Sketch of a double-layer target and characteristic profile of the sheath electric field.
Spatial distribution of the proton velocity (in the units ) for . Time is given in the units.
Evolution of the electric field (a) and the proton density (b) in comparison with results of the hybrid model (dashed lines) for , , and for the case of immobile heavy ions . Panel (c) shows the proton energy spectrum (energy is in units of ). Time is given in the units.
Hybrid simulation of the evolution of the electric field at the heavy-ion front for without a proton layer (curve 1), with it for and (curve 2), and for and (curve 3); . Dashed curves correspond to Eq. (13).
Evolution of the proton density for , , and in the case of [panel (a)]. Panel (b) shows the proton energy spectrum (energy is in units of ). Time is given in the units. Dashed lines correspond to the limit of immobile heavy ions .
Dependence of the peak energy in the proton spectrum on the proton areal density (parameter ) for (large points) and (small points). Solid line corresponds to proposed fit (14).
First stage of the proton energy spectrum evolution obtained in the full PIC simulation. The parameters are given in Sec. III.
Second stage of the proton energy spectrum evolution obtained in the full PIC simulation. Insert shows two spectra at 220 and 496 fs in the linear scale.
Proton phase space obtained in the full PIC simulation at the instant of 351 fs.
Ion density distribution at the instant of 351 fs.
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