Numerical Cherenkov instabilities in electromagnetic particle codes

Abstract Linear dispersion relations for one-dimensional, electromagnetic particle simulation codes are analyzed in order to determine numerical stability properties. It is found that fast particles may resonate with light waves of matching phase velocity to produce a severe numerical instability. A Courant condition for this instability is derived, and comparison of its restrictiveness made among the various differencing schemes. At least two algorithms permitting reasonably large time steps for relativistic simulations are available.