Experimental setup showing the main beam, the target, the probe beam reflecting off the target and the interferometer (in gray shaded box).
Working principle of the TASRI: the plasma expansion on the rear target surface (see Fig. 3) is imaged by the probe beam, goes through a Mach–Zehnder, and is selected by a slit. A central slice of the image is passed through a spectrometer to have time information exploiting the linear chirp of the probe beam. A motion of the fringes corresponds to a phase shift at the target rear surface.
Schematic of the phase measurement. (a) Case of an unperturbed target: the target rear surface acts as a perfect mirror. (b) Case of a weakly perturbed target by the early plasma expansion: the phase shift is significant on the laser axis only, while negligible further away. (c) Case of a strongly expanded target, leading to a pronounced phase shift everywhere, mostly in the central region.
Phase map (in radians) measured from a target irradiated with a , 320 fs laser pulse. The dotted lines indicate the distance from the center of the heated zone. The top and bottom maps are simply sign reversal of each other.
Bulk electron temperature vs laser energy as reported in Refs. 11, 13, 18, and 32 for a target of thickness .
Schematic for the reconstruction of the 2D density expansion maps from a series of side-by-side 1D expansion profiles. Overlaid are shown some rays of the probe beam incident at 45° and propagating in the 2D density profile. Note that the bins shown in the figure are only a schematic representation, the real calculation being made with a much finer mesh, as shown in Fig. 7.
2D profiles of the expanding plasma obtained by binning electron density profiles retrieved using the 1D model described in Ref. 35. (a) Isodensity contour map corresponding to 20 ps after the start of the expansion and (b) 3D view of the expanding plasma after 8 ps, with the trajectory of one probe beam ray.
(a) Radial density distribution of the hot electrons initiating the expansion . (b) Bulk electron temperature resulting from target heating. Both are shown for three Al target thicknesses and a laser intensity with pulse duration .
Schematic of an electron density profile, showing how the phase is calculated by integration of the trajectory through the plasma with changing density. The probe beam is coming from the right side.
Total collision frequency vs temperature for various densities of the Al target (see text for a description of the collision model). The density corresponds to the Al solid density, i.e., to an electron density of . Above the red line, collisional effects cannot be neglected in the dephasing calculation.
(a) Influence of collisions on the dephasing computed with , , and . (b) Same as (a) but with .
Plots of the phase of the exact solution (dotted line) given by Eq. (C14), WKB approximation (dashed line) and the difference between both (solid line) as a function of (in this case and ).
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