Relativistic Two-stream Instability

TL;DR

This paper analyzes the relativistic two-stream instability in a two-fluid system, deriving conditions for causality and stability, and exploring different equations of state in a frame-independent manner.

Contribution

It provides a comprehensive, frame-independent analysis of relativistic two-stream instability across various fluid coupling models, including new stability constraints.

Findings

Identified conditions for causality and stability in relativistic two-fluid systems.

Derived dispersion relations for different equations of state.

Established a new constraint on fluid entrainment.

Abstract

We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow -- either across an interface or when two or more fluids interpenetrate -- and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the "free" (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (eg. no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.