# Generalization of the Grad method in plasma physics

## TL;DR

This paper extends the Grad method in plasma physics by incorporating the Bogolyubov functional hypothesis, providing refined descriptions of plasma relaxation processes and component distributions in a two-component electron-ion plasma.

## Contribution

It generalizes the Grad method using the Bogolyubov idea, leading to improved modeling of plasma relaxation and distribution functions.

## Key findings

- Derived component distribution functions and evolution equations.
- Obtained corrections to known results in perturbation theory.
- Enhanced understanding of Maxwell relaxation in plasma.

## Abstract

The Grad method is generalized based on the Bogolyubov idea of the functional hypothesis for states at the end of relaxation processes in a system. The Grad problem (i.e., description of the Maxwell relaxation) for a completely ionized spatially uniform two-component electron-ion plasma is investigated using the Landau kinetic equation. The component distribution functions and time evolution equations for parameters describing the state of a system are calculated, and corrections are obtained to the known results in a perturbation theory in a small electron-to-ion mass ratio.