Electron-Electron Collision Term Describing the Reflections Induced Scattering in a Magnetized Plasma

For an electron-electron collision with characteristic scale length larger than the relative gyro-radius of the two colliding electrons, when the initial relative parallel kinetic energy cannot surmount the Coulomb repulsive potential, reflection will occur with interchange of the parallel velocities of the two electrons after the collision. The Fokker–Planck approach is employed to derive the electron collision term \mathcalC_\rm R describing parallel velocity scattering due to the reflections for a magnetized plasma where the average electron gyro-radius is much smaller than the Debye length but much larger than the Landau length. The electron parallel velocity friction and diffusion coefficients due to the reflections are evaluated, which are found not to depend on the electron perpendicular velocity. By studying the temporal evolution of the H quantity due to \mathcalC_\rm R, it is found that \mathcalC_\rm R eventually makes the system relax to a state in which the electron parallel velocity distribution is decoupled from the perpendicular velocity distribution.