DISPERSION RELATION FOR COMPUTER-SIMULATED PLASMAS.

Abstract A dispersion relation for a computer-simulated plasma in which the effects of discreteness in space and time are treated exactly is derived. In the limit that the mesh spacing and the time step go to zero independently, the well-known results associated with a collisionless plasma are obtained. Nonphysical Landau damping of a wave by particles traveling at phase velocities associated with frequency “aliases” and numerical dispersion associated with a finite time step are easily avoided with small enough time steps. Discreteness in space plus interpolation between mesh points leads to modes which can be represented as sums of backward and forward traveling sinusoidal waves. The total resonant interaction of the particles with a mode is the sum of their interactions with each of the components. For a Maxwellian distribution the forward traveling components lead to damping, but the backward traveling components lead to growth. Consequently, numerically unstable modes can occur in a Maxwellian plasma.