Formation and dynamics of coherent structures involving phase-space vortices in plasmas

Abstract

We present a comprehensive review of recent theoretical and numerical studies of the formation and dynamics of electron and ion holes in a collisionless plasma. The electron hole is characterized by a localized positive potential in which a population of electrons is trapped, and a depletion of the electron number density, while the ion hole is associated with localized negative potential in which a population of ions is trapped and a depletion of both the ion and electron densities occur. We present conditions for the existence of quasi-stationary electron and ion holes in unmagnetized and magnetized electron-ion plasmas, as well as in an unmagnetized pair-ion plasma. An interesting aspect is the dynamic interactions between ion and electron holes and the surrounding plasma. The dynamics is investigated by means of numerical simulations in which analytical solutions of quasistationary electron and ion holes are used as initial conditions. Our Vlasov simulations of two colliding ion holes reveal the acceleration of electrons and a modification of the initially Maxwellian electron distribution function by the ion hole potentials, which work as barriers for the electrons. A secondary effect is the excitation of high-frequency plasma waves by the streams of electrons. On the other hand, we find that electron holes show an interesting dynamics in the presence of mobile ions. Since electron holes are associated with a positive electrostatic potential, they repel positively charged ions. Numerical simulations of electron holes in a plasma with mobile ions exhibit that the electron holes are, in general, attracted by ion density maxima and repelled by ion density minima. Therefore, standing electron holes can be accelerated by the self-created ion cavities. In a pair plasma, both the temperatures and masses of the positively and negatively charged particles are assumed equal, and therefore one must treat both species with a kinetic theory on an equal footing. Accordingly, a phase-space hole in one of the species is associated with reflected particles in the opposite species. Here standing solitary large-amplitude holes are not allowed, but they must have a propagation speed close to the thermal speed of the particles. We discuss extensions of the existing non-relativistic theories for the electron and ion holes in two directions. First, we describe a fully nonlinear kinetic theory for relativistic electron holes (REHs) in an unmagnetized plasma, and show that the REHs have amplitudes and widths much larger than their non-relativistic counterparts. Second, we extend the weakly nonlinear theories for the electron and ion holes to include the effects of the external magnetic field and the plasma inhomogeneity. The presence of the external magnetic field gives rise to the electron and ion hole structures which have differential scale sizes along and across the magnetic field direction. Consideration of the density inhomogeneity in a magnetized plasma with non-isothermal electron distribution function provides the p...

Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves

“…[13][14][15][16] Lastly there are miscellaneous explorations of the behavior of 1D phase-space vortices ͑"holes"͒ and the like. [17][18][19][20][21][22][23] For historical completeness one should also note a particular laboratory experiment done in a Q-machine resulting in the creation of a single KEEN-like cell rather than in a long wave train. 24 There is also a recent publication by Valentini et al 25 which bears directly on the kind of work presented in this publication.…”

Ion holes in the hydrodynamic regime in ultracold neutral plasmas

“…35,36 Local density enhancements in a plasma are typically referred to as solitons 37,38 and depletions are referred to as holes. [35][36][37] Here, we focus on density depletions in which ion and electron densities closely follow each other, which are referred to as ion holes. 39,40 We create ion holes by sculpting the initial density distributions to have a planar depletion through the center of the plasma.…”

“…39 They are associated with two-stream instabilities, 39,40 and the resulting negative potential produces a population of trapped ions that can create nonlinear effects even in the small-amplitude limit. 35,36 The interactions of overlapping colliding density perturbations have also attracted significant interest because of their possible role in the creation of energetic particles and other collective excitations. 35,47 Electron holes are also possible in the electron component of a neutral plasma.…”

“…35,36 The interactions of overlapping colliding density perturbations have also attracted significant interest because of their possible role in the creation of energetic particles and other collective excitations. 35,47 Electron holes are also possible in the electron component of a neutral plasma. 48,49 II.…”

Comment on “Undamped electrostatic plasma waves” [Phys. Plasmas 19, 092103 (2012)]

“…The remarkable success of hole solutions in the interpretation of laboratory, space, and numerical experiments is underlining this and their physically upgraded nature. 5,[9][10][11][12] Moreover, as pointed out more explicitly in the author's recent review, 5 the hole solutions are effectively not accessible by the BGK method and can, therefore, strictly speaking not be incorporated into the class of BGK waves. Since both methods are of equal generality, physical as well as practical reasons, therefore, favorize hole solutions.…”