Optimized matching conditions for self-guided laser wakefield accelerators

Abstract

We revisit the matching conditions for self-guided laser pulse propagation in plasma and refine their formulation to maximize the energy of electrons produced via laser wakefield acceleration. Bayesian optimization, combined with particle-in-cell simulations carried out in a quasi-three-dimensional geometry and a Lorentz-boosted frame, is employed. The optimization identifies the maximum electron energy that a self-guided laser wakefield accelerator, driven by a laser of a given energy, can produce, together with the corresponding acceleration distance. Our results further demonstrate that electrons with energies close to the maximum value can be obtained across a relatively wide range of input parameters and without the need for their precise tuning. This provides substantial flexibility for experimental implementation and significantly relaxes the operational constraints associated with self-guided laser wakefield accelerators.

Figures (3)

• Figure 1: Mean function of the GP model for the maximum electron energy, $\mathcal{E}_{\mathrm{e, max}}$, and the corresponding acceleration distance, $l_{\mathrm{acc}}$, based on the results of 500 PIC simulations for three different values of proportionality parameter $\kappa$, (a) $\kappa = 1.5$, (b) $\kappa = 2.0$, and (c) $\kappa = 2.5$.
• Figure 2: Locations of the trials in the parameter space and the corresponding maximum electron energies, $\mathcal{E}_{\mathrm{e,max}}$. The black mesh encloses the region where the upper $5\%$ of the maximum electron energy distribution (i.e., $\mathcal{E}_{\mathrm{e,max}} > 73.5~\mathrm{MeV}$) is obtained. The blue areas show the projections of this region onto the respective coordinate planes.
• Figure 3: Spatial distributions of the laser intensity, $I$, electron density, $n_{\mathrm{e}}$, and energy of accelerated electrons, $\mathcal{E}_{\mathrm{e}}$, at three successive time instants, (a) $t = 50 \, T_0$, (b) $t = 100 \, T_0$, and (c) $t = 150 \, T_0$, obtained from the PIC simulation with input parameters closest to the optimum identified by BO. Only test-electron macroparticles with energies within the upper $10\%$ of the maximum electron energy at the given time step, $\mathcal{E}_{\mathrm{e,max}}(t)$, are shown and $I_0 = 2 \mathcal{P}_0 / \pi w_0^2$. The plasma density is sliced along the $x$–$y$ plane to reveal the inner structure of the plasma wave.