Surrogate models study for laser-plasma accelerator electron source design through numerical optimisation

Designing a high-quality plasma injector electron source driven by a laser beam relies on numerical parametric studies using particle-in-cell (PIC) codes. The common input parameters to explore are laser characteristics, plasma species and density profiles produced by computational fluid dynamics studies. We demonstrate the construction of surrogate models (SMs) using machine learning techniques for a laser-plasma injector (LPI) based on more than 3000 PIC simulations of laser Wakefield acceleration performed for sparsely spaced input parameters published by Drobniak et al (2023Phys. Rev. Accel. Beams, 26 091302). The SM developed in this article approximates a nonlinear mapping (Formula presented) (Formula presented). SMs are highly relevant to the design and optimisation of LPI systems, as they enable the rapid mapping of a defined parameter hyperspace at a computational cost that is negligible compared to iterative PIC simulations. Their speed enables more efficient design studies by allowing extensive exploration of the input-output relationship without significant computational cost. We develop and compare the performance of three SMs, namely, multilayer perceptron (MLP), decision trees and Gaussian processes. We show that using a simple and frugal MLP-based model trained on a reasonably-sized random scan data set of 500 particles in cell simulations, we can predict beam parameters with a coefficient of determination score (Formula presented) (Formula presented). The best SM is used to quickly find optimal working points and stability regions and to achieve targeted electron beam energy, charge, energy spread and emittance using different methods, namely random search, Bayesian optimisation and multi-objective Bayesian optimisation. This simple approach can serve more global design study of an LPI in a start-to-end linear laser-driven accelerator.