Effect of collisions on the two-stream instability in a finite length plasm

TL;DR

This paper investigates how collisions affect the two-stream instability in a finite-length plasma, providing analytical, numerical, and simulation results that quantify the impact on growth rates and threshold conditions.

Contribution

It offers a combined analytical and numerical analysis of collisional effects on the two-stream instability in bounded plasmas, including practical formulas for threshold beam current estimation.

Findings

Growth rate decreases linearly with collision frequency

Collision frequency doubles the collisionless growth rate at instability suppression

Particle-in-cell simulations agree with fluid theory predictions

Abstract

The instability of a monoenergetic electron beam in a collisional one-dimensional plasma bounded between grounded walls is considered both analytically and numerically. Collisions between electrons and neutrals are accounted for the plasma electrons only. Solution of a dispersion equation shows that the temporal growth rate of the instability is a decreasing linear function of the collision frequency which becomes zero when the collision frequency is two times the collisionless growth rate. This result is confirmed by fluid simulations. Practical formulas are given for the estimate of the threshold beam current which is required for the two-stream instability to develop for a given system length, neutral gas pressure, plasma density, and beam energy. Particle-in-cell simulations carried out with different neutral densities and beam currents demonstrate good agreement with the fluid theory predictions for both the growth rate and the threshold beam current.