Orbit-averaged implicit particle codes

The merging of orbit-averaged particle code techniques with recently developed implicit methods to perform numerically stable and accurate particle simulations are reported. Implicitness and orbit averaging can extend the applicability of particle codes to the simulation of long time-scale plasma physics phenomena by relaxing time-step and statistical constraints. Difference equations for an electrostatic model are presented, and analyses of the numerical stability of each scheme are given. Simulation examples are presented for a one-dimensional electrostatic model. Schemes are constructed that are stable at large-time step, require fewer particles, and, hence, reduce input-output and memory requirements. Orbit averaging, however, in the unmagnetized electrostatic models tested so far is not as successful as in cases where there is a magnetic field. Methods are suggested in which orbit averaging should achieve more significant improvements in code efficiency.