Steady state electrostatic shock structure as seen from the shock frame. Electrons from the upstream region move freely, while electrons from the downstream region can be either free or trapped. Ions, which flow from upstream to downstream, are slowed down by the electrostatic potential and reflected back into the upstream for strong shocks.
Ion phase space structure as a function of the initial density ratio Γ between two plasma slabs/regions for and MeV. Snapshots are taken at . At t = 0, there is no relative drift between the two slabs.
Shock Mach number (solid lines) and fraction of ions reflected from the upstream (dashed lines) as a function of the initial density ratio Γ between two plasma slabs/regions for and .
Ion phase space structure as a function of the initial relative drift between two plasma slabs/regions for . Snapshots are taken at .
Shock Mach number (solid lines) and fraction of ions reflected from the upstream (dashed lines) as a function of the initial Mach number of the relative drift between two plasma slabs/regions for .
Critical Mach number for ion reflection in electrostatic shocks as a function of the density ratio Γ and temperature ratio Θ between the two plasma slabs/regions, for keV (dashed line 20 ) and MeV (solid line Eq. (10) ). The symbols indicate the simulation values for the non-relativistic (+) and relativistic (o) electron temperatures, which were obtained by measuring the speed of the shock structure (density jump or electrostatic field) when ion reflection is observed.
Electric field structure and accelerated ion spectrum from the interaction of two finite plasma slabs with a density ratio (a) and (b) , (c) and (d) , and (e) and (f) followed by an exponentially decreasing profile. Initially, ( ) and . Left panels show the initial density profile (black) and early time longitudinal electric field (blue), whereas the right panels show the ion phase space (orange) and the spectrum of ions aheadof the shock (black line) at t = .
Temporal evolution of the laser-plasma interaction at near critical densities, from electron heating to shock formation, and ion acceleration. Row 1 shows the evolution of the ion density profile and row 2 shows a central lineout of the density along the laser propagation axis. Row 3 illustrates the evolution of the electron phase-space, row 4 the longitudinal electric field, and row 5 the ion phase-space.
Time evolution of the ion density (green) and longitudinal electric field (orange). The strong feature between and is associated with the laser plasma interaction and the fields driven by the fast electrons. The solid line follows the shock and the dotted line follows the reflected ions.
Ion phase-space and spectrum shock accelerated ions (dashed line) for upstream plasmas with different scale lengths: (a) (sharp plasma-vacuum transition), (b) , (c) , and (d) . The initial density profile is indicated by the solid lines and is given by Eq. (14) .
(a) Electron distribution for different laser intensities corresponding to (green), 5 (light blue), 10 (red), 15 (orange), and 20 (blue). The distributions are fitted to a 3D relativistic Maxwellian of the form (dashed lines). (b) Scaling of the electron temperature with the laser amplitude a 0. The obtained scaling is consistent with Eq. (13) for a laser-electrons energy coupling efficiency .
(a) Spectrum of shock accelerated ion beams for different laser intensities corresponding to (green), 5 (light blue), 10 (red), 15 (orange), and 20 (blue). (b) Scaling of ion energy with the laser amplitude a 0. The obtained scaling is consistent with Eq. (15) .
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