  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.
