Extended Thermodynamics of charged gases with many moments

Recently amodel with many moments for the description of relativistic gases has been studied and an exact closure has been found, depending on an arbitrary set of single variable functions. In the case of a charged gas and when the electromagnetic field acts as an external force, the exploitation of the entropy principle produces an additional condition. A closure compatible with this further condition has been found, when the highest order moment has an even number of free indexes. It amounts in restrictions on the arbitrary single variable functions appearing in the general case. They are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants. When the highest order moment has an odd number M of free indexes the further condition is different from that appearing in the case M even and alternative techniques must be used to find a closure compatible with it. In this paper we take into account this last model and we find a closure compatible with the further condition. As well as in the case M even, also in the case M odd we find that the arbitrary single variable functions of the general theory are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants