Overlapping multigroup approach to a linear extended Boltzmann equation

We introduce a linear Boltzmann equation governing the evolution of charged structureless particles scattering inelastically with heavy field particle s. External electric and magnetic fields are accounted for. Conservation of mass as well as balance equations for momentum and energy transfer are dis cussed in the Lorentz gas limit. A multigroup approximation based on the me thod of weighted residuals is presented. This approach incorporates externa l fields in a natural manner. A P-1 approximation of the multigroup equatio ns is applied to simple test cases.