  Modelling neutral beam injection (NBI) in fusion reactors requires computing
the trajectories of large ensembles of particles. Slowing down times of up to
one second combined with nanosecond time steps make these simulations
computationally very costly. This paper explores the performance of BGSDC, a
new numerical time stepping method, for tracking ions generated by NBI in the
DIII-D and JET reactors. BGSDC is a high-order generalisation of the Boris
method, combining it with spectral deferred corrections and the Generalized
Minimal Residual method GMRES. Without collision modelling, where numerical
drift can be quantified accurately, we find that BGSDC can deliver higher
quality particle distributions than the standard Boris integrator at comparable
cost or comparable distributions at lower cost. With collision models,
quantifying accuracy is difficult but we show that BGSDC produces stable
distributions at larger time steps than Boris.
