An exact fluid model for relativistic electron beams: The many moments case

TL;DR

This paper generalizes an existing relativistic electron beam fluid model to an arbitrary number of moments, providing a broader theoretical framework consistent with entropy and relativity principles.

Contribution

It derives a general solution for a relativistic electron beam fluid model with any number of moments, extending previous 14-moment models and incorporating a velocity dispersion parameter.

Findings

General solution for arbitrary moments derived

Model satisfies entropy and relativity principles

Introduces a velocity dispersion ordering parameter

Abstract

An interesting and satisfactory fluid model has been proposed in literature for the the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy principle and the relativity principle. Here the case is considered with an arbitrary number of independent variables, still satisfying the above mentioned two principles; these lead to conditions whose general solution is here found. We think that the results satisfy also a certain ordering with respect to a smallness parameter $\epsilon$ measuring the dispersion of the velocity about the mean; this ordering generalizes that appearing in literature for the 14 moments case.