PHYSICAL REVIEW E NOVEMBER 1997VOLUME 56, NUMBER 5
Spectroscopic investigation of highly transient pinch plasmas
K. Bergmann,1 O. N. Rosmej,2 F. B. Rosmej,3 A. Engel,1 C. Gavrilescu,4 W. Neff,5 and R. Lebert11 Lehrstuhl fur Lasertechnik, Steinbachstrasse 15, D-52074 Aachen, Germany
The temporal evolution of neon pinch plasmas, generated in a 2 kJplasma focus device, has been investi-gated by x-ray spectroscopic methods for two sets of device parameters. These two sets lead to characteristicdifferences of theK-shell emission. Stationary models are shown to fail to explain the experimental observa-tions even qualitatively. Transient spectra analysis shows that the characteristic differences observed can bereferred to different transient modes of plasma dynamics. The spectra analysis includes beside resonance linesalso dielectronic satellites and recombination continua. The results concerning the development of the plasmaparameters achieved by the spectra modeling are supported by independent measurements of the time resolvedK-shell emission and by optical streak images of the pinch plasma dynamics, which confirms the reliability ofthe transient spectroscopic analysis presented.@S1063-651X~97!12510-7#
PACS number~s!: 52.25.Nr, 52.55.Ez
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I. INTRODUCTION
Dense, high-Z plasmas with electron densities of abo1020 cm23 and temperatures of several 100 eV are intesources of pulsed radiation in the soft x-ray range~about 50eV–5 keV photon energy! and can be generated with labratory scale devices. Various devices for the generationsuch plasmas are under investigation: laser plasmas,Z-pinch,gas puffs, capillary discharges, vacuum sparks, or the plafocus. In this paper the plasma focus device is under dission @1#.
Typical time scales of collisional and radiative procesof such plasmas are of the same order of magnitude aslifetime, which is of about several nanoseconds. The naof the plasma development is therefore essentially transThe understanding of the various transient processes igreat importance for the specification according to differapplications and their optimization. This knowledge allowfor example, the tailoring of flexible x-ray sources havispecial spectral characteristics concerning wavelength reor bandwidth demanded by a given application. Furthermthe transient coupling in plasmas becomes of importancescaling down the devices to lower currents in order to htabletop size for laboratory applications. Especially for x-rlasers based on a gas discharge@2–4# the understanding othe transient coupling of the plasma parameters and radiaprocesses is a necessary precondition for, e.g., scaling dto lower wavelengths.
For the plasma focus under investigation the full setdetermining device parameters is accessible. The possibto correlate uniquely the device parameters and the plaparameters enables the deduction of scaling laws and opzation criteria.
The present paper deals with the experimental and thretical investigation of the plasma dynamics. X-ray spectscopic methods and transient spectra modeling for the in
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pretation of the experimental emission spectra have bemployed.
The usual approach to the investigation of transient pmas is obtaining the time-dependent plasma parametersthe magnetohydrodynamics~MHD! calculations and theirsubsequent use in a spectroscopic postprocessor~e.g.,@1,5–10#!, where often only a part of the spectral information liktotal yield or a few resonance lines is compared to expmental data.
In addition toK-shell resonance lines we also investigain detail dielectronic satellite spectra and recombination ctinua. The transient spectra modeling presented is basedfew crude assumptions concerning the qualitative evolutof the plasma parameters, which are confirmed by timesolved measurements. The absolute values of the plasmrameters are estimated by comparing the calculated timetegrated spectra to experimental highly resolved spectra.overall spectra modeling is shown to deliver reliable infomation about the time-dependent plasma parameters.shown that for the phase of plasma decay dielectronic salite spectra and photorecombination provide informatiabout different possible modes of plasma decay. Time ingrated spectra of transient neon pinch plasmas have bconsistently interpreted.
II. EXPERIMENTAL SETUP AND PLASMA FORMATION
The experiments were carried out using a plasma focuMather type@11#. A schematic drawing is given in Fig. 1The storage capacity (C536 mF! is connected by a lowinductance spark gap to the electrode system, which isbedded in a high-Z gas filling with pressures of several 1Pa. The anode radius wasa51 cm. The inductance of thecapacity bank, the electrical connections, and the switchof aboutL520 nH. The system is operated using a voltabetween 8 kV and 12 kV leading to pinch currents in t
range of 200–300 kA. More details concerning the devare described elsewhere@12,21#.
The current was measured using a calibrated magnprobe which was positioned in the electrode system nearend of the anode. This enables a measurement of thecurrent going through the pinch plasma which was shownbe different from the total device current due to leakage crents above the anode. Details concerning the setup forcurrent measurements and the leakage current behaviogiven in Ref.@12#.
The typical electron densities of the pinch plasma arethe range of 1020 cm23, electron temperatures are of thorder of several 100 eV. These parameters give rise tointensiveK-shell line emission, in particular those of the HHe- and Li-like ionization stages.
The spectra of the neon pinch plasmas were takenmeans of a cylindrically curved defocusing mica crystal psitioned in axial direction~see Fig. 1!. The curvature radiusof the crystal was 1 cm. The distance between the plaand the bent mica crystal (2d51.992 nm! was 33 cm. Toprevent visible light illuminating the detector~Fuji 80 x-rayfilm!, a beryllium foil with thickness 12mm was positionedbetween the pinch plasma and the crystal. The total speresolution, which is determined by that of the crystal~ofabout 1300! and a contribution due to the finite size of thsource in the respective wavelength region~about 400mm!,is of aboutl/Dl.900.
Time resolvedK-shell emission in axial direction~seeFig. 1! was investigated using a microchannel plate dete~MCP!, which has a temporal resolving power better thanns. The entrance of the MCP was covered by a 10mm alu-minum foil restricting the detected spectral range to walengths below 1 nm.
Images in the visible spectral regime of the collapsing aof the expanding pinch plasma were taken using a strcamera. A slit of 25mm width was placed between thplasma and the optics of the streak camera in order to cua small region in axial direction allowing us to measurecollapsing and expanding plasma layer~see Fig. 1!. In a dis-tance of 2.5 mm to the end of the anode a region of ab100 mm width in axial direction is observed. The time reslution of the streak measurement is better than 0.5 ns.
The development of the discharge can be divided ifour phases, which are also indicated in Fig. 1. In the fiphase a sliding discharge builds up on the insulator aapplying the voltage of the charged capacity to the electr
FIG. 1. Scheme of the plasma focus with the four phases ofdischarge development. In addition, the region covered by theused in the optical streak measurements is shown schematica
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system. This sliding discharge leads to a homogeneouslindrical plasma layer. In the second phase this layer iscelerated by Lorentz forces to the end of the anode collecthe neutral gas particles. Simultaneously the current riseits maximum value during this second phase.
The last two phases are similar to aZ-pinch dynamics.The plasma layer is accelerated towards the axis andreaching the axis the accumulated kinetic energy is cverted into thermal energy leading to a dense and hot piplasma. The temperatures achieved lead to emission fhighly charged ions. The process of thermalization of thekinetic energy goes in two steps. First the kinetic energythe ions is converted to thermal energy of the ion gas. Tkinetic energy of the collapsing electrons can be neglecbecause of their low mass. The electrons are heated byhot ion gas.
The last two phases of the discharge determine thenamics of the pinch plasma and the x-ray production. It cbe shown that for the device under investigation three devparameters uniquely determine these two phases for a fielement. These parameters are the currentI 0 at the beginningof the compression phase, the number density of the neugas or the working gas pressurep and the radius of the anoda @13#.
These device parameters can be correlated with the pplasma parameters. Based on similarity consideratiowhich are discussed in more detail in Ref.@13#, the ion andelectron temperatures achievable in the pinch plasma scaTe}I 0
2/(pa2). Keeping this parameter constant, i.e., discuing plasmas in equal temperature regimes, and assumnegligible radiative losses compared to the total energy ininto the pinch plasma the ion density is expected to be pportional to the neutral gas pressureni}p.
The transient plasma dynamics is essentially determiby the confinement parameternet , wheret is the lifetime ofthe pinch plasma. So by using different neutral gas pressthe confinement parameter can be varied as will be shobelow.
III. X-RAY EMISSION OF NEON PINCH PLASMAS
Figures 2~a! and 2~b! show theK-shell emission lines ofH-, He-, and Li-like neon ions taken at working gas pressuof 400 Pa (I 05260 kA 610 kA! and 200 Pa (I 05250 kA 610 kA!, respectively. Figure 2~a! shows the H-like series1s 2S1/2–np 2P1/2,3/2 up to n56 and the corresponding series of He-like ions 1s2 1S0–1snp 1P1 up to the series limit.The present spectral resolution permits the clear identifition up to 1s2 1S0–1s7p 1P1. Also resolved are the He-likeresonanceW line 1s2 1S021s2p 1P1 and intercombinationY line 1s2 1S021s2p 3P1.
Besides the emission lines originating from single excilevels there are observed numerous screened resonancesitions originating from the double excited autoionizing leels 2lnl 8 and 1s2lnl 8. These double excited levels give risto so-called dielectronic satellite spectra. Forn52 these di-electronic satellites are well separated from then52 reso-nance lines. Higher order satellites (n>3) have two radia-tive decay channels:
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56 5961SPECTROSCOPIC INVESTIGATION OF HIGHLY . . .
1s2lnl 8→H 1s2nl81\v
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The first channel gives rise to satellite transitions onred wing of the He-likeW line, which are not resolved. Theresult in a ‘‘red’’ asymmetry of theW line. The second decay channel is resolved from their respective resonance liIn the spectrum of Fig. 2~a! the transitions 1s2lnl 821s22l 8are seen forn53,4. The He-like autoionizing levels 2lnl 8have similar decay channels resulting in a red asymmetrythe Lya line. However, forn>3 the intensity is rather weaand can hardly be used for diagnostics. The observed rnance and satellite lines are well suited for the determinaof plasma parameters~see, e.g., the review of Boikoet al.@14#!.
The spectra taken at 200 Pa and 400 Pa@Figs. 2~a! and2~b!# show characteristic differences in the line emission
~1! Dielectronic satellite spectra and recombination cotinuum are practically absent for the 200 Pa dischargerather strong for 400 Pa.
~2! The intensity ratio of the Lya to W line for the 400 Paspectrum is much higher than for 200 Pa.
In a stationary treatment of the time integrated specconditions~1! and ~2! contradict each other. To obtain verlow satellite spectra, the temperature must be of abouteV. For such electron temperature, the emission inLya-line must exceed that of theW line by a factor of 2.5–4.5 for electron densities in the range of 1018–1020cm23. Theexperimentally observed ratio for the 200 Pa spectrumhowever, only 0.4. On the other hand, the high intense
FIG. 2. ~a! Experimental x-ray neon spectrum showing the 1np and 1s2-1snp series of H- and He-like ions together with iHe-like and Li-like satellites for the 400 Pa case.~b! Experimentalx-ray spectrum at 200 Pa neon pressure.
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ellite spectra in the 400 Pa case@Fig. 2~a!# suggest an electron temperature of about 200 eV resulting in a Lya intensitymuch lower than that of theW line, just opposite to theexperimental observation. We have investigated also varradiation transport effects~different effective photon pathlengths, ionization balance shift!. However, the principal dis-crepancies remain and cannot be resolved in a statiotreatment.
It will be shown below that a complete transient specanalysis can resolve the discrepancies outlined above.
IV. TRANSIENT SIMULATION OF PLASMA DYNAMICS
Transient effects in the line formation become of increing importance if the time scales for atomic processes aresmall in comparison to the time scales for the change ofplasma parameters. E.g., if the plasma suffers a fast heaprocess the ion abundance and the line emission originafrom different ionization levels do not correspond to telectron temperature. Both lag behind the electron tempture. An example for Li-like ions is given in Ref.@15#. In fastrecombining plasmas we encounter opposite relations:degree of ionization is higher compared to equilibrium coditions when the electron temperature decreases. Duringtime history of the pinch plasmas under investigation copression and expansion take place. We therefore meetphenomena, which leave their marks in the emission spe
For the investigation of the transient line formation of tpinch plasma a collisional-radiative, metastable resolvtime dependent model has been employed@16#:
dnj
dt5 (
i ,iÞ jWi j ni2 (
i ,iÞ jWji nj , ~2!
whereni are the atomic level populations,Wi j are the vari-ous collisional and radiative rate processes for the populaand depopulation of the levels, namely, collisional excitatand deexcitation, ionization and three body recombinatidielectronic recombination and autoionization, and radiatrecombination. Radiation transport effects have been tainto account by means of escape factors@17# and iterativelysolving for the level populations. More details have bedescribed elsewhere@16,18,19#.
The interpretation of the plasma dynamics was carriedin the following way.
~1! Generation of time-dependent parametersne(t) andTe(t) from a plasma bag model calculation and subsequuse of these parameters for the calculation of emission stra solving the set of differential equations~2!. In this frameEqs. ~2! can be considered as a postprocessor of the mcalculations. The use ofne(t) andTe(t) implies the assump-tion of a single zone. However, detailed comparison of oand two-dimensional modelings with those of a zedimensional approach have shown that the zero-dimensimodel provides a reasonable characterization of the plaevolution @20#. Details concerning the present plasma bmodel are described elsewhere@21#. The plasma bag modedescribes the compression and the pinch phase in the frawork of a quasi-one-dimensional model making use of a splified geometry of the plasma layer and assuming a homgeneous density and temperature of ions and electrons.
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5962 56K. BERGMANN et al.
model includes the coupling of the device parameters tohydrodynamic motion including acceleration of the plasdue to magnetic forces, shock heating at the boundary ofplasma layer to the neutral gas, thermalizing of kineticergy in the pinch phase, heating of electrons by hot ionsOhmic heating, and the influence of radiative processesthe plasma parameters. These processes are describedzero-dimensional approach within the temporal evolutionelectron density and temperature.
~2! The atomic structure of Eq.~2! includes resonancelines, forbidden transitions, and in a detailed manner theelectronic satellite lines 1s2l2l 8-1s22l 8 and 2l2l 821s2l 8of Li- and He-like ions and the recombination continua. Thoretical emission spectra were therefore used for purely stroscopic investigation of the plasma dynamics:ne(t) andTe(t) are regarded as ‘‘test functions’’ providing a theorecal spectrum to be comparable with the experimental oStarting point for the test functions were the results obtaiby the plasma bag calculations.
This method enables the theoretical investigation of dferent modes of plasma dynamics. Simultaneous fittingmany resonance and forbidden lines provides reliable inmation about time dependent plasma parameters and caused for a refinement of the results of pure MHD calcutions.
The emission spectra strongly depend on the principalhavior of the plasma parameters, namely, duration of copression and expansion together with the maximum value
FIG. 3. Simplified parameter dependence ofTe(t) ~full ! andne(t) ~dotted! which was used for the fitting of the emission spectThe values at the instancesA–E correspond to those given iTables I and II for the 200 Pa case~a! and for the 400 Pa case~b!.The parameter dependence for temperature and density fromplasma bag calculations does not differ essentially in its qualitabehavior but has different numerical values also given in Tableand II.
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Te and ne . Comparing the emission spectra resulting frothe numericalne(t) and Te(t) provided by plasma bag calculations with those of various testing functions allows ususe a simplified dependence, as shown in Fig. 3. A sheating and compression phase ‘‘A-B,’’ a further short com-pression to maximumTe andne ‘‘ B-C,’’ a short expansionand cooling to medium plasma parameters ‘‘C-D,’’ and along lasting cooling and expansion phase ‘‘D-E.’’ Properselection of theTe andne at the instantsA–E leads to emis-sion spectra which practically do not differ from those eploying numerical values from the plasma bag calculatio
The phaseA-B corresponds to the end of the compresiphase before the plasma layer reaches the axis. The fascrease in density and temperatureB-C is due to the thermal-izing of the kinetic ion energy and subsequent heatingelectrons. With the additional internal energy of the kineions the pinch plasma pressure exceeds the magneticsure which will lead to the expansion in the phasesC-D andD-E.
.
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FIG. 4. ~a! Theoretical spectrum fitting together with the expemental data for 200 Pa gas pressure.~b! Theoretical spectrum fittingtogether with the experimental data for 400 Pa gas pressure.
TABLE I. Plasma parameters at the instantsA–E indicated inFig. 3 given by the plasma bag calculations. In parentheses arecorrected values, which lead to an improvement of the fitted sptrum in the 200 Pa case.
56 5963SPECTROSCOPIC INVESTIGATION OF HIGHLY . . .
Figures 4~a! and 4~b! show the total spectrum fitting othe 200 Pa and the 400 Pa experiment obtained withparameter development given in Fig. 3~higher series lines1s-np, 1s2-1snp with n.4 have not been taken into ththeoretical consideration!. The numerical values for theplasma parametersne andTe at the instantsA–E used for thefittings are given in Tables I and II. These two tables contthe numerical values obtained from the plasma bag calctions and a set of corrected values resulting from the trsient spectra modeling. For the fitted spectra shown in F4~a! and 4~b! the corrected values have been taken intocount. The corrections will be discussed below in moretail. With both sets of plasma parameters a good agreembetween experimental and theoretical results is obtainedthe most essential spectral features: occurrence or absenthe recombination continua, lower intensity in the satellines for the 200 Pa case in comparison with the 400experiment, and the line ratios of theW line to the Lya line.
Tables III and IV summarize the most important expemental line intensity ratios together with the theoretical cculations of the ratios of the time integrated intensities:
I K5EtA
tEI K~ t !dt ~3!
for the emission lineK. The I K(t) are determined from Eq~3! using I K(t)5nK(t)AQ(t)\v. A is the coefficient forspontaneous decay andQ(t) the escape factor for radiatiotransport.
As the atomic model includes simultaneously levelsvarious ionization stages~boron-like till nucleus! the solutionof Eqs.~2! provides also the time dependent ion abundashown in Figs. 5~a! and 5~b!. In the 200 Pa case the fachange ofTe and ne in time does not permit the ion abundance to be in a stationary regime. The time to proceedization to the nucleus is too long, the plasma expands bethe He-like ion abundance experiences a considerablepopulation: the confinement parameternet is too small to
TABLE II. Plasma parameters at the instantsA–E indicated inFig. 3 given by the plasma bag calculations. In parentheses arcorrected values, which lead to an improvement of the fitted sptrum in the 400 Pa case.
reach a stationary regime (net,531010 cm23s) @18#. In astationary regime (net.1012cm23s) with Te5550 eV,ne5231019cm23, and Leff50.7 cm (Leff is the effectivephoton path length obtained from experimental estimatiand being in agreement with spectra modeling! the relativeion abundance would ben(nucleus).0.81, n(H).0.18,n(He).531023. So one would expect negligibleW-lineradiation that is in contradiction to the experimental resuThe observed highW-line intensity compared to the Lya lineis due to a long lifetime of the He-like ions with respectthe total lifetime of the pinch plasma.
For the experiments with 400 Pa gas pressure we meeonly different plasma parameters at maximum compressbut also a different regime due to a higher value of the cfinement parameter. Although the temperature at maxim
TABLE IV. Calculated and experimental line ratios of differetransitions for the 400 Pa case.
FIG. 5. ~a! Time-dependent ion abundances for nucleus, H, aHe, ground states obtained from the time-dependent plasma paeters as given in Table I for the 200 Pa gas pressure.~b! Time-dependent ion abundances for nucleus, H, and He, ground sobtained from the time-dependent plasma parameters as giveTable II for the 400 Pa gas pressure.
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compression is considerably lower than for the 200 Paperiment, the He-like ion abundance suffers a much higdepopulation due to a higher electron density and higher cfinement parameter. The nucleus reaches a higher poption. Figure 5~b! shows the time-dependent ion abundanfor the 400 Pa gas pressure. We want to note that also fo400 Pa gas pressure the stationary regime is not compleapproached. ForTe5350 eV, ne5831019 cm23, andLeff50.7 cm one obtains the ion abundancn(nucleus).0.61,n(H).0.36,n(He).0.03.
Taking the average over the time interval fromtB to tE ,where theK-shell emission is most intense, the He-like ioabundance for the 400 Pa experiment is lower than for200 Pa experiment. This is why the Lya intensity exceedsthat of theW-line, although the temperature at maximucompression is lower than for the 200 Pa experiment.
Two-dimensional calculations of a plasma focus dcharge show also a strong fall off inz direction @22#. Exci-tation rates for dielectronic capture^DC& and collisional ex-citation ^C& for dielectronic satellites and resonance linscale according toDC&}ngrneexp(2Es /Te)/Te
3/2 and ^C&}ngrneexp(2DE/Te)/Te
1/2. For the present plasma the eletron temperatures are always smaller than the thresholdergiesEs ~capture energy! and DE ~energy gap!. The de-crease of the respective excitation rates is thereexponential with decreasing temperature. Moreover, Mcalculations show that outer regions with lower temperatcorrespond also to lower density resulting in a furthercrease of excitation processes. The exponential decreaseTe together with the decreasing density in the outer regilead to negligible contributions from the outer plasma. Tpresent selection of emission lines of H-, He-, and Li-liions mainly originate from the hottest and densest pSpace resolved spectroscopy@23# has demonstrated this experimentally.
The influence of plasma regions with lowerTe can there-fore be mainly due to photoabsorption, however, photosorption of satellite transitions in outer cold plasma sheareported in Ref.@24# cannot be responsible for the absencesatellite spectra in the 200 Pa case. Experiments clearly sthe simultaneous absence of Li-like and He-like satellitFor He-like satellites the absorbing ground states aresingle excited He-like 1s2l levels, which do not give rise toany important optical thickness effects.
V. DIELECTRONIC SATELLITE SPECTRAAND RECOMBINATION CONTINUA
Although the use of the parameter development for etron temperature and electron density obtained fromplasma bag calculations leads to a qualitative explanatiothe observed ratios for theW and the Lya line, the differ-ences concerning the intensity of satellites and the ocrence of recombination continua for the two different gpressures, there are still discrepancies in the line intensitthe dielectronic satellites and the forbiddenY line especiallyin the 400 Pa case, namely, the satellites and the forbiddeYline have too low intensity. Higher satellite intensity cancourse be obtained by lower temperatures at maximum cpression. However, this will be in considerable disagreemwith the Lya- and W-line intensities. From purely spectro
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scopic argument it therefore seems that in the case of 40after maximum compression a phase with low electron teperature and higher electron density than predicted byplasma bag calculations takes place, which gives rise to llasting recombination effects. In order to meet the expemental intensities of the satellites and recombination ctinua, densities not much lower than or the same as the mmum values are required. Otherwise the time integraintensity would be too low to compare with the experimenspectra. Furthermore, a lower electron temperature of abofactor of 2 is required. Otherwise the time integrated intesity of the dielectronic satellites would be too low due to texponential behavior exp(2Es /Te)/Te
3/2 for the dielectroniccapture.
As the satellite emission and the Lya intensity is of cen-tral interest we performed detailed transient spectra modeof the He-like satellites 2l2l 8-1s2l 8.
Keeping the behavior of plasma parameters as outlineFig. 3, we arrive at the corrected values for the maximcompression and the expansion phase. These correctedues are given in parentheses in Tables I and II. With the hof this few corrections a favorable agreement for various lintensity ratios is achieved, as is already shown. Figurshows the details of the satellite spectrum close to thealine. There is a good agreement also in every spectral debased on the time-dependent plasma parameters giveTables I and II.
The predictions concerning the evolution of the plasparameters based on the spectroscopic consideratnamely, the existance of a strong recombination radiatafter maximum compression, is supported by time resolmeasurements of the totalK-shell emission and streak images of the plasma dynamics in the visible range.
Figure 7 shows the totalK-shell emission measured wita MCP covered with a 10mm Al foil. For the 400 Pa gaspressure a longer lasting wing in the emission profile istained, which is not so pronounced in the case of 200 Pathe MCP is covered with an Al foil and its direction of observation coincides with those of the high resolution x-rspectrometer the time-dependent MCP measurements cspond to those from the time integrated x-ray spectromeTo correlate the time dependent MCP signals with the e
FIG. 6. Detailed spectrum modeling of the He-like 2lnl 8-1snl9satellites close to the H-like Lya transition for 400 Pa gas pressurThis spectral interval has not been fitted separately but is a resuthe parameter dependence given in Table II, which was also chfor the total fit shown in Fig. 4~b!.
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56 5965SPECTROSCOPIC INVESTIGATION OF HIGHLY . . .
lution of the emission lines and the continua, Figs. 8~a! and8~b! show the time-dependent emission of theW, Y, and Lyalines, of the H-like photorecombination continuum~the se-lected wavelength interval was between 1.0 and 1.05!and the He-like photorecombination continuum~selectedwavelength interval between 0.85 and 0.9 nm! taking intoaccount the absorption in the 10mm Al filter.
Based on these calculations the asymmetric form ofx-ray MCP signal can be referred to recombination procesin the plasma. At the cooling phase the amount of H-lions and nucleons stays high and the radiation resulting frecombination processes forms long lasting wings in
FIG. 7. Experimental time-dependent total emission for the 4Pa and 200 Pa gas pressures.
FIG. 8. ~a! Calculated time-dependent emission of differelines and for the recombination continua for the plasma paramegiven in Table I for the 200 Pa case.~b! Calculated time-dependenemission of different lines and for the recombination continuathe plasma parameters given in Table II for the 400 Pa case.
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x-ray emission. In the case of the 400 Pa experimentwing has a higher intensity, because the electron densityter maximum compression stays at a higher level than in200 Pa case. For 200 Pa the expansion of the plasmfaster, which is connected with a more rapid decrease ofelectron density.
This different behavior of the plasma dynamics in tdecay phase is supported by streak measurements oplasma layer which are shown in Fig. 9. In the low presscase the duration of the high compression state is lower tin the 400 Pa case. The plasma expands almost elasticall200 Pa whereas at the higher pressure value it stays loon the axis and has a lower expansion velocity. This isagreement with the similarity considerations for the MHwhich suggest a velocity of the plasma layervs scaling ac-cordingvs}I 0 /(p1/2a) @13#.
Furthermore, the streak images support a higher mmum compressionk in the 400 Pa case.k is defined as theratio of density of neutral gas atoms to the maximum inumber density in the pinch phase. Using the numerical vues for the electron density shown in Tables I and II and
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FIG. 9. ~a! Streak image of the collapsing and expanding plaslayer in a discharge with 200 Pa neutral gas pressure.~b! Streakimage of the collapsing and expanding plasma layer for the 400case.
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numerical values for the degree of ionization taken froFigs. 5~a! and 5~b! the compression is given byk.60 for200 Pa andk.100 in the 400 Pa case. The minimum diameter of the pinch plasma observed in the visible rangelower in the 400 Pa case, indicating a higher compressiothe pinch plasma.
Finally it should be noted that the results for the electrtemperature from the spectroscopic considerations are alagreement with the scaling law mentioned above. The tperature is assumed to scale according toTe}I 0
2/(pa2). Us-ing the numerical values for the current~270 kA for 400 Paand 250 kA for 200 Pa! the maximum electron temperatufor 200 Pa is assumed to be higher by about a factor ofcompared to the 400 Pa case. Taking the numerical vagiven in Tables I and II for the maximum electron tempeture this factor is about 1.5. A simple scaling law for the idensity according toni}p is not verified quantitatively bythe spectroscopic investigations. The model calculationssented lead to a ratio of maximum ion number densityabout 3.3 comparing the 400 Pa to the 200 Pa case, whethe scaling law would predict a factor of 2.
The zero-dimensional simulations of theK-shell emissionspectra make use of an appropriate choice of the piplasma parameters assuming a homogeneous plasma.ever, in a real plasma gradients in density and temperaturadial direction occur due to finite transport coefficientsdescribed, e.g., in Ref.@25# where a one-dimensional simulation of a dense pinch plasma is presented. The most imtant contribution to the inhomogeneity of the plasma paraeters will occur due to the process of thermalization ofkinetic energy of the ions when the plasma layer of the copression phase reaches the axis. This process leads toflected shock wave running outward in radial direction. Dto finite ionization time a smaller radius for hydrogenlikline emission is expected compared to the heliumlike lemission. In this sense the zero-dimensional approach oestimates the number of ions emitting hydrogenlike linediation, especially in the present case where the pinchtime and the ionisation time from the heliumlike to thhydrogenlike level are of the same order of magnitude. Hoever, this failure of the zero-dimensional approach cancompensated by a proper choice of density or confinemparameter which will not differ substantially from the reradial averaged density. So the zero-dimensional simulatprovide reasonable estimations of the plasma parameter
VI. CONCLUSION
The dynamics of neon pinch plasmas has been invegated theoretically and experimentally for two sets of devparameters, essentially for different neutral gas pressures
, D
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almost the same pinch current. These two sets lead to qtatively different emission spectra.
A multifold use of spectroscopic analysis was developand demonstrated which exceeds the common approacusing spectroscopy as a simple postprocessor of gas dynor MHD calculations.
An overall transient fitting of highly resolved, time integratedK-shell emission spectra leads to a good agreemnot only when comparing resonance lines but also when csidering details of dielectronic satellite spectra. Stationmodels were shown to fail to explain the observed characistic differences in the emission spectra for the two neugas pressures.
The transient spectra modeling allows us to estimateevolution of the plasma parameters leading to an electemperature ofTe
max.530 eV and an electron density one
max.2.531019 cm23 for the 200 Pa case at the instantmaximum compression. The respective values for the 400case are given byTe
max.340 eV andnemax.8.531019 cm23.
These numerical values resulting from the model calcutions are in agreement with scaling lawsTe}I 0
2/(pa2) andne}p which are based on similarity considerations. Thescaling laws predict a lower temperature and a higher denwhen increasing the neutral gas pressure keeping the cuand the anode radius constant. The connection of the deparameters and the plasma parameters—here done forsets of device parameters—allows the tailoring of the trsient pinch plasma dynamics. This is important for bastudies of transient processes in plasmas as well as fordesign of pinch plasmas as laboratory scale x-ray sourcedifferent applications.
The detailed analysis of dielectronic satellite spectra pdicts a long lasting emission after maxiumum compressfor the higher neutral gas pressure. This prediction has bconfirmed independently by time resolved analysis oftotal emission and time and space resolved optical strcamera measurements. The predictive character of the dietronic satellite spectra concerns not only the determinationthe plasma parameters but also the qualitative type of emsion after maximum compression. This is of importancethe understanding of the pinching process, especiallycause the above method is of general use and not conneto the specific type of experiment presented here.
ACKNOWLEDGMENTS
Parts of this work have been supported by the DeutsForschungsgemeinschaft~DFG! under Contract Number He979/17 and the International Atomic Energy Agency Vien~IAEA !.
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