A Spectral Symplectic Algorithm for Cylindrical Electromagnetic Plasma   Simulations
  Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend the symplectic approach to plasmas, which have focused primarily on discrete Lagrangian mechanics. In this paper, we derive a a symplectic electromagnetic macroparticle algorithm using the map formalism. The resulting algorithm is designed to prevent numerical instabilities such as numerical \v{C}erenkov, which result from incorrect dispersion relations for the fields, as well as the artificial heating of plasmas, which arise from the non-symplectic nature of conventional particle-in-cell algorithms. This is the first self-consistent electromagnetic algorithm derived using a map-based approach. 
Stephen D. Webb and Dan T. Abell and Nathan M. Cook and David L.   Bruhwiler
physics.plasm-ph physics.acc-ph physics.comp-ph