A novel adaptive time stepping variant of the Boris-Buneman integrator   for the simulation of particle accelerators with space charge
  We show that adaptive time stepping in particle accelerator simulation is an enhancement for certain problems. The new algorithm has been implemented in the OPAL (Object Oriented Parallel Accelerator Library) framework, and is compared to the existing code. The idea is to adjust the frequency of costly self field calculations, which are needed to model Coulomb interaction (space charge) effects. In analogy to a Kepler orbit simulation that requires a higher time step resolution at the close encounter, we propose to choose the time step based on the magnitude of the space charge forces. Inspired by geometric integration techniques, our algorithm chooses the time step proportional to a function of the current phase space state instead of calculating a local error estimate like a conventional adaptive procedure. In this paper we build up on first observations made in recent work. A more profound argument is given on how exactly the time step should be chosen. An intermediate algorithm, initially built to allow a clearer analysis by introducing separate time steps for external field and self field integration, turned out to be useful in itself already for a large class of problems. 
Matthias Toggweiler, Andreas Adelmann, Peter Arbenz, Jianjun J. Yang
math-ph math.MP physics.acc-ph