A multigroup spline approximation in extended kinetic theory

We introduce an extended linear Boltzmann equation governing the distribution function of charged particles which scatter inelastically with resting heavy background particles. The appearing collision integral is closely connected to a simplified description of the electron-phonon interaction in semiconductors. The particle conservation and the balance equations of momentum and energy are discussed in the Lorentz gas limit. By applying a multigroup spline approximation combined with a P-1-approximation for the angle dependence of the distribution function, the Boltzmann equation is reduced to a system of differential equations. This approach incorporates external forces in a natural way. The multigroup equations are solved numerically for different scenarios.