jaroslav kuba et al- modeling of the transient nickellike silver x-ray laser

8/3/2019 Jaroslav Kuba et al- Modeling of the transient nickellike silver x-ray laser

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Modeling of the transient nickellike silver x-raylaser

Jaroslav Kuba*

Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7,

115 19 Prague 1, Czech Republic, and Laboratoire de Spectroscopie Atomique et Ionique, Batiment 350,Universite Paris XI, 91405 Orsay, France

Raymond F. Smith,* Djamel Benredjem, and Clary Moller

Laboratoire de Spectroscopie Atomique et Ionique, Batiment 350, Universite Paris XI, 91405 Orsay, France

Lee Upcraft and Robert King

Department of Physics, University of York, Heslington, YO10 6DD, York, UK

Annie Klisnick

Laboratoire de Spectroscopie Atomique et Ionique, Batiment 350, Universite Paris XI, 91405 Orsay, France

Ladislav Drska

Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7,115 19 Prague 1, Czech Republic

Geoff J. Pert

Department of Physics, University of York, Heslington, YO10 6DD, York, UK

Jean-Claude Gauthier

Laboratoire pour lUtilisation des Lasers Intenses, Unite Mixte de Recherche 7605, 3705 Centre National de la

Recherche Scientifique/Commissariat a lE

nergie Atomique/Universite Paris VI, E

cole Polytechnique,91128 Palaiseau, France

Received April 19, 2002; revised manuscript received September 4, 2002

Recent high-temporal-resolution nickellike x-ray laser experiments have yielded important insights into theoutput characteristics of picosecond-pumped x-ray lasers. However, current experimental observations do notfully explain the plasma dynamics, which is critical to gain generation within the x-ray laser medium. A nu-merical study of the nickellike silver x-ray laser has therefore been undertaken to complement our experimen-tal results in an attempt to further our understanding of the processes at work in yielding the observed x-raylaser output. High gain coefficients existing with picosecond lifetimes are predicted, which is consistent withthe short x-ray laser durations experimentally observed. The late onset of the continuum emission relative tothe temporal peak of the x-ray laser output is explained as a sign of high electron density evolution near thetarget surface. 2003 Optical Society of America

OCIS codes: 140.7240, 320.5390, 350.5400, 020.1670

1. INTRODUCTIONCollisional, laser-pumped x-ray lasers (XRLs) operate insingle- or double-pass, high-gain (10 cm1), amplified-spontaneous-emission mode. The gain region is createdin an extended plasma column that is produced by inter-action of one or more strong pump laser pulse(s) with asolid target. Population inversion is achieved by colli-sional excitation of the lasing ions with free electrons.

Standard quasi-steady-state XRLs pumped by a rela-tively long laser pulse (of 70600-ps duration) were firstdemonstrated as early as 1985.1 Today they routinelyreach a saturated gainlength product of 15 with a pump

energy of typically 100

1000 J.29

In recent years a com-bined experimental and theoretical approach has yieldedinsight into laserplasma coupling, refraction, and atomicprocesses that influence the gain. This has led to the useof a low-energy prepulse preceding the main pulse by afew nanoseconds that preforms the plasma.37 Satura-tion was hence achieved on a host of soft-x-ray lasinglines in the 5.860-nm range. In the quasi-steady-statepopulation-inversion regime the measured XRL outputdurations are typically of4050 ps for a 100-ps pumppulse9 and of80 ps for a 600-ps pump pulse.3

The pump energy requirement has recently been dra-

208 J. Opt. Soc. Am. B/ Vol. 20, No. 1 /January 2003 Kuba et al.

0740-3224/2003/010208-07$15.00 2003 Optical Society of America


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matically reduced to a few joules when the development ofchirped-pulse amplification (CPA) laser technology en-abled the testing of the transient collisional excitationpumping scheme. This scheme was proposed as early as198910 and investigated theoretically by severalauthors.1113 The first experimental demonstration oftransient gain was achieved in 1995 in neonliketitanium14 with saturation reported in the same elementin 1998.15 The shortest XRL pulse duration observed un-til now was recently demonstrated with a transientscheme in the nickellike 4 d4p silver transition at 13.9nm.16,17 Its unique properties make the transient XRL apromising tool for applications.

The transient pumping scheme consists of target irra-diation by two consecutive laser pulses. The initial long-duration, low-intensity pulse creates a plasma containinga large population of the desired ion species, i.e., nickel-like, neonlike, or possibly others. The second subpicosec-ond high-intensity laser pulse heats the preformedplasma and creates a transient inversion of populationthrough collisional electronion excitation.

Modeling suggests that a large population inversion(with gains of hundreds of cm1) is generated before ion-ization can occur. High gains are expected in the periodbefore collisional redistribution of the excited-statespopulations takes place.1821 Numerical simulations per-formed at Lawrence Livermore National Laboratory19

show that in the transient collisional excitation schemethe population inversion between the lasing levels is ex-tinguished by over-ionization of the gain medium, a be-havior that is also suggested by recent experimentalobservations16,17 in a nickellike silver transient XRL.

In this paper we present the results of our numericalmodeling aimed at giving insight into the gain dynamicsof this laser at 13.9 nm. Modeling is based on the EHY-BRID numerical code developed by G. J. Pert22 Themodel case studied in the paper will be the experimentcarried out in 2000 at the Rutherford Appleton Labora-tory (RAL).16,17

The structure of the paper is the following. In Section2 we will briefly recall the experimental conditions to besimulated, along with the main experimental results ob-tained. Section 3 is devoted to the model used and codedescription; in Section 4 we will discuss the results of oursimulations.

2. TIME-RESOLVED EXPERIMENT

In the experiment at RAL a fast, soft-x-ray streak camerawith a resolution as high as 1.9 ps was used to analyze

the output of the nickellike silver J 0 1 4d

4p las-ing line at 13.9 nm.16,17 Two beamlines from the Nd-glass Vulcan laser at 1.06 m were used to irradiate a 10-mm-long flat silver slab target in the RAL standard line-focus geometry.23 A 300-ps prepulse typically delivered10 J on target into a 21 0.12-mm line focus with in-tensities of 2 1012 W/cm2. This pulse generates aplasma which, after a controlled delay, is strongly heatedto optimum lasing conditions by a 1.3-ps CPA pulse in a19 0.0 8-mm line focus. Because of the previouslyinferred24,25 short gain durations (10 ps) relative to thetransit time of the x-ray photons through the gain me-

dium (30 ps), it was necessary to implement traveling-wave-irradiation pumping.2325 It was observed that the

XRL emission peaked at 5 mrad off-axis for a range ofpumping conditions. Through integration of the signalrecorded on a CCD, the optimum pumping conditionswere estimated to be 4.3 J/cm (1.2 1012 W/cm2) in the300-ps preforming pulse and 11.8 J/cm (1.1 1015 W/cm2) in the CPA pulse with a temporal peak-to-

peak delay of 200 ps between the pulses. Here optimumrefers to the maximum energy yield within the XRLpulse.

For the time-resolved shots an AXIS-Photonique XUVstreak camera26 equipped with a potassium bromide pho-tocathode was positioned at the focal plane of a flat-fieldspectrometer to give the temporal resolution of the XRLemission. In our setup the 1 15-mm photocathodewas placed parallel to the direction of spectral dispersionand at an angular position off-axis corresponding to thepeak of the XRL output. The streak camera thus gavewavelength resolution at an integrated horizontal angleof 1.1 mrad around the angular peak of the XRL emission.The output from the streak camera was amplified and re-corded by the combination of a 50/40 Kentech intensifierbutt-coupled to an optical CCD camera. This configura-tion was estimated to give a temporal resolution of 1.9 0.2 ps.

The FWHM duration of the XRL pulse was measured(after a deconvolution taking into account the temporal-resolution-limit response function) to be 1.9 0.7 ps.The XRL signal was extinguished on the rising edge of thecontinuum emission. This observation was repeatablefor a number of different pump-laser parameters. Onepossible interpretation of this result is that the risingedge of the continuum emission is the result of over-ionization within the plasma which, in turn, signals theextinction of the population inversion on the gain line.One may also postulate, however, that the relative timedelay between the peak XRL output and the peak con-tinuum emission is the result of a thermal wave travelingtowards the dense target surface. Such an occurrencewould not necessarily affect the population dynamics inthe lasing ion. The nature of our experimental setupmeant that no information regarding the spatial distribu-tion of the continuum emission in relation to the XRL out-put was available.

The high-resolution characterization of the XRL outputyielded previously unobtainable insights into the natureof the XRL output for the transient collisional excitationscheme. It is clear, however, that to explain these obser-

vations fully, a comprehensive theoretical modeling effort

is needed to complement the experimental work.

3. MODEL DESCRIPTIONThe simulations of the above experimental conditionswere carried out using the EHYBRID22 hydrodynamicand atomic code. EHYBRID, which was developed to un-derstand the evolution of the lasing material, describesmany physical processes, including pump-laser energydeposition, hydrodynamic motion, electronic thermal con-duction, and ionelectron thermalization coupled withthe atomic physics of the lasant ions.2729 The model is

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1.5-dimensional (or sometimes described as quasi-two-dimensional29), designated to operate in planar geometry.The code uses a 296-Lagrangian-cell matrix in the direc-tion away from the target. The fluid is hence modeled inthe direction parallel to the driving laser by cells that areassumed to be laterally isothermal; as such, the trans-

verse expansion is considered to be self-similar.22

The calculation of the ionization balance within theplasma, and in particular the abundance of the nickellikeions, is of central importance in these simulations. InEHYBRID, time-dependent ionization is calculated usinga collisional radiative model. The model represents themost sophisticated treatment available of time-dependentatomic physics in plasmas. Electron-ion collision (excita-tion, deexcitation, and ionization) and recombination(three-body, radiative, and dielectronic) processes are in-cluded in the coupled rate equations for each ionic level.Radiative losses are taken into account. The escape fac-tors are incorporated into the collisional-radiative modeland can be controlled in the input file. However, the codeEHYBRID does not account for radiative processes in-

volving the x-ray line, such as absorption and inducedemission. In other words, it ignores the line propagation.

The ionization rate of Golden et al.30 is implemented,with three-body recombination calculated from the de-tailed inverse balance. Processes such as excitation,autoionization, and inner-shell ionization are not consid-ered, but this level of detail for the lasing ion is found toproduce good agreement with experiment. Howevercomputational limitations mean that more approximatedescriptions must be implemented for the other ionstages. In the data set for silver, ion stages other thanthe nickellike ion stage are treated with a simpler two-level model based on a modified form of Griems model,31

or with the screened hydrogenic model.The model assumes that absorption of the pumping la-

ser is due to inverse bremsstrahlung (and considers re-fraction). The inverse bremsstrahlung coefficient is cal-culated for the propagation of the laser pulse towards thetarget surface and, for reflection of the laser pulse awayfrom the critical surface. High-field modifications of thiscoefficient are not included. Resonant absorption is mod-eled by assuming a 30% dump of the laser energy reach-ing the critical surface. The thermal conductivity forboth ions and electrons is given by the classical HarmSpitzer expression.32 As this formula is valid only if themean free path of electrons remains small in comparisonwith typical temperature gradient dimensions, the ther-mal conductivity is subject to an empirical flux limit of f 0.1 as usual in this type of code. There are some

modifications to this parameter in the low-temperature,solid-density region (applicable to low-level prepulses22).The atomic physics, hydrodynamics, and transport withinthe plasma are solved self-consistently through a solutionof the electron energy balance.

The atomic data input file for silver was constructed bythe present authors. The nickellike ion stage is modeledwith 272 excited levels including all levels in the n 4and n 5 manifolds and with averaged contributionsfrom the n 6 to n 8 levels. As mentioned above ionstages other than nickellike are treated with varying de-grees of complexity using a screened hydrogenic model or

a simpler two-level model based on the modified form ofthe Griems model.33 Electron-ion collision cross sectionswere calculated at LULI (Laboratoire pour lUtilisationdes Lasers Intenses, Ecole Polytechnique, France) for alltransitions within the n 4 manifold using the codeHULLAC (Hebrew University Lawrence Livermore

Atomic Code).34 For the calculation of the excitation anddeexcitation rates, we did not use the standard EHYBRIDprocedure with d-coefficients that were introduced by vanWyngaarden et al.35 In fact it is more satisfactory to cal-culate all the rates for each electron density and tempera-ture with the help of a subroutine added into EHYBRID.Oscillator strengths for all transitions in the n 4 to n 8 manifolds were calculated with a multiconfigura-tional DiracFock code.36 Our atomic data calculationsallow for one vacancy in the n 3 shell.

4. RESULTSA. XRL Plasma ConditionsThe input conditions to the simulations were set to modelthose that were found to be optimal during the experi-mental campaign cited in Section 2. Figure 1 shows thegain on the primary line for nickellike silver, the 4 d 1S0

1P1 4p lasing transition at 13.9 nm, as a function oftime and distance away from the target surface. Thepeak of the 1.3-ps (FWHM) heating-pump-laser pulse oc-curs at 0.65 ps on the time scale (dashed line in Fig. 1).Two distinct regions are predicted. When the 1.3 psheating pulse is first turned on there is an emergence of aregion of large gain (500 cm1) with small dimensionsboth in space (5 m within 15 m of the target surface)and time (1 ps at FWHM). When the laser is turned offand the plasma expands, a larger plateau with gains400 cm1 extending out to 40 m is observed.

To what extent these gain regions contribute to the

XRL output is largely dependent on the density scalelengths that exist within the plasma. The smaller the

Fig. 1. Local gain on the 4d 1S0 1P1 4p lasing transition as a

function of time and distance away from target surface. Thepeak of the 1.3-ps FWHM CPA pump pulse occurs at 0.65 ps.The maximum gain zone is very restricted both in time andspace. The plot depicts the gain contour lines of 50 cm1, 100cm1 and further consecutive steps of 100 cm1.



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density scale lengths at a given point in space, the morerefraction will tend to preclude spatial sampling by the

XRL beam as it propagates along the line focus. In com-

parison with the predicted evolution of the local gain, wecan see in Fig. 2 that the high gain peaks at electron den-sities close to 1021 cm3. This is the critical density sur-face of the 1.06-m laser driver and coincides spatiallywith a region of steep density gradients. It would be ex-pected, therefore, that spatial sampling of this regionwould be limited by refraction. It is observed that thedensity gradients become more relaxed at distances awayfrom the critical density surface and so, because of re-duced refraction effects and its larger dimensions, thelarger region of lower gain is expected to contribute mostto the XRL output.37,38

Electron temperatures reaching 2000 eV are expectedat the critical density surface (Fig. 3). Temperature fallsquickly at distances farther away from the target, whichis a trend similar to that of the gain profile in Fig. 2. Af-ter the main heating pulse is turned off, the bulk of theplasma stays hot (500 eV) for 1020 picoseconds. Thisprolonged heating causes the average ionization of theplasma to increase rapidly. The effect is illustrated inFig. 4 where the average ionization is given for each of the296 Lagrangian cells as a function of time. In the regionof space-time where high gains are predicted, the fractionof nickellike silver ions (Fig. 5) reaches nearly 40%. It isobserved that after a short time (1 ps) the plasma over-ionizes (Fig. 4). Previous work has shown this effect andthe associated collisional redistribution of the excited-

Fig. 2. Temporal evolution of the free electron density as a func-tion of time and distance away from the target surface. Highgain peak predicted in Fig. 1 is shown to reside 15 m from thetarget where steep density gradients and the associated refrac-tive effects would prohibit extensive sampling by the x-ray laserbeam.

Fig. 3. Heating of the supercritical densities to temperatures ashigh as 1.8 keV is predicted during the main heating pulse.These greater-than-1-keV temperatures coexist spatially andtemporally with the gain spike shown in Fig. 1. The tempera-ture gradients are similar to those observed for the gain, withquick dissipation from a small intense region into a larger moreuniform plateau with temperatures below 500 eV.

Fig. 4. Temporally resolved average ionization within each ofthe 98 Lagrangian cells expanding away from the target surface.

Fig. 5. The ratios of nickellike, copperlike, cobaltlike ion stages(i.e., 19-, 18-, and 20-times-ionized silver ions) at 7 m from thetarget as calculated by the EHYBRID code at optimum condi-tions defined during the RAL 2000 experiment. The temporalpeak of the gain appears clearly before the maximum of nickel-like ions.



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level populations to be the main mechanism for extin-guishing the population inversion on the gaintransition.18 Such a hot, ionizing plasma with consistentdensities would be expected to have enhanced continuumemission, as was observed in Refs. 16 and 17. The calcu-lations described in Figs. 14 are very similar to thosepredicted by other hydrodynamic codes for silver.1921

B. Continuum Emission StudyDuring the experiment cited above the XRL output inten-sity peak appeared on the rising edge of the continuumemission. To explain the continuum emission behavior

we have to study the space-time distribution of plasmaparameters carefully. In our simulation the maximumgain corresponds to the electron temperature peak. Theion density remains maximal near the target and does notdevelop significantly in time. In contrast, both electrondensity (Fig. 2) and average ionization (Fig. 4) rise sub-stantially with time in the zone within a few micrometersof the target surface (the electron density increases byseveral orders of magnitude in the zone near the targetsurface), which is also in opposition to the electron tem-perature behavior (Fig. 3). This is very important for ourestimation of the continuum emission because it is as-sumed to be dominated by bremsstrahlung emission.The bremsstrahlung Q() emitted by a plasma per unit

time and unit volume in a small frequency intervalaround can be described by39

Qd Z2nen iTe1/2 exp/kTed,

where ne and n i stand for electron and ion densities, Z isthe average ionic charge, Te is electron temperature, isthe circular frequency, and k and represent the Boltz-mann and Planck constants, respectively. In our compu-tation we neglect the slowly varying Gaunt factor func-tion as is usual in many practical applications.39 Havingstudied the plasma parameters ne , ni , Z, and Te , we can

easily calculate the radiation developed by bremsstrah-lung in a small wavelength interval around the 13.9 nmnickellike silver line, per unit volume and unit time ineach space-time-cell in the plasma (Fig. 6). Even thoughthis calculation should be considered as an estimate (be-cause a Maxwellian electron velocity distribution is as-sumed, which is not necessarily true in the case of tran-sient XRLs), it clearly shows that the continuum emissionpeak should arrive after the XRL peak, following the be-havior of the electron density.

When calculating the actual continuum emission en-ergy at the plasma exit, we should take into account thepropagation of the radiation by different paths for eachwavelength. In our estimates we show the time-resolvedcontinuum emission (released from a small portion ofplasma along the target) integrated over the horizontalangle only (which, in this one-dimensional model, isequivalent to integration over the transverse distancefrom the target surface; Fig. 7). As observed during theexperiment, the bremsstrahlung emission rises slowlywith its maximum well after the peak of the XRL pulse(17.6 ps after the peak of the pump-laser pulse).

5. DISCUSSIONThe EHYBRID code was shown to give excellent agree-ment with experimental observations for 75-ps pumpingschemes, e.g., those of Refs. 40 and 41. In the case oftransient plasmas, however, the gain region is muchsmaller, lies at high densities close to the critical electrondensity, and exists for shorter time periods. Experimen-tally we have seen many inhomogeneities in the near-fieldimaging of the gain region. Such experimental inhomo-geneities are not modeled by the code and thus contributeto discrepancies between experimentally and theoreti-cally realized observables.

For the transient scheme the short-lived gains at highelectron densities are more sensitive to any slight varia-

Fig. 6. Maximum bremsstrahlung emission appears clearly af-ter the peak of the gain (Fig. 1)as observed during the RAL ex-periment 16,17driven by a high electron density in the latertimes after the gain peak. Bremsstrahlung emission (in arbi-trary units corresponding to the energy per unit volume and unittime in a small wavelength interval at 13.9 nm) developed ineach space-time cell as it was calculated from the EHYBRID re-

sults.

Fig. 7. Bremsstrahlung emission energy in a small wavelengthinterval at 13.9 nm integrated over horizontal angle at the exitfrom the plasma as calculated for the RAL 2000 experimentalconditions.



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tions in the irradiation conditions. Experimentally, near-field imaging of the XRL output has shown the gain re-gion to be highly structured because of target and beamnonuniformities.42 The short picosecond time scale in-

volved in the traveling wave heating and gain generationmeans that the inhomogeneities within the plasma arefully experienced by the XRL pulse during transit alongthe line focus. Such results clearly indicate that thesmoothly evolving gain profile predicted in Fig. 1 is notexperimentally realized.

The very limited maximum gain zonelimited both inspace and timepredicted by EHYBRID simulations in-creases requirements on (1) the traveling wave velocitysmatching with the photon speed and on (2) suitable con-ditions in the plasma, especially electron density gradi-ents. The first problem has recently been addressedtheoretically by several authors.43,44 They predict XRLbeam retardation (compared to the speed of light in

vacuum c) and line profile transformations in an activemedium when the beam is amplified. According to thelatter paper, these effects should, however, remain weak(but not negligible) and have not yet been confirmed ex-perimentally. On the other hand, the second problemdefinitely plays an important role. When there is anelectron density gradient in the XRL plasma, the beam isdeflected. For such small-gain zones and such highplasma-density gradients, as is the case in transient XRLplasmas, the beam leaves the zone of maximum amplifi-cation before reaching the end of the target. We dealtwith beam deflection in Refs. 37 and 38. The calculationshows that the beam would leave such a small maximumgain zone typically after a 3.5-mm propagation at most.

Our simulation results are, however, similar to the re-sults obtained with other codes, namely theCHIVAS-LASIX20,21 set of numerical codes and the LAS-NEX code at the Lawrence Livermore NationalLaboratory19 where extremely high local gains are alsopredicted.

6. CONCLUSIONExperimental observations at RAL have shown the tran-sient nickellike-silver XRL to have a duration of1.8 psunder optimum pumping conditions. The time-resolvedoutput of the XRL plasma has consistently shown thatlasing is extinguished on the rising edge of continuum.One possible explanation is that this increased emissionis indicative of over-ionization within the plasma, andthis is the main mechanism for destroying the populationinversion.

An atomic data file was constructed for the atomicphysics code EHYBRID to better understand populationand plasma dynamics. High gains (700 cm1) werepredicted near the critical surface with a broad lower gain(400 cm1) plateau at subcritical densities. Theplasma is expected to over-ionize after 510 picosec-onds. The gain peaks 1.1 ps after the pump laser peakand lasts for only 3.1 ps (FWHM). Its distance from thetarget is of the order of 7 m.

The calculated parameters enabled us to explain whythe XRL always appeared in the rising edge of the con-tinuum emission from the plasma, as observed during the

RAL experiment in 2000. This effect is caused by thefast variations in plasma electron density and other pa-rameters in the plasma so that the maximum emission ar-rives after the XRL peak. Previous observations with alow-resolution streak camera (as reported, for example inRef. 21) did not allow distinguishing the XRL peak fromthe maximum of the continuum emission.

ACKNOWLEDGMENTSThe authors would like to thank Joseph Nilsen of theLawrence Livermore National Laboratory and Jir Lim-pouch of the Czech Technical University in Prague forhelpful discussions in preparing this paper. R.F. Smithwas funded by the European Union Training and Mobilityof Researchers X-ray Laser Network contractERBFMRXCT98-0185. J. Kuba was supported in part bygrant CTU300111714 of the Czech Technical Universityin Prague.

J. Kuba may be reached by e-mail at [email protected].

*Present address, Lawrence Livermore National Labo-

ratory, 7000 East Avenue, L-251, Livermore, California94550.

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