a 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 -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. We also show that, although these drivers are constructed to be shape-invariant in vacuum, their structure can be modified by the laser–plasma interaction in the nonlinear regime, an effect that should be taken into account when designing wakefield accelerators with ST pulses. 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.
Laser dynamics in transversely inhomogeneous plasma and its relevance to wakefield acceleration