Bayesian Optimization of a Laser-Plasma Accelerator

Generating high-quality laser-plasma accelerated electron beams requires carefully balancing a plethora of physical effects and is therefore challenging—both conceptually and in experiments. Here, we use Bayesian optimization of key laser and plasma parameters to flatten the longitudinal phase space of an ionization-injected electron bunch via optimal beam loading. We first study the concept with particle-in-cell simulations and then demonstrate it in experiments. Starting from an arbitrary set point, the plasma accelerator autonomously tunes the beam energy spread to the subpercent level at 254 MeV and $4.7\mathrm{pC}/\mathrm{MeV}$ spectral density. Finally, we study a robust regime, which improves the stability of the laser-plasma accelerator and delivers sub-five-percent rms energy spread beams for 90% of all shots.

Figure 1

Optimization PIC simulations of localized ionization injection: longitudinal electron phase spaces (a)–(c) and corresponding setups (d)–(f) with tunable nitrogen-hydrogen mixture (purple) and pure hydrogen (blue) region, plasma density (gray) and variable laser energy and focus position (red line). (g) The objective function, $\sqrt{Q}\tilde{E}/\mathrm{\Delta }E$, a measure for the spectral density, improves during the optimization.

Figure 2

Setup of the LUX accelerator. The laser energy and focus position in the plasma source with variable gas flows are controlled with a movable lens and an attenuator. Circular inset: plasma density (blue and green) and the laser envelope from a particle-in-cell simulation. The laser drives a spherical plasma cavity in the back of which an electron beam is injected and accelerated.

Figure 3

Experimental optimization of LPA electron beams: (a)–(c) Measured energy spectra; (d) measured objective function (dots) with the cumulative best result (blue line); (e)–(g) Input parameters with shot to shot measurements of the laser energy, focus position, and gas flows for each input setting.

Figure 4

Energy spectrum at optimized settings: averaged spectrum (black) and standard deviation (gray area) over the best 100 of 2500 measured shots with a Gaussian fit (${\sigma }_{E,\mathrm{fit}}$, blue) and corresponding statistics. The energy spectra are normalized to their respective median energy, to eliminate the effects of shot-to-shot energy variations (1.5% rms) from the statistics.

Figure 5

Stability-optimized LPA: (a)–(d) Measured (heat maps) and simulated (circles) correlations between the laser focus position and beam parameters for a typical reference (purple) and the stability optimized (blue) setting. Color maps indicate the number of recorded events. (e) Longitudinal phase spaces from PIC simulations. (f) Percentile of measured shots with given energy spread.