Shock ion acceleration by an ultrashort circularly polarized laser pulse via relativistic transparency in an exploded target

We investigated ion acceleration by an electrostatic shock in an exploded target irradiated by an ultrashort, circularly polarized laser pulse by means of one- and three-dimensional particle-in-cell simulations. We discovered that the laser field penetrating via relativistic transparency (RT) rapidly heated the upstream electron plasma to enable the formation of a high-speed electrostatic shock. Owing to the RT-based rapid heating and the fast compression of the initial density spike by a circularly polarized pulse, a new regime of the shock ion acceleration driven by an ultrashort (20–40 fs), moderately intense (1–1.4 PW) laser pulse is envisaged. This regime enables more efficient shock ion acceleration under a limited total pulse energy than a linearly polarized pulse with crystal laser systems of $\lambda \sim 1\mu \mathrm{m}$.

Figure 1

One dimensional simulations with $a_0=18$, circular polarization, and pulse duration 20 fs. $l_f=2\mu \mathrm{m}$ for (a)–(c) and (f). (a) Compression of initial density spike, (b) during RT, and (c) after RT along with the ion phase space. (d) Average electron temperature in the upstream for different $l_f$ and (e) Mach numbers. (f) Comparison of Eq. (2) and simulation data for $l_f=2\mu \mathrm{m}$.

Figure 2

Energy spectra of the accelerated ion beams for three different cases: $l_f=1,2$, and $3\mu \mathrm{m}$ at $t=240$ fs.

Figure 3

Mach number oscillation for increased laser intensity from $a_0=18$ to 22 for $l_f=2\mu \mathrm{m}$. Inset represents the density spikes for $a_0=22$ (dotted black line) and 18 (solid red line).

Figure 4

Scaling of ion (${\mathrm{C}}^{6+}$) energy as a function of laser amplitude, obtained from one-dimensional PIC simulations. Four different cases are presented; circularly polarized (CP) pulses with $\tau =20$ fs and $l_f=2\mu \mathrm{m}$ (circles), where $\tau$ is the pulse duration. They can be directly compared with the linearly polarized (LP) pulses with $\tau =40$ fs and $l_r=2\mu \mathrm{m}$ (inverted triangles). LP pulses with $\tau =500$ fs and exponential plasma tail in the rear side with $l_r=20\mu \mathrm{m}$ (squares). LP pulses with varying $a_0$ and $\tau$, keeping the pulse energy ($\sim a_0^2\tau$) constant by that of $a_0=18$ and $\tau =20$ fs case of CP, and with $l_r=20\mu \mathrm{m}$ (triangles). Dashed line represents the ion energy scaling law from Ref. [28] for $\tau =500$ fs, ${\mathrm{C}}^{6+}$ ion, and $l_r=20\mu \mathrm{m}$.

Figure 5

Three dimensional PIC simulation with $a_0=16$, circular polarization, ${\tau }_f=33$ fs and ${\tau }_r=13$ fs, and $l_f=0.33\mu \mathrm{m}$. (a) Ion density and longitudinal field $E_x$ on $Z=25\mu \mathrm{m}$ plane (which is drawn on the upper side of the box) after leaving the laser field at $t=120$ fs. (b) The half cut of a $V_{x}XY$-phase space of ions. (c) Temporal evolution of the Mach number. (d) Ion energy spectrum at $t=120$ fs.