Improved derivation of the modified BGK collision term and applications to the Hall effect and cold plasma dispersion relation

We improve our previously derived addition to the BGK collision term, and express it in a simple form. The collision frequency for scattering now depends anisotropically on the velocity vector. We also apply the improved macroscopic equation of momentum flow to the Hall effect, the cold plasma dispersion relation and the cyclotron resonance. The Hall coefficient which is constant in the case of the BGK collision term now depends on the magnetic field. It is also shown that, compared with the almost symmetric classical curves of cyclotron resonance, the new curves are considerably asymmetric and their half-widths are about 3/2 times the classical ones.