Charged Particle Diffusion in a Magnetic Dipole Trap

Abstract

When particles are magnetized, a diffusion process is influenced by the ambient magnetic field. While the entropy increases, the constancy of the magnetic moment puts a constraint. Here, we compare the E-cross-B diffusion caused by random fluctuations of the electric field in two different systems, the Penning-Malmberg trap and the magnetic dipole trap. A Fokker-Planck equation is derived by applying the ergodic ansatz on the invariant measure of the system. In the dipole magnetic field particles diffuse inward and accumulate in the higher magnetic field region, while, in a homogeneous magnetic field, particles diffuse out from the confinement region. The properties of analogous transport in a more general class of magnetic fields are also briefly discussed.