Numerical stability of 2nd order Runge-Kutta integration algorithms for use in particle-in-cell codes
An essential ingredient of particle-in-cell (PIC) codes is a numerically accurate and stable integration scheme for the particle equations of motion. Such a scheme is the well known time-centered leapfrog (LF) method  accurate to 2nd order with respect to the timestep Δt. However, this scheme can only be used forces independent of velocity unless a simple enough implicit implementation is possible. The LF scheme is therefore inapplicable in Monte-Carlo treatments of particle collisions  and/or interactions with radio-frequency fields . We examine here the suitability of the 2nd order Runge-Kutta (RK) method. We find that the basic RK scheme is nummerically unstable, but that conditional stability can be attained by an implementation which preserves phase space area. Examples are presented to illustrate the performance of the RK schemes. We compare analytic and computed electron orbits in a traveling nonlinear wave and also show self-consistent PIC simulations describing plasma flow in the vicinity of a lower hybrid antenna.
Key wordssimulation tokamak edge plasma lower hybrid antenna
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