Robustness Optimization for Compact Free-electron Laser Driven by Laser Wakefield Accelerators

TL;DR

This work tackles the fragility of compact LWFA-driven FELs caused by shot-to-shot laser and plasma instabilities. It introduces a CMA-ES-based conceptual design to optimize a beamline based on start-to-end simulations, using objective functions $\langle L_G^{-1}\rangle$ and $E_{min}$ to promote robust gain. Start-to-end results show that the optimized system can sustain FEL radiation above $1\,\mu\mathrm{J}$ at $25\,\mathrm{nm}$ even when parameter jitters are doubled and beam pointing jitter reaches $1\mathrm{\,mrad}$. This demonstrates a viable path toward robust, table-top LWFA-driven EUV FELs and highlights a practical optimization framework that couples LWFA modeling, beamline optimization, and FEL simulations.

Abstract

Despite the successful demonstration of compact free electron lasers (FELs) driven by laser wakefield accelerators (LWFAs), the inherent shot-to-shot fluctuations in LWFAs, including both laser and plasma instabilities, remain a primary obstacle to realizing LWFA-driven FELs with robust operation. Here, we present a conceptual design for LWFA-driven FELs with sufficient tolerance against shot-to-shot fluctuations using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Start-to-end simulations demonstrated that this systematic optimization resulted in a significant improvement in the robustness of FELs. With the optimized configurations, the radiation energy can be maintained above 1 microjoule at a wavelength of approximately 25 nm, even when accounting for twice the root-mean-square (RMS) ranges of these instabilities. This proposed scheme represents a substantial advancement in the development of compact LWFA-driven FEL systems, enabling robust operation and paving the way for the realization of reliable and widely accessible sources.

Figures (9)

• Figure 1: PIC simulation results of LWFA with inherent parameter jitters. (a) Schematic of plasma density profile and fluctuation sources, with the pink shaded area region and the orange solid line represent the range of focal position jitter and the initial shock-front position. (b)-(g) Electron beam properties with inherent parameter jitters: the blue, red and orange curves represent the laser energy variations, laser focal position displacement and shock front position instability, respectively. Horizontal axes denotes $\pm2$ folds RMS range of these three parameter jitters, and the vertical axes represent beam energy (b), charge (c), slice energy spread (d), global energy speread (e), horizontal (f) and vertical (g) normalized projected emittance.
• Figure 2: Schematic of the optimized beamline.
• Figure 3: The optimization results of the $E_{min}$ for the 13-electron ensemble. (a) The simulated objective function $E_{min}$ (dots) with the cumulative best results (black dashed line). The y-axis is plotted on a logarithmic scale. (b)-(c) The evolution of the beam size (b) and the normalized projected emittance (c) along the beamline in horizontal (blue) and vertical (orange) directions. The tracking beamline was configured using the best parameters obtained from the optimization.
• Figure 4: Radiation energy as a function of (a) normalized vector potential $\Delta a_0$, (b) laser focal position $\Delta {z_{foc}}$ and (c) the shock-front position $\Delta {z_{shock}}$. Mean values (black squares) and standard deviation (error bars) calculated from 20 independent simulations with varying random seeds, where the blue curve represents optimization using $<L_G^{-1}>$ as objective function and the red curve represents optimization using $E_{min}$ as the objective function. The y-axis is plotted on a logarithmic scale.
• Figure 5: Simulation results for FELs with the 13-electron-beam ensemble. (a) Radiation energy along the undulator with the y-axis on a logarithmic scale. (b) Pulse duration and (c) spectrum of the generated radiation pulses at the exit of the undulator. Each line represents the average value of 20 distinct simulations with random seeds.