Kinetic equation for a magnetized plasma

The effect of the magnetic field on the collision operator of a two-species hot plasma is described without approximation on the strength of the field. The motivation consists to describe microscopic relaxation processes in the intermediate range of values of the field, as can be found in Tokamak plasmas. From the Klimontovich equation, the generalization of the Landau equation is derived by taking into account both the effects of the magnetic field and those of the space non-homogeneity. The original technique used is based on the propagator formalism and on a systematical use of the rotation matrices describing the Larmor rotation of the particles. Simpler explicit results are also given for the cases of (i) a homogeneous two-species plasma, and of (ii) a non-homogeneous single-species plasma. In analogy with cosmic ray turbulent diffusion, a singular contribution is found for collisions between particles with the same velocity parallel to the magnetic field. The previously-known limit results for infinite and vanishing field are unable to describe the results obtained here for intermediate values of the strength of the field, where non-negligible effects are expected on transport coefficients