Connection between the two branches of the quantum two-stream instability across the k space

TL;DR

This paper explores how two quantum electron beams become unstable across different wave vectors, revealing a connection between their unstable modes through a continuum of oblique wave vectors, and provides analytical stability criteria.

Contribution

It demonstrates that the two quantum two-stream unstable branches are connected by a continuum of unstable modes with oblique wave vectors, extending understanding of quantum plasma instabilities.

Findings

Unstable branches are connected via a continuum of oblique modes.

Analytical stability domain and growth rate are derived.

Quantum effects influence the instability structure across k space.

Abstract

The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed connected by a continuum of unstable modes with oblique wave vectors. Using the longitudinal approximation, the stability domain for any k is analytically explained, together with the growth rate.