Journal of Quantitative Spectroscopy & Radiative Transfer 65 (2000) 23}30
Towards an experimental benchmark for aluminum X-ray spectra L. Aschke!, S. Depierreux", K.G. Estabrook#, K.B. Fournier#, J. Fuchs", S. Glenzer#, R.W. Lee#,*, W. Rozmus$, R.S. Thoe#, P.E. Young# !Ruhr-Universita( t Bochum, Germany "Ecole Polytechnique, France #Lawrence Livermore National Laboratory, L-399, P.O. Box 808, Livermore, CA 94550, USA $University of Alberta, Canada
Abstract To test the validity of kinetics for laser-produced plasmas, one would like to measure the X-ray spectrum emitted from a plasma volume whose characteristics are determined by diagnostics that do not rely on interpreting the X-ray spectrum itself. An experimental test bed has been developed at the Janus laser at Lawrence Livermore National Laboratory to simultaneously characterize the electron temperature, the electron density and the X-ray emission from laser-irradiated aluminum dot targets. Thomson scattering, interferometry and pinhole imaging are implemented to achieve this. Further, the X-ray spectrum from 1}2 keV is spatially integrated and is obtained using a #at crystal (PET) and an X-ray streak camera for time resolution. Spectra have been calculated using the HULLAC and FLY atomic physics codes which use the measured density and temperature as input, and DCA which calculates X-ray spectra from the 2-D expanding plasma calculated by a hydrodynamics code. Comparisons of the models with the data will be discussed and future directions will be indicated. ( 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Measurements of the X-ray emission spectrum from laser-produced plasmas has been used for many years to diagnose plasma characteristics such as the electron temperature and density [1}3]. For a number of years, tracer elements have been introduced into targets irradiated by intense lasers as a non-perturbative method for diagnosing the conditions in the coronal plasmas [4}11].
* Corresponding author. Tel.: 001-925-423-6172; fax: 001-925-422-7209. E-mail address:
[email protected] (R.W. Lee) 0022-4073/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 9 ) 0 0 0 5 2 - 7
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Experiments of this sort have shown a large discrepancy between the electron temperatures indicated by the X-ray line ratios and the temperatures predicted by hydrodynamic codes [11], e.g., LASNEX [12]. The X-ray spectra were interpreted using collisional-radiative equilibrium (CRE) models which assume a steady-state ionization distribution. Better agreement is obtained, however, with a quasi-steady-state model which allows an empirically determined non-equilibrium ionization balance, but assumes the excited level populations are in a steady state because of the short time scale for level equilibration [13}15]. The agreement of this approach indicates that ab initio kinetics models are not accurately representing the laser produced plasma. This means that unresolved questions remain concerning the entire plasma spectroscopic analysis process. That is, several possible, not necessarily unrelated, avenues remain to be evaluated. First, one needs to determine whether the hydrodynamic simulations, that will serve as input to the kinetics models, accurately represents the target plasma. Second, the range of the validity of the assumptions used in the CRE models needs to be investigated. In this area the assumptions of, e.g., Maxwellian electron distributions, restrictions to single-step processes, and the role of ions in the kinetics are ripe for study. Third, the assumptions underlying the experimental measurements and data reduction need to be validated. All of these questions require an independent means of measuring the local temperatures and densities as functions of time and space. In this paper, we describe results derived from an experimental setup that takes a "rst step towards the goal of a benchmark capability. We use Thomson scattering to measure the electron temperature and obtain information on the ionization stage of an aluminum plasma which simultaneously measures the emitted X-ray spectrum and the plasma density distribution. We will "rst describe the experiments and the initial results. Brief comparisons are then made to hydrodynamic and kinetic models.
2. Experimental setup The present experiment was performed using the Janus laser at Lawrence Livermore National Laboratory. The laser pulse was Gaussian in time (1 ns FWHM) and 1.064 lm wavelength with a nominally top-hat pro"le at the target plane [16]. The pulse energy was varied up to 100 J. The beam was focused with a 20-cm focal length, f/2 lens. The focal spot was 400 lm in diameter and was on the diverging side of best focus. An Al dot target, which is often used in X-ray spectroscopy experiments, was used (see Fig. 1). With this technique, the Al is constrained by the plastic to expand in 1-D, so the emission volume is limited to a well-de"ned size minimizing the self-opacity of the plasma, as well as variations in temperature and density due to gradients produced by 2-D expansion. In the experiment described here, the target was a 100 lm diameter Al dot 2 lm thick which was deposited on a 75 lm thick mylar substrate that was larger than the laser spot. The Al was overcoated with 200 As of CH (parylene) to better match with the hydrodynamic simulation which requires an outer low-Z zone to avoid unrealistic X-ray emission from the outermost propagating zone. Time-resolved X-ray spectra from the target are measured using a #at crystal spectrometer and a streak camera. A PET crystal (atomic spacing "8.742As ) is used which provides a wavelength coverage between 6.5 and 9 As . The di!racted X-rays are collected by the CsI photocathode of a steak camera which has a microchannel plate intensi"er and "lm as the recording medium. The
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Fig. 1. The schematic experimental setup where the target and laser geometry are shown.
streak camera views the target at 453 with respect to the incident laser axis; this angle was dictated by the available target ports. A time-integrated pinhole camera viewed the target at an angle of 903 with respect to the laser axis. The pinhole was "ltered with 25 lm of beryllium and had a size of 25 lm. This was used to con"rm that the Al dot expanded as a column. Thomson scattering provides a measurement of the electron temperature and the expansion velocity. The probe beam was of wavelength 0.35 lm, of 1 ns duration, and was incident at an angle of 453 with respect to the laser axis. Thomson scattered light was collected in a direction perpendicular to both the incident laser beam and the probe beam. An optical system imaged the scattering volume onto the entrance slit of a 1-m Czerny}Turner spectrometer which provided 0.5 As wavelength resolution. The exit plane of the spectrometer was imaged onto the S-20 photocathode of a streak camera which provided time resolution of approximately 20 ps. Calibration of the diagnostic showed that the scattered light was collected from a spherical volume of (50 lm in diameter. The background plasma pro"le was measured by a folded wave interferometer that used a 0.35 lm wavelength, 50 ps probe beam. This measured pro"le provides after analysis a two-dimensional measurement of the electron density, thus providing independent con"rmation of the electron density derived from the Thomson scattering measurements.
3. Analysis of results We now examine the experimental results. The pinhole images for three di!erent targets are shown in Fig. 2. The image obtained using only the plastic substrate shows bright emission only near the target interface from the continuum. An Al slab target shows expansion in two dimensions with bright emission at large distances from the target due to line emission. In the third image, the material from a dot of Al placed on the mylar is constrained to expand in a column, as is desired, which can be inferred from the image of the emission. The results of the Thomson scattering diagnostic for the three types of targets are summarized in Fig. 3. The signal shows two peaks whose wavelength separation is proportional to 2c where c is 4 4
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Fig. 2. Pinhole images of the X-ray emission from three di!erent targets used to ascertain the con"nement of the Al in the dot target geometry.
Fig. 3. The Thomson scattering signal for the three target experiments shown in Fig. 2. Time in each plot increases to the right and wavelength increases down.
the sound speed "(Z¹ /M )1@2 (see Fig. 4). There is an additional, unshifted signal which is due to % * stray light scattered from the solid target rather than from Thomson scattering. We see that in the case of the plastic target and an Al dot target in which the Thomson scattering volume is centered on the Al volume, the Thomson scattering has a distinct two-peaked structure along the wavelength axis at a "xed time implying a single distinct temperature for each plasma species. The signals from the Al dot targets are, in most cases, similar to the solid Al targets when the Thomson scattering volume is centered on the boundary between the plastic and Al, however, as is the case in Fig. 3c, one observes a more complex structure which resembles a sum of the signals in Figs. 3a and 3b. We interpret this signal to mean that the species are mixed in the scattering volume and have di!erent temperatures and #ow velocities, in contrast to the usual assumption concerning dot targets. The dot targets, for a beam energy of 87 J, give an Al temperature of 430 eV with an error bar of $10%. Fig. 5 shows an interferogram produced using an Al target. When no plasma is present, there are a series of horizontally spaced vertical fringes. The presence of a plasma phase-shifts the probe beam which moves the fringes proportionally to the line integral of n ¸, the electron density times % the path length. Assuming that the plasma is cylindrically symmetric about the main laser axis, the phase distribution can be Abel inverted to obtain the axial density pro"le which is shown in Fig. 5b. For reference the location of the Thomson scattering volume is shown.
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Fig. 4. A trace of Fig. 3a along the wavelength direction for a "xed time at the peak of the main laser pulse. The separation of the peaks provides information on the temperature.
Fig. 5. The density measurement is achieved by interferometry. The raw interferometric data is shown in (a) where the two-dimensional nature of the information is clear. The Thomson scattering volume is indicated by the blue dot. The data is reduced to give density as a function of space. In (b) the density in units of the critical density for the main laser beam is shown versus distance from the target along the axis of the incident laser.
The streak camera record is shown in Fig. 6 where the time increases upward and the spectral energy increases to the right. The "rst observation is that the He-like ion stage appears "rst with the H-like line becoming intense later in time. By looking at the raw data one sees that the He-like transition lasts well past the duration of the main laser pulse.
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Fig. 6. The raw data from the X-ray streak camera. The time increases upward and the spectral range covers the K-shell line of He-like and H-like Al from 1600 eV for the He-like 1s2}1s2p through the H-like Lyman series up to 2200 eV.
4. Preliminary analysis The atomic physics code HULLAC has been run to obtain an indication of the sensitivity of the line ratios to the electron temperature. HULLAC is a fully relativistic atomic structure code that uses an analytic potential to create the basis set and contains detailed calculations for the energy levels and detailed rates for radiative and collisional bound}bound, bound}free, auto-ionization and dielectric recombination. The code uses the electron density and temperature as input. Fig. 7 shows the line structure for three di!erent temperatures where 430 eV is the experimental ¹ and % 500 eV shows the best "t to the observed line ratios, still relatively close to the experimental value. It is important to stress that our goal is to make the experiment su$ciently well diagnosed that one can obtain a critical evaluation of the computational capability. This means being able to evaluate both time-dependent initial value problems as well as testing the kinetics at speci"c times. Another modeling problem that needs to be addressed is the continued discrepancy between hydrodynamic models and the experiments. Fig. 8 shows the results of a 2-D LASNEX run for the experimental conditions. One can see that the di!erence in temperature between experiment and theory is still signi"cant. This runs counter to recent measurements in gold plasmas [17] in which the agreement between modeling and electron measurements was good. We will continue to investigate this issue although for testing the atomic physics models it is important to note that the experiment provides all the data required to model the line strengths. Finally, there is still some uncertainty in the location of the volume of the X-ray emission seen by the spectrometer relative to the Thomson scattering volume because the X-ray spectrometer collects all of the light from the target. One expects that the volumes are close because, whether one uses the hydrodynamics simulations as a guide or the fact that the emissivity scales as n2, the X-ray % emission will be weighted towards the highest densities where the aluminum is fully ionized. This issue will be resolved in the near future by implementing a gated X-ray spectrometer to observe the plasma edge-on to give the X-ray spectrum as a function of spatial position at a "xed time. The Thomson scattering volume will be scanned axially to obtain temperature and #ow velocity pro"les to make better contact with the LASNEX simulation, and eventually to remove the need for hydrodynamic simulations from the problem.
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Fig. 7. A calculation of the spectrum using the HULLAC suite of codes. The calculations are the solid lines and the data is denoted by a symbol. The three plots represent the HULLAC calculations for three di!erent temperatures.
Fig. 8. The results of a two-dimensional hydrodynamics simulation. The temperature and the electron density (in unit of the critical density) are associated to the left ordinate, and the mean ion charge is associated to the right ordinate. The results are for the central part of the plasma moving away from the target surface for increasing z and at a time of 0.5 ns after the peak of the laser pulse.
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5. Conclusion In summary, we have described an experiment in which detailed plasma diagnostics are used to constrain computer codes used to kinetics in a laser-produced plasmas. With this method one can determine the accuracy of plasma spectroscopy in regimes where probe laser beams can be used so that understanding can be obtained about the plasma spectroscopic accuracy in those cases where laser-based probes are not available or cannot be used, as is the case of certain target designs.
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