Extended Thermodynamics of charged gases with many moments: an alternative closure.

In 2011 a macroscopic extended model with many moments for the description of relativistic gases under the influence of an external electromagnetic field has been proposed. An exact closure of this model, up to whatever order with respect to thermodynamical equilibrium, has been found. Such closure is given in terms of the entropy density at equilibrium and the expression for the higher order terms involves a family of arbitrary constants. It allows to know the value of the constitutive functions up to every desired degree of approximation, but paying the cost of a large amount of arbitrary terms. Moreover if one wants to use the closure for applications it is necessary to cut it at a chosen order with respect to thermodynamical equilibrium. In this paper we propose a different method to find the closure that, starting from a fixed order with respect to thermodynamical equilibrium, allows to obtain univocally all the lower order terms in terms of two arbitrary functions depending on a scalar variable and of one polynomial which degree depends on the order of approximation.