Magnetized plasma kinetic theory. I. Derivation of the kinetic equation for a uniform magnetized plasma

A kinetic equation for a multi-species plasma in an external uniform magnetic field is derived from the BBGKY hierarchy of equations. The equation generalizes the equation of Rostoker (1960), which assumes that the distribution function is independent of the azimuthal angle, and all previous results can be derived from it. An additional advantage is that the collision integral is obtained in a form which is free from infinite sums of Bessel functions, and this greatly facilitates calculations based on it.