Transverse instability magnetic field thresholds of electron phase-space holes

Formation of multiple BGK-like structures in the time-asymptotic state of collisionless Vlasov-Poisson plasmas

The time-asymptotic state of a finite-amplitude perturbation in a collisionless and Maxwellian plasma is typically represented as a steady state of two nonlinearly superposed, counterpropagating Bernstein-Greene-Kruskal (BGK) modes. Using high-resolution Vlasov-Poisson simulations, we show that the plasma evolves self-consistently into a time-asymptotic state of multiple vortexlike structures that gradually fill the phase space and reduce filamentation. This occurs without the need for external forcing or the presence of an energetic plasma population. This finding suggests that the time-asymptotic regime of the plasma is rather akin to a nonlinear superposition of multiple BGK-like modes associated with nearly constant phase-speed waves. The electric field and the space-averaged particle distribution function exhibit a power-law broad spectrum, which is consistent with an energy cascade towards smaller scales in both position and velocity spaces.

Asymmetric one-dimensional slow electron holes

Slow solitary positive-potential peaks sustained by trapped electron deficit in a plasma with asymmetric ion velocity distributions are in principle asymmetric, involving a potential change across the hole. It is shown theoretically how to construct such asymmetric electron holes, thus providing fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a wide variety of prescribed background ion velocity distributions. Because of ion reflection forces experienced by the hole, there is generally only one discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is unstable unless there is a local minimum in the ion velocity distribution, in which the hole velocity then resides. For stable equilibria with Maxwellian electrons, the potential drop across the hole is shown to be Δϕ≃2/9f^{'''}T_{e}/e(eψ/m_{i})^{2}, where ψ is the hole peak potential, f^{'''} is the third derivative of the background ion velocity distribution function at the hole velocity, and T_{e} is the electron temperature. Potential asymmetry is small for holes of the amplitudes usually observed, ψ≲0.5T_{e}/e.

How can slow plasma electron holes exist?

One-dimensional analysis is presented of solitary positive potential plasma structures whose velocity lies within the range of ion distribution velocities that are strongly populated: "slow" electron holes. It is shown that to avoid the self-acceleration of the hole velocity away from ion velocities it must lie within a local minimum in the ion velocity distribution. Quantitative criteria for the existence of stable equilibria are obtained. The background ion distributions required are generally stable to ion-ion modes unless the electron temperature is much higher than the ion temperature. Since slow positive potential solitons are shown not to be possible without a significant contribution from trapped electrons, it seems highly likely that such observed slow potential structures are indeed electron holes.