# X-Dispersionless Maxwell solver for plasma-based particle acceleration

## TL;DR

This paper introduces a semi-implicit Maxwell solver for plasma-based particle acceleration that eliminates numerical dispersion and Cerenkov instability, enabling efficient, Lorentz-invariant simulations suitable for parallel computing.

## Contribution

A novel semi-implicit Maxwell solver projecting onto transverse planes to remove dispersion and instability in plasma acceleration simulations.

## Key findings

- Eliminates numerical dispersion of electromagnetic waves.
- Removes numerical Cerenkov instability (NCI).
- Enables efficient parallel computation with local stencil.

## Abstract

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) that makes the scheme quasi-one-dimensional. The scheme 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 removes 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.