Symplectic integration of magnetic systems

Abstract Simulation of the long time behavior of systems requires more than just numerical stability to return dependable results – it must preserve the underlying geometric structure of the continuous equations. Symplectic integrators are the most common form of geometric integrator, and are therefore of interest in simulating plasmas for many plasma periods, for example. We present here results on generating symplectic integrators for magnetic systems, and in particular show that the algorithms due to Boris and Vay are symplectic.