Schematic representation of laser and x-ray foci in the transverse plane. The volume shown represents the Rayleigh range of the laser focus while the dark banded region demonstrates the narrow slice of the plasma viewed by the detectors. The x-ray probe samples the plasma at various locations along the vertical -axis to obtain spatial distributions in the transverse plane. In practice, this is achieved by translating the laser focus vertically. It can also be translated along the -axis to obtain longitudinal distributions.
Measured x-ray absorption spectrum showing fitted and contributions. A small neutral contribution has already been subtracted. The fit procedure is described in Ref. 17. The arrow indicates the excitation energy of 14.313 keV where ion density measurements were carried out.
Spatial distributions of ions for various delays between the x-ray probe beam and the laser-induced ionization. Plotted is the dimensionless normalized ion density as defined in Eq. (2). At saturation the value is 1. The solid lines show the effect of deconvoluting the Gaussian x-ray beam profile. The difference is barely observable at and inconsequential at longer times.
The time evolution of various features of the experimental spatial profiles. Lines show the results of the model simulation for different initial electron temperatures. A 2:1 aspect ratio was assumed for the initial plasma geometry (at ) as shown in Fig. 1. The central amplitude (value at ) is plotted in (a) while (b) shows the rms width of each of the distributions of Fig. 3. The sum of each distribution is plotted in (c). The apparent rapid decrease in the case of the linear polarization data seen for in (a) and (c) is a consequence of dealignment (Ref. 21) as described in the text.
Simulated spatial distributions of ions for various delays between the x-ray probe beam and the laser-induced ionization. The four different columns correspond to different simulation conditions with (a)–(c) showing results for isothermal expansion, while (d) incorporates adiabatic cooling of the electrons as described above. The initial conditions are as follows: (a) 1 eV electron temperature and 1:1 aspect ratio of the laser focus, (b) 8 eV electron temperature and 1:1 aspect ratio, (c) 8 eV temperature and 3:1 aspect ratio, and (d) 8 eV initial temperature with adiabatic cooling and 3:1 aspect ratio. Plotted is the normalized ion density relative to the value at . The starting -distributions are identical in all four cases.
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