An approximate analytical expression is obtained for the orbits of a
charged particle moving in a cusp magnetic field. The particle orbits pass close
to or through a region of zero magnetic field before being reflected in regions
where the magnetic field is strong. Comparison with numerically evaluated
orbits shows that the analytical formula is surprisingly good and captures all
the main features of the particle motion. A map describing the long-time
behaviour of such orbits is obtained.
Efficient pseudospectral method for the computation of the self-force on a charged particle: Circular geodesics around a Schwarzschild black hole