Electron-ion binary collisions in the presence of a magnetic field
  Binary collisions between ions and electrons in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the electrons. The calculations are done with the help of an improved BC which is uniformly valid for any strength of the magnetic field and the second-order energy and velocity transfers are treated in the interaction in Fourier space without specifying the interaction potential. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and less singular than the Coulomb interaction at the origin and as the limiting cases involves the Debye (i.e., screened) and Coulomb potentials. Two particular cases are considered in detaile: (i) Ion motion parallel to the magnetic field with an arbitrary strength. The energy transfer involves all harmonics of the electron cyclotron motion. (ii) The ion arbitrary motion with respect to the strong magnetic field when the electron cyclotron radius is much smaller than other characteristic length scales (e.g., screening length, pitch of electron helix etc.). In the latter case the energy transfer receives two contributions which are responsible for the electron guiding center and cyclotron orbit perturbations. 
Hrachya B. Nersisyan