# Landau dispersion relationship in self-consistent field theory

## TL;DR

This paper analyzes the Landau dispersion relationship within the framework of self-consistent field theory, deriving formulas for instability indices and conditions for two-stream instability in collisionless plasma.

## Contribution

It introduces a new formula for the instability index and effective conditions for two-stream instability in collisionless plasma.

## Key findings

- Derived formula for instability index
- Established effective conditions for two-stream instability
- Analyzed spectral problem in Maxwell-Boltzmann plasma

## Abstract

The spectral problem is studied associated with Maxwell-Boltzmann equations describing collisionless plasma. Formula for instability index is obtained and effective conditions of two-stream instability are given.