Simulation Design for Velocity-Controlled Spatio-Temporal Drivers in Laser Wakefield Acceleration

Abstract

Velocity-controlled spatio-temporal (ST) laser drivers offer a route to tailoring laser-plasma interactions by allowing the velocity of the intensity peak to be controlled independently of the envelope group velocity. In this work, we present a simulation-design workflow for PIC modelling of subluminal velocity-controlled ST pulses in OSIRIS based on a Maxwell-consistent spectral construction expressed as a superposition of exact vacuum solutions, and we describe its discrete k-space representation for numerical initialisation. We then examine wakefield excitation with velocity-controlled drivers, showing how the ST geometry couples the effective longitudinal extent of the high-intensity region to the transverse scale and deriving scaling guidelines for near-resonant excitation in the subluminal regime. Finally, we discuss the geometric constraints that make long-distance simulations costly, including focus-envelope slippage and strong transverse expansion, and we show that continuous wall injection can reproduce the intended vacuum propagation while substantially reducing the transverse domain size. Together, these results provide practical guidelines for accurate and computationally efficient PIC simulations of velocity-controlled ST drivers in wakefield-relevant regimes.

Figures (8)

• Figure 1: Spectral design of ST pulses with controllable focal velocities. The desired spectral components (red curve) are defined by the intersection of the vacuum light cone (green surface) with the plane imposed by the spatio-temporal coupling (purple plane). (a) In the superluminal regime ($v_f = 1.5c$), the intersection yields an open hyperbolic trajectory, characteristic of X-waves with infinite spectral extent. (b) In the subluminal regime ($v_f = 0.5c$), the coupling plane cuts through the time-like region of the cone, confining the allowed spectral range to a closed elliptical loop.
• Figure 2: Two examples of spatio-temporal pulses obtained with the discrete implementation in OSIRIS. In (a), we have an example of the shape of a superluminal pulse with $v_f= 1.5c$. In (b), we have an example of the shape of a subluminal pulse with $v_f= 0.5c$. The blue-red colour-scale represents the electric field, and the black line corresponds to the pulse's full longitudinal envelope $f_\parallel(z)$ in configuration space.
• Figure 3: Comparison of the injected pulse electric field for three choices of the longitudinal and transverse repetition lengths used in the spectral reconstruction. (a) $k_0T_{\mathrm{rep},z}=700$ and $k_0T_{\mathrm{rep},(x,y)}=1000$, for which the reconstructed pulse is smooth and free of aliasing artefacts. (b) $k_0T_{\mathrm{rep},z}=200$ and $k_0T_{\mathrm{rep},(x,y)}=100$, where the longitudinal repetition length is too small, producing spurious replicas along the propagation axis. (c) $k_0T_{\mathrm{rep},z}=700$ and $k_0T_{\mathrm{rep},(x,y)}=200$, where the transverse repetition length is insufficient, and replicas enter the simulation domain, leading to distorted, unphysical structures.
• Figure 4: Wakefield excitation for different choices of $v_f$ and $w_0$. Panels (a) and (b) show the case $v_f=0.8c$: for (a) $k_0w_0=10$ the driver is too long and overlaps with most of the first plasma period, whereas for (b) $k_0w_0=7.1$ the driver length is better matched and a clearer wake structure is obtained. The same trend is more pronounced in panels (c) and (d) for $v_f=0.6c$, comparing (c) $k_0w_0=10$ with the tighter-focus case (d) $k_0w_0=4.3$. The greyscale shows the electron density, and the blue--red colour scale shows the laser electric field. All cases use $\omega_0/\omega_p=10$ and $a_0=2.2$.
• Figure 5: Waterfall plots of the accelerating electric-field amplitude for different focal velocities: (a) $v_f=0.8c$, (b) $v_f=0.99c$, and (c) $v_f=1.4c$.