Double layer structure of the laser piston maintained by the radiation pressure. Curves: laser field amplitude—dotted-dashed line (blue), laser intensity—thin solid (brown), electron density—dashed (green), electrostatic field—thick solid (red), ion density—solid (black). We distinguish an ion charge separation layer and the electron sheath in front of it. The curves stem from the analytical description of both layers discussed below. The data (in arbitrary units along the vertical axis) are taken from solutions for the laser field amplitude and the ion density of a deuterium plasma. Ion and electron density profiles are limited on the left by their asymptotes at and , correspondingly.
(a) Dependence of the piston velocity on the ion density in a deuterium plasma for laser pulses with a circular polarization. The values of the dimensionless vector potential are shown in the legend. (b) Ion kinetic energy as function of ion density for the same values of as in (a).
(a) Density dependence of the laser pulse duration (normalized to the laser period ) that is required to traverse an exponential plasma layer with the density scale length for several laser amplitudes. (b) Same dependence for different values of the plasma scale length and a fixed amplitude . In both panels circular laser polarization and deuterium plasma are assumed.
(a) Energy distributions of accelerated ions for various laser amplitudes in an exponential plasma layer with the density scale length . Curves: thick lines—, dashed lines—. Different lines show the dependence on the parameter for the maximum density . The distribution is normalized by the total number of ions in the layer, the ion energy is normalized to . (b) Dependence of the average, minimum, and maximum ion energies on the laser amplitude for the same conditions as shown in panel (a). We assumed circular laser polarization and deuterium plasma.
Thickness of the ion charge separation layer normalized to the value in dependence on the piston relativistic factor .
Results of the numerical integration of Eq. (16). (a) Velocity of the accelerated ions in the piston reference frame for a circularly polarized laser pulse with the amplitude and several deuteron densities. The spatial coordinate is normalized to the ion inertia length. In comparison, the thick curves demonstrate the cases , —solid line, and , —dashed. (b) Ion gamma factors. (c) Ion density distributions normalized to the density of the unperturbed plasma. Vertical lines show the asymptotes at . (d) Spatial distributions of the normalized electrostatic potential and field. Curves (orange/grey for the electrostatic field): thin—, thick—. The line style of the curves for different ion densities follows the legend in panel (b). Blue lines and the magenta curve (double lines) show the solution for the case and , when the corrected boundary condition for is used (see Sec. ???).
Results of the numerical integration of Eqs. (25) and (31). (a) Electron and ion velocities in the piston reference frame for a circularly polarized laser wave with the amplitude and several values of the ion density. The spatial coordinate is normalized to the electron inertia length. (b) Electron and ion gamma factors. (c) Electron density distributions normalized to the critical density. The ion density normalized to the initial value is also shown. Ion characteristics in panels (a)–(c) are plotted as tiny dashed curves. [(d)–(f)] Spatial distributions of the normalized vector potential, electrostatic potential and the electric field. In panels (a)–(f), similar initial ion densities are used and the corresponding results are plotted with the same line style [see legend in panel (b)].
Dependence of the maximum evanescent field on the plasma density for two amplitudes of the incident laser pulse, and 100.
Results of PIC simulation of ion acceleration in plane wave geometry by a circularly polarized laser pulse with intensity illuminating a deuterium plasma layer with a density , at the instant of . (a) Intensity of the transverse electromagnetic field (upper curve) in comparison with the initial profile at (lower curve). (b) Spectrum of the magnetic field in vacuum. (c) Dependence of the maximum electrostatic field on time and (d) its spectrum. Phase plots for (e) electrons and [(f) and (g)] ions and (h) ion energy distribution. Phase plots for (i) electrons and (j) ions for the case of a linearly polarized laser pulse with the same intensity .
Ion acceleration in plane wave geometry by a laser pulse with intensity in a plasma layer with density . The same dependencies as in Fig. 9 are shown for [(a)–(h)] circularly and [(i) and (j)] linearly polarized pulses at the instant .
Oscillations at the laser-plasma interface for the case of a circularly polarized laser pulse with an amplitude interacting with a plasma layer of a density . Upper row: transverse electromagnetic field intensity (left axis, red) and longitudinal electrostatic field (right axis, black). Middle row: electron (left, red) and ion densities (right, blue). Bottom row: longitudinal momenta of electrons (left, red) and ions (right, blue). The corresponding instants for the columns (in units of ) are shown on top of each column.
Phase plots of electrons and ions after 100 cycles of interaction of the laser pulse of intensity with a plasma layer of density . [(a)–(d)] Circularly and [(e)–(h)] linearly polarized cases are shown. Panels (a) and (b) and (e) and (f) present the case where the high-frequency radiation losses are taken into account, panels (c), (d), (g), and (h) present the cases without electron radiation losses.
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