Moments of the Inverse Scattering Operator of the Boltzmann Equation: Theory and Applications

In this paper useful physical objects called moments of the inverse scattering operator (MISO) of the Boltzmann equation (BE) are studied. The existence and uniqueness of the MISO is proven and a simple, generally valid, iterative scheme to actually compute those objects is given. The applications of the MISO extend from the computation of the solution for the space-homogeneous BE for small electric and magnetic fields to the exact computation of any transport parameter. This can be done for all moments of the space-inhomogeneous BE and for arbitrary electric and magnetic field intensities. The concept of MISO offers an elegant way to avoid the relaxation time approximation (RTA) every time it comes into play, not only theoretically but also in practical computations.