Machine learning-based virtual diagnostics of dielectric laser acceleration

Abstract

We present the development of a digital twin-based reconstruction framework for dielectric laser acceleration (DLA) based on machine-learning-assisted inversion of single-shot electron energy spectra. DLA as a promising candidate for compact electron accelerator designs using optical nearfields in dielectric nanostructures lacks on direct diagnostics on the laser-electron interaction. Thus, the outgoing electron energy distribution is one of the few experimentally accessible observables. To exploit this information, DLA interaction and mapping on the downstream spectrometer are treated as nonlinear measurement device whose response is described by the symplectic sixdimensional tracking code DLAtrack6D. This forward simulation model serves as a digital twin mapping laser-electron interaction parameters onto resulting energy spectra. For diagnostics, we are interested in the inverse mapping represented by a neural network trained by synthetic datasets generated with the forward simulation model. The reconstruction performance and parameter identifiability of the inverse model are evaluated for parameter ranges relevant to planned experiments at the ARES linac in the SINBAD facility at DESY. Simulation studies demonstrate that the method can recover pulse front tilt angles with an accuracy of about 1 deg and phase offsets with an RMSE of about 0.36 rad corresponding to a difference of 0.4 fs in arrival time. Training with noisy spectra further improves robustness against spectrometer noise. The trained surrogate model evaluates in the millisecond range, enabling shot-to-shot parameter estimation compatible with the 50 Hz repetition rate of ARES. The approach effectively transforms the DLA interaction region into a virtual in situ diagnostics for otherwise inaccessible laser parameters during experiment and provides a foundation for real-time monitoring and control of future DLA experiments.

Figures (9)

• Figure 1: Computing time of the Forward model using DLAtrack6D as function of the number of used CPU kernels (red and blue line for $10^5$ and $2.5\times10^5$ macroparticles, respectively) showing the parallelization properties of the applied tracking code, and as function of the number of simulated DLA periods showing the almost linear dependence.
• Figure 2: Simulated spectrometer response for different PFT angles and phases of the resonant harmonic. The initial Gaussian energy distribution (dashed line) evolves into a modulated spectrum due to the DLA interaction.
• Figure 3: Simulated mean energy gain as a function of pulse front tilt angle and phase offset. The plot shows a quasi-symmetry plane in the PFT angle dependence at 45°.
• Figure 4: Time and position of interaction between electron (black line) and laser pulse: longest interaction length for $\theta_\textrm{PFT,opt}=45°$ (green ellipse), shorter interaction lengths for non-optimal PFT angles, but almost symmetric for $\theta_\textrm{PFT}=\theta_\textrm{PFT,opt}\pm\Delta\theta$ (red and blue ellipses).
• Figure 5: Reconstruction accuracy of pulse front tilt angle (left) and phase offset (right) on an independent test dataset (5000 samples). The neural network achieves a RMSE of about 1.5° in the PFT angle interval [35°,45°] and a RMSE of 0.36 on the phase offset corresponding to 0.4fs timing offset. The symmetry in the PFT angle is clearly visible. The plot color depicts the second parameter: 30° PFT angle, 0rad phase offset (purple) $\rightarrow$ 45° PFT angle, $\pi$ phase offset (blue-green) $\rightarrow$ 60° PFT angle, $2\pi$ phase offset (yellow).