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.

Numerical Investigations of Electromagnetic Oscillations and Turbulences in Hall Thrusters Using Two Fluid Approach

“…These disturbances can also limit the operating life of a Hall thruster and therefore, suppression of this oscillation has become an essential task for Hall thrusters. These fluctuations are responsible for electron transport across magnetic field lines, performance and ionization of propellant [27][28][29][30]. The magnitude of these oscillations strongly depend on the magnetic field, location of the cathodes, the discharge voltage and the mass flow rate.…”

Pattern formation in Vlasov-Poisson plasmas beyond Landau caused by the continuous spectra of electron and ion hole equilibria

“…As an application we refer to the series of subcritical plasma simulations by Mandal, Schamel and Sharma [20][21][22][23][24], in which the latter case was omnipresent in all cases considered. As an example we refer to Fig.…”

“…Another important, if not the most important, aspect is the fact that the total energy of a plasma can be less than that of the undisturbed plasma due to the presence of a hole.This implies that when this state is approached, for example by achieving a higher phase velocity through acceleration, free energy is available which can be the source for the excitation of other modes and thus for a higher degree of intermittent plasma turbulence. As an example I refer to the simulations of [21,22] and the corresponding video [https://youtu.be/-nxIokKORwU] (with gratitude to the simulators). We see an acceleration that is particularly efficient for θ > 1.…”

“…In this article, the theory of electron-hole equilibria is unfolded in detail, with an emphasis on its occurrence in collision-free, current-carrying, noisy plasmas. It offers new insights into the dynamics of holes triggered by tiny seeds particularly in linearly subcritical plasmas as seen in the highly accurate numerical simulations of Mandal & Sharma [20][21][22][23][24]. It explains why a hole is suddenly accelerated during its evolution and why it settles on the high energy tail of the distribution where the slope is negative, rather than on the low energy, positively inclined tail, i.e.…”

“…The existence of privileged electron holes, which exist as nonlinear structures up to the infinitesimal amplitude limit, is discussed in detail and further simplified modes are recovered. The appearance of intrinsic substructures in the trapped particle distribution and in the macroscopic particle densities are further new elements that can be understood as well [20][21][22][23][24]. Several new solitary wave types are presented and it is proved that the majority of possible solitary wave solutions refer to mathematically undisclosed potentials φ(x) [13,25].…”