Electron hole instability as a primordial step towards sustained intermittent turbulence in linearly subcritical plasmas

Abstract

Electron and ion holes are highly stable nonlinear structures met omnipresently in driven collisionless hot plasmas. A mechanism destabilizing small perturbations into holes is essential for an often witnessed but less understood subcritically driven intermittent plasma turbulence. In this paper we show how a tiny, eddy-like, non-topological electron seed fluctuation can trigger an unstable evolution deep in the linearly damped region, a process being controlled by the trapping nonlinearity and hence being beyond the realm of the Landau scenario. After a (transient) transition phase modes of the privileged spectrum of cnoidal electron and ion holes 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 a nonlinear 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 nonuniformity, accelerating the SEH and positioning it into the right place assigned by the theory.