Description
Laser wakefield acceleration (LWFA) generates high-energy electron beams over centimeter-scale distances rather than the kilometer-scale facilities required by conventional accelerators. Intense ultrashort laser pulses propagating through underdense plasma create wakes sustaining electric fields exceeding 100 GV/m, capable of accelerating electrons to tens of MeV within millimeters. However, electron energy spectra depend sensitively on experimental parameters including laser energy, plasma density, and gas jet timing, making optimization challenging due to complex nonlinear physics and extensive parameter spaces.
We present a machine learning framework combining conditional diffusion models [1, 2] with three-stage gradient-based optimization. Diffusion models are generative neural networks that transform random noise into realistic data through iterative denoising. We adapt the EDM framework to generate one-dimensional electron spectra conditioned on laser energy (12–26 mJ), gas jet pressure (10–38 bar), and valve timing (10–40 ms). Our differentiable implementation enables gradient-based parameter optimization toward target spectra.
The optimization employs three complementary stages to navigate pathological loss landscapes: Bayesian optimization for global exploration using Gaussian process surrogates [3, 4], L-BFGS quasi-Newton optimization for rapid local refinement, and RAdam stochastic optimization to escape sharp minima and find robust solutions.
Using experimental data from ELI Beamlines' ALFA beamline [5] operating at 1 kHz, we achieve mean squared errors below 10⁻⁵ in spectrum matching while recovering target parameters with high fidelity. This methodology extends to general inverse design problems involving physics-informed surrogates where traditional simulation is computationally prohibitive.
[1] Jech et al., Denoising Diffusion Implicit Models for Laser-Plasma Accelerator Simulation Trained With Physical Constraint Loss. ECML PKDD 2025. Lecture Notes in Computer Science. https://doi.org/10.1007/978-3-662-72243-5_24
[2] Jech et al., Laser wakefield electron acceleration simulation using physics-informed diffusion probabilistic models, Proc. SPIE 13534, Laser Acceleration of Electrons, Protons, and Ions VIII, 1353407 (5 June 2025); https://doi.org/10.1117/12.3058379
[3] P. Valenta et al., Bayesian optimization of electron energy from laser wakefield accelerators. Physical Review Accelerators and Beams, September 2025. https://doi.org/10.1103/knh7-hbr3
[4] P. Valenta et al., Optimized matching conditions for self-guided laser wakefield accelerators. 2025-12. https://doi.org/10.48550/arXiv.2512.10728
[5] C. M. Lazzarini et al., Ultrarelativistic electron beams accelerated by terawatt scalable kHz laser. Phys. Plasmas, 1 March 2024. https://doi.org/10.1063/5.0189051