Charged Particle Diffusion in a Magnetic Dipole Trap

TL;DR

This paper investigates how charged particles diffuse in magnetic dipole traps, revealing that particles tend to accumulate in regions of higher magnetic field, contrasting with diffusion in uniform magnetic fields.

Contribution

It derives a Fokker-Planck equation for particle diffusion in magnetic traps and compares diffusion behaviors in dipole versus homogeneous magnetic fields.

Findings

Particles diffuse inward in dipole magnetic fields.

Particles diffuse outward in homogeneous magnetic fields.

Transport properties vary with magnetic field configuration.

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.