Stable Laser-Driven Proton Beam Acceleration from a Two-Ion-Species Ultrathin Foil

By using multidimensional particle-in-cell simulations, we present a new regime of stable proton beam acceleration which takes place when a two-ion-species shaped foil is illuminated by a circularly polarized laser pulse. In the simulations, the lighter protons are nearly instantaneously separated from the heavier carbon ions due to the charge-to-mass ratio difference. The heavy ion layer expands in space and acts to buffer the proton layer from the Rayleigh-Taylor-like (RT) instability that would have otherwise degraded the proton beam acceleration. A simple three-interface model is formulated to explain qualitatively the stable acceleration of the light ions. In the absence of the RT instability, the high quality monoenergetic proton bunch persists even after the laser-foil interaction ends.

Figure 1

(a) Density distribution of the electrons (black), protons (green), and carbon ions (blue) at $t=20T_0$. The red dashed curve shows the electric field $E_x$, which is normalized to $E_0=m_{e}c\omega /e=3.2\times {10}^{12}\mathrm{V}/\mathrm{m}$. (b) The corresponding phase space distribution at $t=20T_0$. (c) Energy spectrum of the carbon ions (dark blue) and protons (light green) at $t=30T_0$. (d) Energy evolution in time from PIC simulations and the 1D theory. The laser pulse is incident from the left side and touches the foil at $t=10T_0$.

Figure 2

(a) Contours of protons (dark red) and carbon ions (light teal) in the 2D case at different time points: $t=30T_0$, $50T_0$, and $70T_0$. The color bar represents the proton numbers $\log (N)$. (b) Proton energy spectrum at: $t=30T_0$ (square, black), $t=50T_0$ (circle, green), $t=70T_0$ (triangle, red), and $t=90T_0$ (star, blue). For comparison, Frame (c) shows the proton density distribution in a pure hydrogen foil and frame (d) corresponds to its energy spectrum evolution.

Figure 3

Phase space of (a) protons and (b) carbon ions at $t=30T_0$. An obvious spiral structure is observed only for protons. Frames (c) and (d) show the carbon ion and proton energy distribution as a function of the divergency angle at $t=30T_0$.

Figure 4

Schematic of the laser-foil interaction in (a) C-H case and (b) pure H case. Here, $L_{\mathrm{H}}\ll L_{\mathrm{C}}$. In case (a), there are three interfaces: carbon-vacuum, carbon-proton, and proton-vacuum. Only the first interface is unstable. In case (b), both interfaces are finally unstable.