Bayesian Optimization of Laser-Wakefield Acceleration via Spectral Pulse Shaping

TL;DR

This work tackles optimizing laser wakefield acceleration by jointly shaping the drive-laser spectrum and engineering the plasma channel to maximize the trailing-bunch energy $E_m$ and charge $Q$. A Bayesian optimization framework with Gaussian process surrogates navigates a high-dimensional parameter space that includes spectral coefficients (GDD, TOD, FOD) and plasma-channel properties, all evaluated through WarpX PIC simulations of a tapered HOFI channel. The study demonstrates that spectrally shaped pulses can dramatically increase charge while maintaining or enhancing energy, yielding high-energy (HE) and high-charge (HQ) regimes (e.g., $E_m$ up to 15.3 GeV with $Q$ around 85 pC, and $Q$ up to ~600 pC with $E_m$ around 8 GeV). The findings underscore the potential of data-driven, surrogate-assisted design for advancing compact, tunable LWFA sources, while acknowledging real-world factors like laser-amplification distortions and the value of multi-fidelity approaches for future work.

Abstract

In this paper, we investigate the effect of spectral pulse shaping of the laser driver on the performance of channel-guided, laser-plasma accelerators. The study was carried out with the assistance of Bayesian optimization using particle-in-cell simulations. We used a realistic plasma profile based on a novel optical-field-ionized channel technique with ionization injection and low on-axis plasma densities to maximize the energy gain of the electron bunch trailing the laser. Spectral shaping allows us to modify the temporal profile of the laser driver while keeping the laser energy constant, affecting the acceleration and injection processes. Given the complexity and breadth of the parameter space in question, we used numerical optimization to identify high performers. In particular, we found laser profiles with additional spectral content that, when used with optimal plasma channel parameters, result in charge content an order of magnitude higher than the baseline Gaussian case while also increasing the mean energy of the electron bunch.

Figures (11)

• Figure 1: Depiction of the process of spectral shaping. In (a) we can use the physical BELLA spectrum (blue), convolve it with b) a polynomial based on the Taylor expansion of the phase, where we chose the coefficients of the 2nd, 3rd, and 4th order terms, and take the inverse Fourier transform to derive a new, spectrally shaped temporal profile in (c). Keeping the same polynomial phase but using idealized spectra of a Gaussian (orange) or super-Gaussian (green), we can see some variation to the final temporal profile. We also consider a skewed spectrum (red), which can be seen in experiments.
• Figure 2: The a) transverse and b) longitudinal profiles used to describe the plasma column through which the laser drive propagates. The transverse profile is based on FLASH simulation results while the longitudinal profile includes a dopant layer, where the fully ionized hydrogen is doped with a few percent of nitrogen. In a) we compare the transverse profile to a Gaussian pulse with 50 $\mu m$ spot-size and a matched Jinc profile. Longitudinally, a density slope can be added to the plasma profile along its length, the propagation axis of the laser driver.
• Figure 3: Grid scans of GDD, TOD, and FOD while keeping other parameters constant relative to the baseline listed in Table. \ref{['tab:bounds']}. Plotted are the laser intensities normalized to the transform-limited pulse (GDD=TOD=FOD=0), the mean energy of the accelerated bunch $E_m$, and the bunch charge $Q$. The reference Gaussian pulse and its results are shown in black.
• Figure 4: Initial Bayesian optimization where we show the simulation iteration number in a) with respect to the spectral components b) GDD, c) TOD, and d) FOD.
• Figure 5: The laser profiles and associated electron energy spectra for a,b) the Gaussian with respect to the simulation run distance for BO scan #1 (orange, 40 cm) and #2 (blue, 75 cm), c,d) the peak performer for BO scan #1, e,f) the high energy (HE) and g,h) the high charge (HQ) cases from BO scan #2. The laser profiles are normalized to the transform-limited intensity.