Laser ion acceleration from concave targets by subpicosecond pulses

Abstract

Laser-driven proton acceleration provides a powerful route for generating ultrashort, high-charge proton beams. Many applications, including secondary neutron sources and inertial fusion, benefit from tight proton beam focusing. Concave targets offer a robust solution, yet the scaling of proton focusing with laser and target parameters remains poorly understood. Here, we present a numerical study of laser-driven proton acceleration and focusing from hemispherical targets using the fully kinetic, relativistic Particle-In-Cell code EPOCH. We focus on the sub-picosecond laser-pulse regime (duration $\lesssim 10^2$ fs), centering on the laser parameters of our recent experiment at the CSU ALEPH laser facility. We investigate the proton acceleration mechanisms, characterize proton focusing, and assess how focal spot parameters scale with laser and target parameters. We identify Target Normal Sheath Acceleration as the dominant mechanism, supplemented by a secondary post-acceleration stage near the geometrical center of the hemisphere. We demonstrate that both the proton focal spot size and focal plane position scale approximately linearly with the hemisphere radius, with the focal plane consistently located downstream of the geometrical center. The opening angle of the concave target mainly affects the proton beam waist. Energy-dependent proton focusing is interpreted as a consequence of the evolving curvature of the accelerating structure, which departs from the target curvature. Evidence for self-similar proton focusing is found in the regime of nearly uniform target irradiation.

Figures (13)

• Figure 1: (a) Sketch of the 2D EPOCH simulation setup. A laser pulse enters from the left boundary and propagates along the $y=0$ axis, interacting with a gold hemispherical foil and accelerating protons from the contamination layer on the rear side of the target. A zoom-in of the front target surface highlights the presence of preplasma on the laser side of the target. (b) Illustration of 3D simulation result showing protons focused near the geometrical center of the hemispherical target.
• Figure 2: Proton density distributions in laser-driven proton acceleration from concave targets. (a) $R_{\rm hemi}=\infty$ (flat), (b) $R_{\rm hemi}=120\, \rm \mu m$, and (c) $R_{\rm hemi}=20\, \rm \mu m$. Dashed lines indicate the initial target location, and red lines show the transverse laser intensity profile.
• Figure 3: Acceleration mechanism in quasi-1D (along the laser axis) for $R=\infty$ (flat, red), $120$ (dotted blue line), and $20~\mu$m (dashed green line) hemispheres. (a,b) Electron densities, (c,d) electron temperatures, (e,f) proton densities, and (g,h) longitudinal electrostatic fields at $t=t_{\rm peak}+0.15~\rm ps =0.4$ ps (a,c,e,g) and $t=t_{\rm peak}+0.95$ ps (b,d,f,h). Vertical semitransparent dashed line denotes $R_{\rm hemi}=20\,\mu$m center. TNSA-like acceleration, a post-acceleration stage, and plasma focusing for $R_{\rm hemi}=20~\mu$m are evident.
• Figure 4: Dependence of laser ion acceleration on hemisphere target radius in 2D PIC simulations. (a) Hot electron temperature and (b) hot electron density at the rear side of the target at $t=t_{\rm peak}+0.15$ ps. (c) Temporal evolution of the hot electron cloud temperature. (d) Peak accelerating field as a function of $R_{\rm hemi}$. (e) Laser-to-proton conversion efficiency (all protons, fast protons only, and normalized by the total number of protons). (f) Maximum proton energy at $t=1.25$ ps for $R_{\rm hemi}=20,\,40,\,80,\,120,\,\infty~\mu$m. Theoretical estimates for the hot electron temperature, peak accelerating field, and proton cutoff energy (based on Refs. wilks2001mora2003) are also shown.
• Figure 5: Role of the sheath field and secondary acceleration in hemispherical targets. (a) Time evolution of the peak electrostatic field along $x$ in 2D PIC simulations for varied $R_{\rm hemi}$. The red band shows analytical field estimates from Eq. \ref{['eq:TNSAt']}. (b) Absolute and signed (inset) proton energy gain per unit length along the laser axis for $R_{\rm hemi}=20,\,120,\, \infty~\rm \mu$m. Vertical dashed lines depict the location of the geometrical center of the respective hemisphere. The contribution of secondary acceleration near the geometrical center is highlighted.