Robust direct laser acceleration of electrons with flying-focus laser pulses

TL;DR

Direct laser acceleration in near-critical-density plasmas is challenged by nonlinear propagation and filamentation, limiting energy transfer. The authors demonstrate that superluminal flying-focus pulses can stabilize propagation, enabling robust DLA and enhanced channel formation. Three-dimensional PIC simulations show that flying-focus pulses yield ~80× more electrons above 100 MeV, raise the energy cutoff by ~20%, and triple the high-energy x-ray yield, with a spectral peak near 27 keV and a narrow ~10° emission cone. These results illustrate how spatiotemporal laser structuring provides a practical route to brighter, more collimated electron and x-ray sources for compact radiation generation and high-field physics.

Abstract

Direct laser acceleration (DLA) offers a compact source of high-charge, energetic electrons for generating secondary radiation or neutrons. While DLA in high-density plasma optimizes the energy transfer from a laser pulse to electrons, it exacerbates nonlinear propagation effects, such as filamentation, that can disrupt the acceleration process. Here, we show that superluminal flying-focus pulses (FFPs) mitigate nonlinear propagation, thereby enhancing the number of high-energy electrons and resulting x-ray yield. Three-dimensional particle-in-cell simulations show that, compared to a Gaussian pulse of equal energy (1 J) and intensity (2x10^20 W/cm^2), an FFP produces 80x more electrons above 100 MeV, increases the electron cutoff energy by 20%, triples the high-energy x-ray yield, and improves x-ray collimation. These results illustrate the ability of spatiotemporally structured laser pulses to provide additional control in the highly nonlinear, relativistic regime of laser-plasma interactions.

Figures (7)

• Figure 1: Comparison of DLA with flying focus pulses (FFPs) and conventional Gaussian pulses (GPs) of equal energy and intensity. (Top row) (a) A GP propagates through vacuum and comes to focus at a fixed point in space. (b) A FFP propagates through vacuum with a focal point that moves at $v_f=1.2 c$. (Bottom rows) (a) The GP breaks up into multiple filaments, producing multiple small channels. (b) The FFP resists filamentation, producing a single, wide channel. (c) The wider and more uniform channel created by the flying focus results in more high energy electrons and a larger cutoff energy, independent of the electron density. Here, $\bar{E}_y/E_0$ is the transverse electric field envelope of the laser pulses normalized to their maximum amplitude in vacuum $E_0$, $n$ is the electron density, and $\epsilon$ the electron energy. The rainbow colorbar in the bottom row shows the average energy of electrons with energy greater than 30 MeV.
• Figure 2: Enhanced collimation and energy gain of accelerated electrons in the wider, more-uniform channel produced by the FFP. The trajectories of representative high-energy electrons are colored by their energy at the corresponding location in the channel. The highest cutoff energy for a GP occurs for $n_e = 0.16~n_c$, whereas the highest cutoff for a FFP occurs for $n_e = 0.08~n_c$ [See Fig. \ref{['Fig:FF_vs_G']}(c)]. The time-averaged density (gray) was calculated in a 8 $\mu$m window moving at the speed of light.
• Figure 3: Magnetic field structure and maximum achievable electron energy in GP- and FFP-driven DLA. The channel produced by an FFP supports a higher maximum energy than that produced by a GP. (blue-to-red) The time-averaged azimuthal magnetic field driven by (a) the GP in a $n_e = 0.16~n_c$ plasma and (b) the $v_f = 1.2c$ FFP in a $n_e = 0.08~n_c$ plasma. Here, the magnetic field was averaged in a 30 $\mu$m window moving at the speed of light and normalized to the peak magnetic field of the laser pulse in vacuum $B_0$. The densities were chosen to maximize the cutoff energy for each pulse. (c) The maximum supported energy along the channel (solid curves) and range of energies up to the maxima (shaded) for the GP (black) and FFP (blue). The dashed lines show the average energy of the top 10% most energetic electrons at each time step, plotted at their mean longitudinal position. The average energies increase monotonically until they approach the maximum energy supported by the channel.
• Figure 4: Optimization of the focal velocity $v_f$ for DLA and comparison of FFPs with the optimized GP. (left) Evolution of the electron energy spectrum. (right) Overlap between the transverse electric field envelope of the laser pulse (green) and electrons with energies greater than 100 MeV (pink). In all cases, the results for the optimal plasma density are displayed: $n_e = 0.08~n_c$ for the FFP and $n_e = 0.16~n_c$ for the GP. By stabilizing propagation, the superluminal FFPs allow for sustained overlap between the laser field and energetic electrons, leading to continued acceleration and higher energies.
• Figure 5: Enhancement of x-ray emission in FFP-driven DLA relative to GP-driven DLA. (left) The angularly resolved energy spectra of emitted photons for (a) the GP and (b) the $v_f = 1.2c$ FFP, each at its optimal electron density: $n_e = 0.16~n_c$ and $n_e = 0.08~n_c$, respectively. Here, $\theta_y$ is the emission angle of the photons in the polarization plane of the pulses, $y$-$z$. (right) Projections of the photon energy distributions on a unit sphere. The dashed circles indicate polar angles, and the arrows mark the $y$-axis (polarization direction) and $z$-axis. (c) Cumulative photon energy above $\mathrm{\epsilon_\gamma}$ for the GP (black) and FFP (blue). The dashed curve shows their ratio, demonstrating a threefold increase in conversion efficiency for photons above $\mathrm{200~keV}$ with the FFP.