High-charge relativistic electrons by vacuum laser acceleration from plasma mirrors using flying focus pulses

TL;DR

The paper tackles velocity mismatch in vacuum laser acceleration by using plasma mirrors as injectors. It introduces flying-focus laser pulses with subluminal focal velocity to keep injected electrons synchronized with the accelerating phase and maintain strong longitudinal ponderomotive forcing over extended distances. 3D PIC simulations show the approach can boost relativistic electron yield by up to an order of magnitude, achieving around 10 nC of electrons with energy at or above 5 MeV at high intensities. This method promises compact, high-charge electron sources for high-flux Thomson scattering and radiography, with potential impact on high-energy density physics applications.

Abstract

Relativistic electron beams produced by intense lasers over short distances have important applications in high energy density physics and medical technologies. Vacuum laser acceleration with plasma mirrors injectors has garnered substantial research interest recently. However, a persistent challenge remains unresolved that electrons inevitably detach from the laser acceleration phase due to velocity mismatch. Here, we employ flying focus lasers to address this limitation. Through three-dimensional particle-in-cell simulations, we demonstrate that flying focus lasers can achieve a substantial enhancement in relativistic electron charge yield compared to conventional Gaussian lasers. This improvement stems from two key attributes: (1) The subluminal propagation velocity of the peak intensity keeps a larger electron population synchronized within the longitudinal ponderomotive acceleration region, and (2) Flying focus lasers sustain higher magnitudes of the longitudinal ponderomotive force over longer distances in comparison to Gaussian lasers. This approach offers high-charge relativistic electron sources ideal for demanding applications such as high-flux Thomson scattering and radiography.

Figures (4)

• Figure 1: (a) Schematic illustration of the simulation setup. A relativistic laser pulse with $a_0=3$, incident at a $45^{\circ}$ angle along the $y$-axis, irradiates a solid-density plasma target. Upon reflection, the electrons injected from the plasma surface are accelerated by the reflected laser fields propagating along the $x$-axis. (b)-(c) Snapshots of the electron bunches ($\ge5$ MeV) distribution at $t=100T_{0}$ for the (b) Gaussian and (c) flying focus lasers. The electrons are represented by green scattered dots, while the distribution of the electric field $E_y$ along the polarization direction is shown in a blue-red color scale. (d)-(e) Comparison of the electron energy spectra generated by the Gaussian (blue dots) and flying focus lasers (red dots) at (d) $t=15T_{0}$ (d) and (e) $t=100T_{0}$.
• Figure 2: (a)--(b) Spatial distribution of representative electrons within the electric field $E_{y}$ driven by the (a) Gaussian laser and (b) flying focus laser, respectively, at the moment of electron emission from the target surface at $t=20T_{0}$. (c)--(f) Dynamics of the electron from panel (a), showing: (c) its trajectory in the x-y plane; temporal evolution of (d) transverse momentum, (e) longitudinal momentum, and (f) total energy. (g)--(j) These subfigures correspond to (c)--(f) for the electron shown in panel (b). (k) The instantaneous power delivered to a single electron by each field component as a function of time.
• Figure 3: The spatial profiles of longitudinal ponderomotive forces derived from the on-axis intensities of the Gaussian laser (red markers) and flying focus laser (blue markers), respectively, after reflection from the plasma target at different time instants: (a) $t=25T_{0}$, (b) $t=50T_{0}$, (c) $t=75T_{0}$, (d) $t=100T_{0}$. The longitudinal ponderomotive force is calculated as $F_{p}=-e^{2}\nabla_{x}E_{y}^{2}\ /\ 4m_{e}\omega_{0}^{2}$, where $E_y^2$ is sampled at intervals of one optical cycle.
• Figure 4: The charge of high-energy electron bunches (with energies $\ge5$ MeV) generated by the Gaussian and flying focus lasers as a function of (a) the laser dimensionless parameter $a_{0}$ and intensity, and (b) the focal velocity. The energy of flying focus pulses in (a) spans from approximately 268 mJ up to 2.2 J. The FWHM pulse durations of the flying focus and corresponding Gaussian pulses in (b) are $14T_0$, $13T_0$, $12T_0$, $11T_0$, $8T_0$, $6T_0$, and $5T_0$ at focal velocities of $0.90 c$, $0.92 c$, $0.94 c$, $0.95 c$, $0.97 c$, $0.98 c$, and $0.99 c$, respectively.