Reanalysis of the beam-plasma instability using the Dyson-like equation formalism

TL;DR

This paper reexamines the beam-plasma instability using Dyson-like equations, comparing analytical predictions with numerical simulations and highlighting the importance of self-consistent evolution in the model.

Contribution

It introduces a Dyson equation-based analytical framework for the beam-plasma instability and identifies its limitations related to self-consistency.

Findings

Analytical model predictions align with N-body simulations when self-consistency is maintained.

Breakdown of self-consistent evolution explains discrepancies in the model.

Highlighting the importance of self-consistency in plasma instability analysis.

Abstract

We analyze the problem of the beam-plasma instability via the analytical treatment of the so-called Dyson equation. We first compared the prediction of the model constructed by fixing the electric field amplitude with respect to a N-body Hamiltonian numerical simulation. Then, we demonstrate that the shortcomings of such an analytical formulation must be essentially identified with the breaking-down of the self-consistent evolution of the field and the particle distribution function.