Brownian motion of electrons

The concepts of Chandrasekhar are used to derive a new theory which describes the random motion of a particle less massive than the fluid particles. A low-density Lorentz gas with isotropic scattering is used as a model. Probability densities are calculated and the mean square displacement is found to agree with Ornstein's result, only if all particles have the same collision rate. An expression is given for the displacement in a magnetic field, which is valid at all times; in the limit of t -> infinity the usual diffusion constant is obtained. The theory is applied to the scattering of radiation by electrons in a plasma, and the spectra are found to be narrowed by collisions, although features such as the peaks at the plasma frequency or multiples of the cyclotron frequency are broadened. The collision term used in the linearized Boltzmann equation is more realistic than the widely used BGK term, and the collision rate can vary with speed.