THE GENERALIZED DIFFUSION-CONVECTION EQUATION

I have derived, from the Boltzmann equation, the transport equation for energetic particles in a moving, magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically, (2) in this frame the scattering will not disturb an isotropic distribution, and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified the derivation should be as valid for plasma microturbulence as for hard sphere scattering. The results, though somewhat more complex than the usual results do show more clearly which phenomena are responsible for tying the particles to the plasma in the transport equation. As a bonus a new 1 second-order acceleration term arises in the case where there is a component of the scatterers velocity that is perpendicular to the magnetic field in the plasma rest frame.