X-dispersionless Maxwell solver for plasma-based particle acceleration

•The new Maxwell solver completely removes the numerical dispersion along one selected direction.•It accurately simulates the electromagnetic pulse down to its phase•the new solver removes greatly reduces the numerical Cerenkov instability completely.•The new solver is local and thus is infinitely scalable via simple domain decomposition. A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee lattice into planes transverse to a selected axis (the particle acceleration direction). The scheme - by design - removes the numerical dispersion of electromagnetic waves running parallel the selected axis. The fields locations in the transverse plane are selected so that the scheme is Lorentz-invariant for relativistic transformations along the selected axis. The solver results in “Galilean shift” of transverse fields by exactly one cell per time step. This eases greatly the problem of numerical Cerenkov instability (NCI). The fields positions build rhombi in plane (RIP) patterns. The RIP scheme uses a compact local stencil that makes it perfectly suitable for massively parallel processing via domain decomposition along all three dimensions. No global/local spectral methods are involved.