A generalized kinetic approach for the study or relativistic electron beams

Recently a macroscopic extended model with many moments for the description of mono atomic gases has been proposed and an exact closure, up to whatever order with respect to thermodynamical equilibrium has been determined. Afterwards a further condition arising from the imposition of the entropy principle to extended models of fluids under the influence of an external electro-magnetic field has been considered and a closure compatible with this condition has been found, by using a macroscopic approach. Such condition was never imposed before in literature, in the context of relativistic Extended Thermodynamics with many moments. In this paper an alternative closure for this last model, compatible with the further condition, is proposed. It is obtained by using a generalized kinetic approach. If one fixes a certain order with respect to equilibrium the closure is determined in terms of a polynomial and two functions of one scalar