Non-adiabatic charged particle motion near a magnetic field zero line

It is known that the adiabatic invariance of the magnetic moment of a charged particle breaks down when the particle passes near a field zero. The extreme case of this breakdown, arising when the particle orbit encloses the field zero, is investigated by computation of particle orbits. It is found that the magnetic moment changes by a factor with a maximum value of about 5.75; the exact value depends on the phase of the particle in its orbit, and the details of the dependence are explained on a simple model.