(Color online) 2D PIC simulation results of the evolution of averaged proton density transverse to laser beam (the first column), proton density map (the second column), averaged electron density transverse to laser beam (the third column), electron density map (the fourth column), normalized electromagnetic field energy density over incident laser energy density (the fifth column), and energy spectrum of the protons (the sixth column) at three instants. Top, middle, and bottom rows are at , 15.5TL , and 17TL , respectively. The vertical dashed lines in the first and the third columns show the critical density value. In the last column, dark-blue histograms in dark color show proton spectra collected within a window of and a width of in x co-moving with the foil; light-colored ones show proton spectra within and covering the entire simulation range in x.
(Color online) Simulation results with the same input parameters as in Fig. 1(a). Time evolution of ion momentum averaged within a window co-moving with the target from simulation (red line) and 1D theoretical calculation (blue line) using Eq. (2). (b) The evolution of ion energy spectra collected within the window as defined in (a). (c) The time evolution of normalized average density , of the electron layer (blue line), average , , and within a window co-moving with the target. The time when is around . (d) Evolution of the spatial distribution of the normalized ion energy density. The energy density is averaged over in y. The normalization factor is the incident laser energy density.
(Color online) The energy scaling from 2D PIC simulations for protons and carbon ions. The saturation time ts is recorded when the maximum of quasi-monoenergy (under the constraint ) is obtained. The dashed lines are theoretical calculations of the energy scaling.
(Color online) (a) The transverse ion density distribution averaged over a window along the laser propagation direction with the normalized laser wave amplitude and at , , and . (b) The case of incident laser amplitude and target density at the same time instants as in (a). (c) The dependence of the total growth of the mode with wave number ks at the saturation time on the laser amplitude. (d) Values of vs. normalized laser amplitude a 0. (e) vs. a 0, where 2π/ks is the dominant transverse periodic structure scale length just before the broadening of the proton energy spectrum in the simulation.
(Color online) The same simulation as in Fig. 1 but the Gaussian beam is replaced by a plane wave.
(Color online) The same simulation as in Fig. 1 but the foil density is doubled and thickness is halved.
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