The mechanism of magnetic pumping consists of two processes, the adiabatic motion of charged particles in a time-varying magnetic field and their pitch angle diffusion. The result is a systematic increase in the energy of charged particles trapped in mirror (and particularly, magnetospheric) magnetic fields. A numerical model of the mechanism is constructed, compared with analytic theory where possible, and, through elementary exercises, is used to predict the consequences of the process for cases that are not tractable by analtyical means. For energy dependent pitch angle diffusion rates characteristic 'two-temperature' distributions are produced. The model is applied to the outer Jovian magnetosphere for two purposes; to find magnetospheric regions in which the mechanism may energize trapped particles, and to generate distribution functions involving pitch angle diffusion caused by wave-particle interactions. We find that beyond 20 RJ in the outer magnetosphere particles may be magnetically pumped to energies of the order of 1--2 MeV and we predict two-temperature distribution functions with 'break points' at 1--4 keV for electrons and 8--35 keV for ions.