Charged-particle orbits near a magnetic null point

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