Optimizing laser-driven proton acceleration from overdense targets

Abstract

We demonstrate how to tune the main ion acceleration mechanism in laser-plasma interactions to collisionless shock acceleration, thus achieving control over the final ion beam properties (e. g. maximum energy, divergence, number of accelerated ions). We investigate this technique with three-dimensional particle-in-cell simulations and illustrate a possible experimental realisation. The setup consists of an isolated solid density target, which is preheated by a first laser pulse to initiate target expansion, and a second one to trigger acceleration. The timing between the two laser pulses allows to access all ion acceleration regimes, ranging from target normal sheath acceleration, to hole boring and collisionless shock acceleration. We further demonstrate that the most energetic ions are produced by collisionless shock acceleration, if the target density is near-critical, ne ≈ 0.5 ncr. A scaling of the laser power shows that 100 MeV protons may be achieved in the PW range.

Figure 1

Simulation setup: (a) The high-density target is irradiated by a laser with large focal area (b) leading to hydrodynamic expansion of the target. (c) A second, stronger laser pulse launches (d) the acceleration process.

Figure 2. Maximum proton energies expected from theory as function of the relativistic target density for a₀ = 10 due to different acceleration mechanisms: target normal sheath acceleration (green), collisionless shock acceleration (blue), hole boring (brown).

The time axis corresponds to the time delay between the heating pulse with a₀ = 0.1 initiating a hydrodynamic expansion and the second laser pulse. The maximum proton energies in the simulations measured inside the target are compared for a cubed (black squares) and a spherical target (red dots).

Figure 3

Density (a) and magnetic field (b) evolution along x₁ at x₂ = x₃ = 200 c/ω₀ for initial target density n₀/γn_cr = 1, laser intensity a₀ = 10 and . The grey and black lines show the hole boring velocity, v_hb, and shock velocity, v_sh, respectively. The green dashed lines have a slope v = 0.01 c and the inset shows B₃ at tω₀ = 806.

Figure 4

(a) Proton energy spectra for a₀ = 10 at t = 0.8 ps and varying target densities given in y = n₀/γn_cr. (b) Number of protons with energy above a threshold energy E_th vs. threshold energy and target density n₀/γn_cr.

Figure 5. Maximum proton energy vs. time.

Figure 6. Maximum proton energy vs. varying target density n₀γn_cr: Simulation with (blue squares) compared to case a₀ = 10 (cf. Fig. 2) showing .