Self-Organizing GeV, Nanocoulomb, Collimated Proton Beam from Laser Foil Interaction at $7\times {10}^{21}\mathbf{W}/{\mathrm{cm}}^2$

We report on a self-organizing, quasistable regime of laser proton acceleration, producing 1 GeV nanocoulomb proton bunches from laser foil interaction at an intensity of $7\times {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$. The results are obtained from 2D particle-in-cell simulations, using a circular polarized laser pulse with Gaussian transverse profile, normally incident on a planar, 500 nm thick hydrogen foil. While foil plasma driven in the wings of the driving pulse is dispersed, a stable central clump with $1–2\lambda$ diameter is forming on the axis. The stabilization is related to laser light having passed the transparent parts of the foil in the wing region and enfolding the central clump that is still opaque. Varying laser parameters, it is shown that the results are stable within certain margins and can be obtained both for protons and heavier ions such as ${\mathrm{He}}^{2+}$.

Figure 1

Foil density evolution. Left: electrons, right: ions, at times (a),(d) $t=16$, (b),(e) $t=36$, (c),(f) $t=46$, in units of laser period. The laser pulse is incident from the left and hits the plasma at $t=10$. Only half the transverse size of the simulation box is plotted in frames (b), (c), (e), (f), for better resolution of fine structures.

Figure 2

(a) Laser field $\sqrt{E_y^2+E_z^2}$ at $t=46$, the dashed line marks the concave pulse front pushing the ion clump; (b) charge density distribution ($n_i-n_e$) at $t=46$; (c) current density at $t=36$ (normalized by $e{n}_{e}c$); (d) current density at $t=46$. The black arrows in the clump region indicate the direction of electron motion.

Figure 3

(a) Number of protons in the center of the foil ($r\le \lambda$) versus time in units of laser cycles; (b) proton energy; (c) evolution of energy spectrum for beam ions located inside the central clump ($r\le \lambda$); (d) density and energy distributions of protons at $t=58$ (the color bar gives ion energy in MeV).

Figure 4

Scaling studies (scan a parameter and all other parameters are fixed) (a) scaling the proton energy/charge with the normalized vector potential $a$; (b) proton energy/charge with the laser spot size; (c) scaling the helium energy/charge with $a$; (d) Proton energy/charge with the rise time in the unit of laser cycles.