Electron hole instability in linearly sub-critical plasmas

TL;DR

This paper investigates how tiny seed fluctuations can destabilize linearly damped plasmas, leading to the formation of electron holes and complex nonlinear wave interactions beyond traditional Landau damping theory.

Contribution

It introduces a mechanism for electron hole instability triggered by small seed fluctuations, involving nonlinear eigen-modes and trapped particle dynamics, expanding understanding of sub-critical plasma turbulence.

Findings

Tiny seed fluctuations can trigger electron hole instability.

Nonlinear eigen-modes explain the transition to unstable plasma states.

Energy transfer from electrons to ion acoustic modes accelerates electron holes.

Abstract

Electron holes (EH) are highly stable non-linear structures met omnipresently in driven collision-less hot plasmas. A mechanism destabilizing small perturbations into holes is essential for an often witnessed but less understood sub-critically driven intermittent plasma turbulence. In this paper we show how a tiny, eddy-like, non-topological seed fluctuation can trigger an unstable evolution deep in the linearly damped region, a process being controlled by the trapping non-linearity and hence being beyond the realm of the Landau scenario. After a (transient) transition phase modes of the privileged spectrum of cnoidal EH are excited which in the present case consist of a solitary electron hole (SEH), two counter-propagating "Langmuir" modes (plasma oscillation), and an ion acoustic mode. A quantitative explanation involves employing non-linear eigen-modes, yielding a non-linear dispersion relation with a forbidden regime and the negative energy character of the SEH, properties being inherent in Schamel's model of undamped Vlasov-Poisson structures identified here as lowest order trapped particle equilibria. An important role in the final adaption of nonlinear plasma eigenmodes is played by a deterministic response of trapped electrons which facilitates transfer of energy from electron thermal energy to an ion acoustic non-uniformity, accelerating the SEH and positioning it into the right place assigned by the theory.