Accelerating monoenergetic protons from ultrathin foils by flat-top laser pulses in the directed-Coulomb-explosion regime

We consider the effect of laser beam shaping on proton acceleration in the interaction of a tightly focused pulse with ultrathin double-layer solid targets in the regime of directed Coulomb explosion. In this regime, the heavy ions of the front layer are forced by the laser to expand predominantly in the direction of the pulse propagation, forming a moving longitudinal charge separation electric field, thus increasing the effectiveness of acceleration of second-layer protons. The utilization of beam shaping, namely, the use of flat-top beams, leads to more efficient proton acceleration due to the increase of the longitudinal field.

Figure 1

(Color online) Principal scheme of foil fraction acceleration by Gaussian (radius of the area with all electrons expelled is $r_0^G$) and flat-top beams (radius of the area with all electrons expelled is $r_0^{\mathrm{ft}}$).

Figure 2

Dependencies of the ratio of maximum proton energy gained in the longitudinal field generated by a laser pulse with super-Gaussian beam profile and the one gained in the field generated by a pulse with Gaussian profile on laser pulse power for different beam profiles ($\alpha =4,6$, and 8); $n_e=400n_{\mathrm{cr}}$, $l_{\mathrm{Al}}=0.1\lambda$ (2D case, presented to compare with PIC simulation results)

Figure 3

(Color online) Evolution of heavy ion density (from cycle 11 to cycle 20) in the 500 TW laser pulse interaction with a $0.1\lambda$ thick aluminum foil.

Figure 4

Interaction of a 500 TW laser pulse $(f∕D=1.5)$ with ultrathin double-layer foil. (a) The dependence of the electric longitudinal field strength on spatial coordinates at $t=23$, the inset represents the longitudinal field behavior along $y=0$. (b) Ion density distribution at $t=23$.

Figure 5

(Color online) Interaction of a focused $(f∕D=1.5)$ 500 TW laser pulse with a $0.1\lambda$-thick aluminum foil with $0.05\lambda$-thick hydrogen second layer. (a) The dependence of the total charge (1 for flat-top and 2 for Gaussian beams) in the area $0<x<20$, $-1.5<y<1.5$ on time. (b) The dependence of maximum values of the accelerating longitudinal electric field (1 for flat-top and 3 for Gaussian beams) and proton energy (2 for flat-top and 4 for Gaussian beams) on time. Charge is measured in units of electron charge, time in wave periods, proton energy in MeV, and electric field in units of $m_{e}c\omega ∕e$.

Figure 6

(Color online) Spectra of protons that are accelerated inside an angle of 10° to the target normal by Gaussian (1) and super-Gaussian (2) pulses.