Description
Progress in laser-driven ion acceleration is increasingly constrained by the need to characterise highly transient, stochastic plasma dynamics while preserving the ion beam for downstream applications. Many emerging uses require continuous, reliable spectral information without intercepting or perturbing the beam, yet the proton energy spectrum—encoding key information on sheath formation, hot-electron transport, and acceleration physics—is still predominantly measured using interceptive diagnostics. These approaches limit repetition rate and hinder systematic exploration of correlations across large experimental parameter spaces. In this context, machine learning provides a promising framework for developing data-driven, non-invasive diagnostics that complement conventional measurements.
Here, we present a neural network–based synthetic diagnostic that reconstructs the full energy spectrum of laser-accelerated protons using only laser parameters and non-intrusive secondary measurements of the laser–plasma interaction [1]. The framework combines a variational autoencoder to obtain compact, physically meaningful representations of proton spectra with a feed-forward neural network that maps experimentally accessible inputs to this latent space. From this representation, spectra are reconstructed in real time without perturbing the interaction or beam transport.
Despite being trained on fewer than 700 interaction shots, the model achieves a mean prediction error of 13.5% across the spectral range, demonstrating that essential features of the acceleration process can be captured robustly in a data-limited experimental regime. Continuous, non-destructive access to spectral information enables systematic investigation of correlations between laser parameters, plasma conditions, and ion spectra, providing new insight into the reproducibility and variability of the underlying acceleration mechanisms.
Beyond its immediate diagnostic utility, this work represents a step toward surrogate modelling of laser-driven ion sources, in which fast, predictive models are used to support real-time inference and experimental interpretation. We further report deployment of the same methodology in a separate experimental campaign, demonstrating portability across different operating conditions and diagnostic configurations.
[1] C. J. G. McQueen et al. Communications Physics 8, 66 (2025)