Kinetic and transport theory for a non-neutral plasma taking account of strong gyration and non-uniformities on the collisional scale

From the BBGKY equations for a pure electron plasma a derivation is made of a collision integral that includes the combined effects of particle gyration in a strong magnetic field and non-uniformities of both the distribution function and the self-consistent electric field on the collisional scale. A series expansion of the collision integral through the distribution function and the electric field on the collisional scale is carried out to third order in derivatives of the distribution function and to second order in derivatives of the electric field. For the strong-magnetic-field case when collision-term contributions to only first order in 1/B are included, a particle flux transverse to the magnetic field proportional to l/B² is derived. The importance of long-range collective collisions in this process is shown. The result is in contrast with the classical l/B⁴ proportionality, and is in accordance with earlier studies.