  Explicit electromagnetic Particle-In-Cell (PIC) codes are typically limited
by the Courant- Friedrichs-Lewy (CFL) condition, which implies that the
timestep multiplied by the speed of light must be smaller than the smallest
cell size. In the case of boosted-frame PIC simulations of plasma-based
acceleration, this limitation can be a major hinderance as the cells are often
very elongated along the longitudinal direction and the timestep is thus
limited by the small, transverse cell size. This entails many small-timestep
PIC iterations, and can limit the potential speed-up of the boosted-frame
technique. Here, by using a CFL-free analytical spectral solver, and by
mitigating additional numerical instabilities that arise at large timestep, we
show that it is possible to overcome traditional limitations on the timestep
and thereby realize the full potential of the boosted-frame technique over a
much wider range of parameters.
