state 1 density popu-lation. The solutions of Eqs. �1� and �2� are
�x ,v�, d=1 /1+B01��x ,v�. C1 and C2 are the coefficients,which are determined using the initial conditions for the
plasma ion Maxwell velocity distribution prior to the appli-
cation of the laser pulse: f0�x ,V , t�0�=n0�M /2�Te−MV2/2T,
f1�x ,V , t�0�=n1�M /2�Te−MV2/2T where n0 and n1 are the
population density of ions in states 0 and 1 and M and T arethe ion mass and temperature, respectively.
The LIF photons are emitted as a result of spontaneousdecay from upper state �1� to state �2�. Thus, the total num-ber of collected fluorescence photons reads
113504-3 Laser induced fluorescence of the ferroelectric plasma… Phys. Plasmas 16, 113504 �2009�
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Here �1,2=1 /2�−�b+d���b2−2bd+d2+4ac� are the eigen-values of Eqs. �1� and �2� and �=b−d= �1 /0�+B10��x ,V�− �1 /1�−B01��x ,V�.
Now, using Eq. �5�, one can calculate the dependence ofthe LIF photon flux and the FWHM of the LIF spectrum onthe intensity of the laser with a given bandwidth, i.e., esti-mate the laser power, which one requires for its nonsaturatedoperation. Namely, using the npl�1013 cm−3 determined inour previous research �see Ref. 15� the following dependen-cies were calculated: �a� the dependence of the LIF photonflux on the laser intensity when the laser was turned to reso-nance frequency �see Fig. 2�a�� and �b� the dependence of theLIF spectrum FWHM on the laser intensity for differentplasma ion temperatures �Fig. 2�b��. The dependenciesshown in Fig. 2 were used to estimate the optimum laserpower as described in Ref. 21. For instance, assumingTi=8 eV and Ti=0.1 eV, one does not obtain artificial LIFspectrum broadening until the laser power is �3�103 and�30 W /cm2, respectively.
To summarize, the LIF diagnostic technique is a power-ful tool for pulsed plasma study, namely, for determiningVDF with high time and space resolutions. However, the useof a pulsed tunable laser requires that the laser intensity becarefully adjusted in order to avoid an error in the ion VDFmeasurements due to artificial LIF spectrum broadening.
III. EXPERIMENTAL RESULTS
The LIF experiments were carried out at different dis-tances from the central FPS �3, 6, 10, and 14 cm� during theHA discharge. Typical waveforms of the HA discharge cur-rent and voltage are shown in Fig. 3, where zero time corre-sponds to the beginning of the FPS driving pulse.
In order to determine the LIF linear mode, experimentson laser power optimization were carried out. Experimentaldependencies of the FWHM of the LIF spectrum and LIFintensity on the laser intensity at the laser resonant wave-length are shown in Fig. 4. One can see that the nonlinearmode of the LIF is realized when the laser intensity is�2.5�103 W /cm2. This agrees satisfactorily with the simu-lation data �see Fig. 2�.
First, the LIF measurements were carried out with thedye laser tuned to the Ar II resonance transition 3d 2G9/2→4p 2F7/2. This condition leads to the maximal LIF signal-to-noise ratio �the collected LIF photons are irradiatedmostly by Ar II ions with velocities in the orthogonal planerelative to the laser beam direction�. In the case of linear LIF,the temporal evolution of the fluorescence photon flux rep-resents the plasma Ar ion density evolution. The temporaldependence of the LIF intensity during the HA discharge isshown in Fig. 5. One can see a significantly faster rise in theplasma density at d=3 cm and d=6 cm �Fig. 5, curves 2and 3, respectively� than at d=10 cm and d=14 cm �Fig. 5,curves 4 and 5, respectively�. In addition, at all tested
FIG. 2. �Color online� Dependencies of �a� a number of LIF photons onlaser intensity at resonant wavelength of the laser and �b� FWHM of the LIFspectrum on the laser intensity for different plasma ion temperatures: ���0.1 eV, ��� 1 eV, and ��� 8 eV.
FIG. 3. �Color online� Typical waveforms of the HA discharge current andvoltage. Background pressure of 2�10−4 Torr.
113504-4 Vekselman et al. Phys. Plasmas 16, 113504 �2009�
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distances the LIF photon flux has maximum amplitude with adecrease following it. The time delay �with respect to thebeginning of the HA discharge� when the LIF photon fluxreaches its maximum amplitude increases gradually with theincrease in the distance d. Also, one obtains a gradual de-crease in the amount of LIF photons versus the distance fromthe FPS, which can be associated with a decrease in the HAplasma density.
The measurements of Ar ions VDF were also performedat different distances from FPSs during the HA discharge.The summarized data are presented in Fig. 6, where the VDFwere fitted by Gaussian and the “effective” temperature wasintroduced. The main feature of Ar ions temperature behav-ior is that it monotonically increases from �1 eV up to 8 eVduring the HA discharge.
In addition, the investigation of the LIF intensitydependence on the HA discharge current Id �in the range430–970 A� showed that the number of fluorescence photonsis proportional to the value of Id �see Fig. 7�. These data canbe explained by the increase in the HA plasma density with
the increase in Id value, which agrees with our spectroscopicdata �described in Ref. 22� and confirms the coupling be-tween the population of upper level 4p 2F7/2 and plasmadensity.
Finally, in order to check the LIF results concerning thehigh Ar II ion temperature, spectroscopic measurements werecarried out as well. A 750 mm Jobin–Yvon 750M spectrom-eter �2400 gr/mm� with a fast ICCD camera 4Quik 04Aat the spectrometer output slit was used to record theplasma spectra. However, there were several limitations inspectroscopic measurements related to spectral resolution,0.13 Å/pixel and the large time interval of the light acquisi-tion ��10 �s�. These limitations were related to the neces-sity to collect sufficient light in order to obtain a reliableintensity of spectral lines. Also, because the HA plasma den-sity decreases with the increase in the distance with respectto the FPS, these measurements were successful only at dis-tances �30 mm. The plasma ion temperatures were ob-tained from the measured broadening of the C II �6578Å�
FIG. 4. Experimental dependencies of �a� FWHM of the LIF spectrum onlaser intensity and �b� LIF intensity on laser intensity at the laser resonantwavelength.
FIG. 5. �Color online� Time dependences of the LIF intensity obtained atdifferent distances with respect to the FPS: �1� 3 cm, �2� 6 cm, �3� 10 cm,and �4� 14 cm.
FIG. 6. Time dependence of the plasma Ar ions temperature during the HAdischarge at different distances from the FPS: �1� 6 cm, �2� 10 cm, and �3�14 cm.
FIG. 7. Dependence of the LIF intensity vs the HA discharge currentamplitude.
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and Ar II �4348� ion spectral lines. In these experiments, acarbon thin layer was added at the front surface of the ferro-electric. It was found that C II and Ar II ion temperatures are7.2�2 and 17�12 eV, respectively. Thus, one can see thatthe spectroscopic data also show high plasma ion tempera-tures. Also, one can see that the available spectral resolutionof the experimental setup leads to a significant increase inthe errors in ion temperature with the increase in the atomicnumber of element.
IV. DISCUSSION
The data presented in Fig. 5 indicate the time and spaceevolution of the plasma density inside the HA. Let us con-sider a simplified one-dimensional �1D� model of HA plasmaevolution. The HA discharge triggered by the FPS plasmadevelops gradually with a time delay of d�8 �s with re-spect to the FPS plasma generation �see Fig. 2�. During thistransition period the density of the plasma generated by theFPSs increases up to Nf =2.5�1014 cm−3, which can be ap-proximated as
Ni�t� � Nf tanh���t + �� , �6�
where =1 ns is the time constant and ��0.3 �s−1 is theparameter, which determines the asymptotic increase in Ni�t�up to Nf during the first 8 �s of the HA discharge. TheseFPS plasma flows expand inside the HA cavity and causeionization of Ar neutrals by the plasma electrons and fastnonthermal electrons.10 The ionized Ar atoms �Ar II� becomeinvolved in the plasma expansion, experiencing further ion-ization �Ar II→Ar III�. The density of Ar II ions dependson the temporal and spatial parameters of the HA plasmaand nonthermal electron density and energy. Here it is as-sumed that the density of the Ar neutral is smaller than thedensity of the HA plasma, which is reasonable for the back-ground pressure of the Ar gas �10−4 Torr� used in the presentexperiments.
Following the model described in Ref. 23, the expansionof the plasma having width L� ld �here ld is the Debyelength� in vacuum toward the output HA grid can be charac-terized by a plasma front layer, where significant deviationfrom quasineutrality occurs �see Fig. 8�. The rear plasmaboundary is located at x=0, namely, in the vicinity of theFPS front surface, i.e., behind the electrical sheath existingbetween the FPS front surface and the HA plasma where theplasma density can be estimated using Eq. �6�. At the frontplasma layer a negative space charge exists, which is com-pensated by the adjacent and rear �at the rear edge of theplasma� positive space charges. These boundary charges areresponsible for the potential difference ���Const betweenthe plasma boundaries and, respectively, for the electric fieldE�t�=�� / �D�t+�� in the plasma, where D�Const is theplasma front expansion velocity. Here let us note that thiselectric field does not lead to a violation of the plasmaquasineutrality, i.e., in the plasma bulk ne=�iZini. The equa-tion for the plasma ion motion under the electric field E�t�can be written as
�U
�t+ U
�U
�x=
vt +
; v =e��
MiD. �7�
Here e, M, and U�x , t� are the charge, mass, and velocity ofthe plasma ions, respectively. Further it will be shown thatthe parameter v determines the ion velocity in the vicinity ofx=0. The self-similarly solution of Eq. �7� can be presentedas a rarefaction wave,
U�x,t� = v + x/�t + � . �8�
Taking into account approximately conical plasma expan-sion, the discontinuity equation for plasma ions reads:
��NS�x���t
+��NUS�x��
�x= 0. �9�
Here N�t ,x� is the ion density and S�x�=S0+��xtg��2 is thecross-sectional area of the plasma flow having conical formwith half divergence angle �. The solution of Eq. �9� reads:
N�x,t� = �S0N0
S�x�exp�− � x
v�t + ��� �tanh���t + �exp�− � x
v�t + ���� . �10�
Here let us note that this model does not consider theplasma front boundary with a typical thickness of ld wherethe violation of the plasma quasineutrality occurs. The veloc-ity of the plasma front D�106 cm /s was roughly estimatedusing the data of the beginning of the Ar II ion spontaneousradiation at different distances from the FPS. This value of Dis close to the double ion sound velocity cs= �Te /M��4.5�105 cm /s, where Te�8 eV and M is the mass of the Arion. Concerning the plasma velocity v in the vicinity x�0,one can suppose that, due to the adiabatically slow change inthe plasma density at this location during the HA discharge,i.e., at t�8 �s, this velocity is v�cs. In the opposite case,
FIG. 8. �Color online� Qualitative scheme of the expanding plasma with itspotential distribution.
113504-6 Vekselman et al. Phys. Plasmas 16, 113504 �2009�
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i.e., if v�cs or v�cs, one should obtain either a decrease oran increase in the plasma density during the HA operation atthis location. The equality of v�cs allows one to considerthat the rarefaction wave, propagating in the direction x�0with velocity cs, is transferred with velocity v toward theplasma layer front. Thus, the ion density N �t ,x�0� is deter-mined by the processes that govern plasma generation nearthe FPS �see Eq. �6��.
Results of this model, i.e., plasma density evolution in-side the HA at different distances from the FPS and at dif-ferent times of the HA discharge, are shown in Fig. 9. Now,using modeling results of the plasma density evolution, time-dependent collisional radiative modeling24 �CRM� was car-ried out with regard to the Ar atoms for the plasma electrontemperature in the range of Te=4–8 eV and in the presenceof a nonthermal electron flux having energy in the range40–80 eV and density in the range 10%–20% of the HAplasma density. The best fit between the CRM and experi-mental results was obtained for Te=8 eV and a flux of non-thermal electrons with energy of 50�20 eV and density of20% of the HA plasma density. Examples of the results ofthis modeling are shown in Fig. 10. Namely, the temporalevolution of Ar I, Ar II, and Ar III particles at a distance of6 cm from the FPS are presented in Fig. 10�a� and Ar II iontemporal evolution at different distances from the FPS isshown in Fig. 10�b�. One can see that the time delay in theAr II ions’ appearance, the rise in their density, and theirburning �ionization� time increase with the distance from theFPS. These data agree well with the experimentally obtaineddata. Moreover, CRM allows one to obtain the temporal evo-lution of the density population of the desired atomic states,which are metastable 2G and upper 2F levels of Ar II ion inthe case of the LIF scheme applied in the present research. Atypical time evolution of these levels subjected to laser ra-diation is shown in Fig. 11 and in the inset in this figure withthe increased time scale. One can see the expected drasticdecrease in the population of the metastable level with asimultaneous increase in the density population of the upperlevel. Let us note that in a time scale of �10−5 s the density
population of 2F level already returns to its equilibrium valuedetermined by the collision excitations process in the plasma.Based on the CRM data obtained at different time delayswith respect to the beginning of the HA discharge, the tem-poral evolution of the population density of the upper level,i.e., the time-dependent LIF photon flux, was obtained fordifferent distances from the FPS. The comparison betweenthe time dependent density population of the 2F level and theexperimentally obtained LIF photon flux at a distance of6 cm from the FPS is shown in Fig. 12. One can see a goodagreement between the simulated and experimental data.Thus, one can conclude that the suggested model of plasmaflows generated at the surface of the FPS and expanding intothe HA anode gives a correct scenario of the HA high-currentdischarge development. Also, the relatively fast increase inthe LIF intensity at distances of 3 and 6 cm from FPSs oc-curs due to the overlapping of plasma flows generated by
FIG. 9. �Color online� The time evolution of the plasma density at differentdistances from the FPS.
FIG. 10. �Color online� Results of CRM calculations for Te=8 eV, electronbeam density of 0.2ne. �a� The time dependence of Ar I–Ar III particlesrelative density at a distance of 6 cm from the FPS. �b� Time dependence ofAr II ion density at different distances from the FPS.
FIG. 11. �Color online� Time evolution of the population density of themetastable IIG and upper 2F levels of Ar II ion subjected to the laserradiation.
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individual FPSs. A rough estimate gives the growth in LIFintensity by a factor of 7 at these distances, which agreeswell with the experimental data.
Now, let us discuss the ion temperature. Data obtainedusing LIF showed that the Ar II ion effective temperaturegradually increases during the HA high-current dischargefrom less than 1 to 8 eV at distances �10 cm from the FPS.At smaller distances the Ar II ion effective temperature wasfound to be �5 eV already at d�8 �s increasing up to�9 eV at d�20 �s. The increase in the plasma iontemperature cannot be explained by the plasma electron-ioncollisions because of the too-small plasma electron-ion col-lision rate, which can be estimated as25 ei=0.7ee=2.05�10−6neTe ln �e=1.3�10−7 s−1 for Te�6 eV and plasmaelectron density ne�1013 cm−3, where ee is the plasmaelectron-electron frequency and ln ��10 is the Coulomblogarithm. In the case of the Maxwellian energy distributionof electrons and ions one can estimate the equilibration timeas26 �eq= �3.15�108ATe� / �ni ln ��=7.56�10−4 s, whereni=ne is the plasma ion density, A=40 is the atomic numberof Ar and Te is measured in eV. Also, a large ion temperaturecannot be explained by the fast nonthermal electron heating.Indeed, the typical time of the ion heating by “hot” electronscan be estimated as27 h�17A ·The
3/2 /ne�10−3 s, where The isthe “hot” electron “temperature” in 0K degrees.
At present we do not know the exact phenomena�phenomenon�, which govern�s� plasma ion heating duringthe HA high-current discharge, and additional research is re-quired. For instance, searching for electric fields �amplitudeand frequency spectrum� in the HA plasma can be a keyissue in determining the mechanism governing the plasmaion heating. Below, we will qualitatively and briefly considersome of these phenomena, which may lead to the highplasma ion “temperature” that was obtained.
Let us start with kinetic plasma instabilities, which canarise in the current-carrying plasma in the presence of a non-thermal electron beam. In such plasma one can consider fastarising beam instability with a nanosecond timescale incre-
ment ����p�ne /np��Ve2 / ��V�2�, where ne is the density of
the electron beam and Ve is the electron beam velocity�.28
This instability occurs due to resonance energy exchange be-tween the beam electrons having a velocity distributiondf /dV�V=� /k��0 and the plasma wave with phase velocityV�Ve, where � and k are the frequency and wave number ofthe plasma wave, respectively. This instability leads to theelectron beam bunching and, respectively, the plasma waveenergy density increasing up to E2 /4��nemeVe�ne /np�1/3
�1.5�1014 eV /cm3, where me is the electron mass. Thedissipation of the plasma wave energy leads to the plasmaion heating up to �10 eV. Approximately the same resultscan be obtained in the case of the Buneman instability29 �theincrement ��0.69�p�me /mi�1/3 of this instability rise time isalso in the nanosecond time scale� when one considerscurrent-carrying plasma electrons with average velocity ex-ceeding that of the plasma ion.
Other kinetic instabilities typical for the current-carryingplasma are the ion acoustic and parametricinstabilities.28,30–33 The ion acoustic instability, which hasa qualitative explanation similar to that of beam instability,is realized when the plasma electron current velocity�Vec= je /ene� is less than the plasma thermal velocity VTe
but exceeds ion sound velocity cs= �kTe /mi�1/2. This typeof instability with an increment in �=��me /mi����Vec /cs�cos �−1�, where � is the angle between the di-rection of the current carrying electrons’ velocity and thedirection of the ion-sound wave propagation, leads to plasmaion heating due to Landau damping of the ion-sound waveson plasma ions when the phase velocity of the ion-acousticwave becomes comparable with Vec. The saturation of thisinstability occurs when the plasma ions acquired velocityequals ion sound velocity. A parametric instability occurs dueto nonlinear interaction between low frequency ion-acousticand high-frequency Langmuir plasma waves. This type ofinstability, which also can be realized in our current-carryingplasma �low frequency ion acoustic instability� with nonther-mal electron beam �high-frequency Langmuir plasmawaves�, could be a reason for the large ion temperature.
The other phenomenon, which also could be responsiblefor the increase in the ion temperature, is the charge ex-change of the plasma ions when they interact with the HAwalls. In our earlier research16 it was shown that the plasmaacquires a positive potential of �10 V with respect to theHA walls. Thus, during the HA discharge inside the sheathformed between the plasma and the HA walls there is anemission of ions with energy Ei�10 eV from the plasmaboundary toward the walls. According to the data presentedin Ref. 32, during the interaction with the walls, almost allplasma ions capture electrons and reflect back toward theplasma as neutrals with energy �0.8 Ei. These neutrals willbe neutralized by the plasma electrons within the first fewhundreds of nanoseconds �see Fig. 9�, thus increasing the“effective temperature” of the HA plasma ions.
Finally, let us consider a simple model, which gives astraightforward explanation of the large ion temperature aswell. In the case of the plasma density ni=1013 cm−3, anaverage distance between two ions is ri= �3 /4�ni�1/3
�0.3 �m and the Debye radius rD=740�Te /ne�1/2�6 �m.
FIG. 12. �Color online� The comparison between the time dependent densitypopulation of the 2F level and the experimentally obtained LIF photon fluxat a distance of 6 cm from the FPS.
113504-8 Vekselman et al. Phys. Plasmas 16, 113504 �2009�
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Thus the location of the Ar atom can be considered in therange r0=0.1 �m�r�ri, where r0 is the radius of the Arneutral atom. In the case of ionization due to collisions withthe plasma electrons, the Ar ion acquires an average potentialenergy �U�= �ri�−1�r0
ri U�r�dr= �e2 ln�ri /r0�� /4��0ri. Whenthis potential energy is transferred to the kinetic energy ofthe ion, the latter acquires a velocity of �5�105 cm /s,which is close to ion sound velocity cs. This estimate con-siders that the mass of the neighboring ion, i.e., the nearestion with respect to the Ar II ion, is significantly larger thanthe Ar II ion mass. In the case of ion mass equality, the Ar IIion velocity will be �2�1/2 times smaller than cs and signifi-cantly smaller than cs in the case of light neighboring ions.The FPS generated plasma consists of different ions includ-ing ions with A�100.22 It is reasonable to consider that ionswith smaller mass will diffuse and fill the HA cavity fasterthan the ions with larger mass. Thus, at the beginning of theHA discharge one obtains a smaller Ar II ion effective tem-perature, which gradually increases when the heavy ions fillthe HA cavity.
V. CONCLUSIONS
Experimental research of the HA high-current dischargeusing time- and space-resolved pulsed LIF diagnostics re-vealed that the plasma filling of the HA cavity occurs due toexpansion of the plasma flows generated by the FPS. Theobtained LIF data showed a gradual time-dependent increasein the plasma density along the length of the HA cavity.These data were verified by the results of 1D modeling of theplasma expansion in vacuum and time-dependent CR mod-eling, which includes the presence of the nonthermal electronbeam. Thus, it was shown that, indeed, FPS can be consid-ered an almost unlimited source of the plasma, allowing oneto operate HA discharge at a low background pressure inmicrosecond and millisecond time scales without applyingadditional plasma sources.
Also, pulsed LIF diagnostics, which was tested on thesaturation effect both experimentally and numerically,showed that the HA plasma ion temperature gradually in-creases during the HA discharge, reaching �8 eV at the endof the discharge. Different phenomena, which could be re-sponsible for such an unusually large ion temperature, wereconsidered, namely, several plasma kinetic instabilities,charge-exchange processes during plasma ion interactionwith the HA walls, and a simple model of neutral atom ion-ization inside the Debay’s sphere. However, additional re-search related to electric field amplitude and frequency de-termination is strongly required in order to clarify the natureof this high plasma ion temperature.
ACKNOWLEDGMENTS
We wish to thank Evgeny Stambulchik for fruitful dis-cussions and comments. This research was supported by theBSF �Grant No. 2006373�.
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