Diffusion in a Magnetic Field

Returning to the problem of a charged tagged particle in a magnetic field, we write down the corresponding Fokker-Planck equation in velocity space. This is solved to obtain a modified form of Ornstein-Uhlenbeck distribution for the conditional PDF of the velocity. The conditional mean velocity is found, and the result is analyzed in physical terms. Passing to the high-friction approximation, the diffusion equation satisfied by the PDF of the position of the particle in the long-time limit is derived. The diffusion tensor is calculated. Its longitudinal and transverse parts are identified and shown to behave as expected on physical grounds.