Hybrid integration and acceleration techniques are used to speed up th
e electron guiding centre orbit calculations in a toroidal axisymmetri
c magnetized plasma in the presence of a dc electric field. Accelerati
on of the computation is introduced to bridge the gap between the two
different time scales: the rapid circulations of the electron around t
he magnetic axis and the relatively infrequent collisions and slow res
ponse to the electric field. The constants of motion method is utilize
d in correcting the particle position after each guiding centre step,
which makes long time steps in the integration possible. The method de
scribed is applied to the simulation of reverse runaway electrons in a
tokamak plasma. It is shown that in some cases fairly large average a
cceleration factors (100-10000) are acceptable: the statistics for an
ensemble of electrons remain correct and the transition of a single el
ectron through the trapped orbit velocity cone is properly described.
A good agreement is found with 2-D Fokker-Planck calculations in the s
traight cylinder approximation for a cold plasma. The finite temperatu
re and toroidal effects on the reverse runaway rate are calculated, an
d the adverse effects of runaway electrons on current ramp-up in tokam
aks are discussed.