2D PIC simulation results of the evolution of the electron density distribution (the first row), the proton density distribution (the second row) and the proton energy spectra (the third row) with the normalized incident laser intensity , the maximum plasma density , and the plasma thickness . From the left column on, the snapshots are at the times , , , and , respectively. Part I is the shock reflected protons, part II is the shock front.
Energy spectrum at and with input parameters , , and .
(a)-(d) are the proton energy phase space distributions at , , , and , respectively. (e)-(h) are proton momenta distributions at the same times. Part I is the shock reflected protons, part II is the shock front.
The smooth curves present the theoretical calculations of the proton energies evolving with time, and the piecewise linear curves with data points show the 2D simulation results of the proton energies evolving with time. The simulation parameters for blue, red, and black curves are (, , ), (, , ), and (, , ), respectively.
(a) and (b) are the curves of the electron density (black), proton density (red), electromagnetic energy density (blue), and electro-static field (magenta) at ; (c) and (d) are the proton energy phase space distributions at and ; (e) and (f) are the proton energy phase space distributions at and ; (g) and (h) are proton energy spectra at and . The input parameters are , , .
The obtainable proton energy comparison for (a) different initial plasma densities with plasma thickness and (b) different initial plasma thickness with plasma density . In both (a) and (b), blue lines are corresponding to , and red lines are of .
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