Implicit time integration for plasma simulation

To increase the size of the time step, and threrby extend the applicability of kinetic plasma simulation, analysis of the stability and accuracy of implicit time integration schemes for plasma particle-in-cell simulation and the synthesis of new algorithms have been undertaken. Three classes of implicit algorithms are considered in general form. Stability and accuracy calculations provide guidelines for the design and application of implicit simulation algorithms, as illustrated in the construction of new difference schemes with desirable properties. Of particular interest are the relaxation of stability constraints on the time step, strong damping of unwanted high-frequency modes, accuracy of the simulation of low-frequency phenomena, numerical secular acceleration, and numerical stability of fast and slow space-charge waves. The potency of higher order accurate differencing schemes in reducing undesirable numerical effects is demonstrated