Collision term for uniformly magnetized plasmas

Collision process is crucial to the transport in magnetized plasmas. This article reviews the three typical approaches, i.e. the Fokker-Planck (FP) approach, the Bogoliubov-Born-Green-Kirwood-Yvon (BBGKY) approach, and the quasilinear (QL) approach, to deriving the kinetic equation for weakly coupled uniformly magnetized plasmas. The collision terms derived based on these three approaches are shown to be identical and satisfy the conservation laws and H theorem. Relatively speaking, the BBGKY and QL approaches are more systematic and readily to be generalized from weakly magnetized plasmas to strongly magnetized plasmas. The FP approach is pretty simple for weakly magnetized plasmas and has the advantage that the collision term derived based on it can be naturally separated into two parts, one part arising from the polarization and the other from the correlation of the fluctuating electrostatic field. However, the usual form of the FP equation is not suitable for strongly magnetized plasmas. To derive the magnetized collision term based on the FP approach, a general form of the FP equation for magnetized plasmas has to be found first.