X-ray spectroscopy of isochorically heated matter driven by ultrashort laser pulses

K. Eidmann, U. Andiel, and F. Pisani


By irradiating a plane solid target surface with ultrashort laser pulses of a duration of $\approx$100 fs and an energy of $\approx$100mJ, plasma at solid density and temperatures of a few 100 eV can be generated, which process is called isochoric heating. Matter in this extreme state is present in the interior of stars and is therefore of interest for astrophysics. In experiments on earth such plasmas are achievable in the compressed core of inertial confinement fusion pellets, whose realization requires large high energy laser facilities firing a few shots per day only. The attractiveness of using fs-lasers for generating such plasmas results from their high repetition rate (10Hz or more) and their low cost, which opens the unique possibility to systematically study the complex behavior of dense hot plasmas.

Principle of isochoric heating

The principle of isochoric heating is sketched in Fig. 1. The short laser pulse, which must have a very low pre-pulse contribution to avoid low-density pre-plasma formation, deposits its energy within the skin layer of a thickness of 5-10nm. This very thin layer expands rapidly already during the duration of the laser pulse. In order to achieve isochoric heating the energetic electrons generated in the absorption zone are crucial. They penetrate deeper into the target and heat a region whose thickness is determined by their mean free path. For our conditions the typical energy of the electrons is 20 keV and the thickness of the heated layer exceeds 400nm. This thick layer remains during 1-2 ps in the dense state before significant expansion sets in. Typical atomic properties of the dense aluminum plasma generated in our experiment are illustrated in Fig. 2. At solid density the distance between the highly ionized Al ions amounts to 3Å  only. Thus the outer orbitals overlap and most of the free electrons are moving within the orbitals. As a consequence the energy levels are perturbed. They are broadened and, due to the sceening effect of the free electrons, lowered. Line broadening and a line red-shift in the emitted x-ray spectra is expected, therefore.


In our experiments we have isochorically heated aluminum and studied its K-shell emission. To obtain laser pulses with a high power contrast (i.e. with a low pre-pulse level), the 200mJ output pulses of the ATLAS laser at 790 nm were frequency doubled yielding 60mJ per pulse at 395nm and at a duration of 150 fs. After focusing by an off-axis parabola the peak intensity on target is $\approx$1018W/cm2 and the average intensity in the typical spot of x-ray emission (of 10$\mu$m diameter) is a few 1017W/cm2. The laser is incident on the target at an angle of 45o with p-polarization in order to optimize the conversion of laser energy into hot electrons. To measure the x-ray emission we use a von Hamos spectrometer with x-ray film for achieving time-integrated spectra of high spectral resolution ( $\lambda /\Delta\lambda$=2000). An ultrafast x-ray streak camera (time-resolution $\Delta t$=1ps) coupled to a conical von Hamos spectrometer was used for time resolved measurements [1,2]. Our first experiments have been performed with a massive Al target. It was covered by a thin layer of MgO or C to avoid emission from the hot rapidly expanding front layer [3]. By changing to a new type of target consisting of a thin Al sample layer (SL) of 25nm thickness embedded in solid carbon, substantial advantages were achieved: (i) The emission is generated in a layer of well defined thickness. (ii) The small thickness of the SL results in negligible temperature and density gradients. (iii) Opacity effects become less important, because the SL is thin. (iv) Embedding the SL at different depths originates in different time-averaged densities, because a deeply buried SL expands slower than a SL buried close to the surface. A series of K-shell spectra ranging from the He$_\alpha$  line to the Ly$_\beta$  line is plotted in Fig. 3 for SL's at different depths.
Although the spectra are looking similarly on a first glance, they show significant differences in details. The widths of the lines increase with the SL depth, which is clearly visible in Fig. 3 for the He$_\beta$  and Ly$_\beta$  lines. The He$_\gamma$  line is present at the smallest depth of 25nm only. These detailed differences in the spectra are caused by the density which increases with depth. A rough value of the temperature can be obtained from the line ratios. The Ly$_\beta$/He$_\beta$  line ratio yields a temperature of 450 eV for all depths. Also, one notices that the spectrum is sitting on the recombination continuum of the carbon with a slope yielding a temperature of 250eV. This value is lower than the value in Al and represents the space-averaged temperature of the total hot carbon layer including the colder matter deep in the target. Besides an increase of the line width the spectra show also a redshift of the lines increasing with depth. The presence of a line shift was discussed controversially during the past. This is because its verification needs (i) considerably high densities and (ii) a very accurate wavelength calibration. The latter point was met by us by superimposing the cold Si K$_\alpha$ line as a fiducial on the Al spectra. It is very close to the Al Ly$_\alpha$  line. The result of this measurement is shown by Fig 4. Clearly the Ly$_\alpha$  line shifts more and more to the red with increasing depth of the SL.
The increase of redshift with depth is plotted in Fig. 5 for the Ly$_\alpha$  and Ly$_\beta$  lines. Since the red shift increases approximately with the forth power of the quantum number of the upper level it is much larger for the Ly$_\beta$  line than for the Ly$_\alpha$  line. Information on the lifetime of the hot dense plasma is obtained from time-resolved measurements. Examples of the duration of different lines are shown in Fig. 6. It shows the time dependence of the Ly$_\alpha$  and He$_\alpha$  lines at two different SL depths. Typical durations of the line emission amount to a few ps. The He$_\alpha$  line duration is somewhat longer than the Ly$_\alpha$  duration. The emission from the SL close to the surface (depth=25nm) takes somewhat longer due to enhanced recombination radiation in the expanding plasma.

Theoretical modeling

For the analysis of our spectroscopic data a collaboration exists with R. Mancini of the University of Nevada in Reno (USA). The theoretical curves in Figs. 3,5 and 6 are the result of a time-dependent analysis. For this purpose time-histories of the density and temperature, which are obtained from hydrodynamic calculations, were postprocessed by atomic-kinetic and spectral line shape computer codes [4]. The shifts of the resonance lines and the satellites, which are included in our model, are taken from a recent quantum-mechanical calculation [5]. The good agreement between theory and experiment indicates that we have reached a high level of understanding of the isochoric heating process and the Al K-shell emission. In particular, the agreement of the calculated and measured line shifts support the recent quantum-mechanical lineshift calculations and help to terminate a long-lasting controversy on this subject. For more details we refer to reference [6].


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  2. U. Andiel et al., submitted to Revue Scientific Instruments
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  4. R. C. Mancini, D. P. Kilcrease, L. A. Woltz, and C. F. Hooper, Jr., Comp. Phys. Comm. 63, 314(1991)
  5. G. C. Junkel, M. A. Gunderson, C. F. Hooper, Jr., and D. A. Haynes, Jr, Phys. Rev. E, 62, 5584(2000)
  6. U. Andiel, K. Eidmann, P. Hakel, R. C. Mancini, G. C. Junkel-Vives, J. Abdallah, and K. Witte, accepted for publication as Europhys. Lett.