Optimization of laser-driven proton acceleration in a near-critical-density plasma

TL;DR

The paper addresses maximizing laser-driven proton energy under fixed laser energy by exploring how focus size and plasma density profile influence acceleration in near-critical-density targets. It combines 2D and 3D PIC simulations with analytic modeling to show that smaller focal spots enhance the longitudinal ponderomotive force, yielding higher proton energies (e.g., from 3 μm to 0.8 μm) and stronger electron heating that strengthens the accelerating fields. A two-component field model and a velocity-matching density down ramp are developed and validated, demonstrating near-GeV proton energies (exceeding 600 MeV) with relatively narrow energy spreads. The findings suggest that advanced focusing and tailored plasma density profiles can achieve high-energy proton beams with lower laser energies, improving prospects for compact laser systems in medicine and science.

Abstract

Optimizing laser and plasma parameters is crucial for enhancing accelerated proton energy in laser-driven proton acceleration with finite laser energy for applications such as cancer therapy. Tight focusing plays a significant role in improving laser-driven proton acceleration, which is generally believed as a result of the enhancement of laser intensity. However, we find that even at a fixed laser intensity, reducing the focal spot size still enhances the proton energy. Through particle-in-cell simulations and theoretical modeling, we find that at a small spot size (0.8 μm), the maximum proton energy is enhanced by 56.3% compared to that obtained at a conventional spot size (3 μm). This improvement is attributed to the dominance of ponderomotive-force-driven electrons at reduced spot sizes, which generate stronger charge-separation fields that propagate at higher velocities. Furthermore, to optimize proton acceleration, we analytically derive an ideal plasma density profile that promotes phase-stable proton acceleration, yielding an additional energy increase of 61.3% over the case of a tightly focused laser interacting with a planar target of uniform density. These findings remain robust under parameter variations, indicating that advanced focusing techniques combined with optimized plasma profiles could relax the demand for high laser energies, thereby reducing the reliance on large-scale laser facilities in medical and scientific applications.

Figures (4)

• Figure 1: (a) Variation of the energy of the highest-energy proton ($E_p$) with time under focal spot sizes of 3 $\mu$m and 0.8 $\mu$m. (b) Solid lines represent proton energy ($p$) spectrum at the end of acceleration (t = 90$T_0$), showing significantly higher proton energy with a smaller focal spot compared to the larger one. Dotted lines depict electron energy ($e$) spectrum at t = 24$T_0$, exhibiting higher electron temperature with a smaller focal spot, revealing a faster electron pushing at a smaller focal spot. The dashed lines depict the proton energy spectrum in 3D simulations, confirming the validity of our results. The transverse laser electric field distribution and plasma electron density distribution for focal spot sizes of 3 $\mu$m (c) and 0.8 $\mu$m (d) at t = 24$T_0$, respectively. The red solid lines indicate axial electron density profiles, revealing more pronounced electron accumulation at a smaller focal spot.
• Figure 2: (a) Accelerating electric field and proton phase-space distribution at t = 40$T_0$ (a) and t = 60$T_0$ (b). At t = 40$T_0$, a Hole-Boring field forms inside the target while a TNSA field emerges behind it. By t = 60$T_0$, these two fields have merged and then drift backward. The axial accelerating fields at different times for 3 $\mu$m (c) and 0.8 $\mu$m (d) focal spots, with green lines representing the trajectories of the highest-energy proton. The dotted lines represent t = 40$T_0$ corresponding to (a) and the dashed lines represent t = 60$T_0$ corresponding to (b). The proton accelerated to the highest-energy is from a position more close to the target front surface in (d), showing earlier proton capture by the accelerating field at a smaller focal spot.
• Figure 3: (a) Proton energy as a function of focal spot size under different electron densities. (b) Proton energy versus focal spot size at varying laser intensities. The theoretical predictions are represented by solid lines and the simulation results are represented by scatters. Across all parameters, proton energy consistently increases as the focal spot size decreases at a spot size smaller than 2 $\mu$m.
• Figure 4: (a) Density profiles derived from numerically solved and function fitted solutions of velocity-matching equation of protons and accelerating field. (b) Proton energy spectrum under this velocity-matching phase-stable acceleration. Electron density distributions, accelerating field distributions, and proton phase-space distributions at t = 50$T_0$ (c) and t = 70$T_0$ (d), demonstrating velocity-matching between protons and the accelerating field. The dotted line in (d) represents the front edge of the accelerating field, illustrating the reflection of protons by the shock.