Theory of phase-space density holes

Abstract

A Bernstein–Green–Kruskal mode consisting of a depression or ’’hole’’ in the phase-space density is shown to be a state of maximum entropy subject to constant mass, momentum, and energy. The parameter space of such holes is studied. The maximum entropy property is used to develop a simplified approximate analytic method as well as to infer the results of hole collisions including coalescing and decay. The maximum entropy property suggests that random, turbulent fluctuations tend to form into such self-trapped structures and this nonperturbative concept is related to the physics of ’’clumps’’ which occur in a renormalized perturbative theory of turbulence.

Studies of ion solitary waves using simulations including hydrogen and oxygen beams

“…In the simulations these structures developed from the interaction of one or more ion or electron beams with background ion and electron populations. The BGK phase hole theory is based on the idea that holes in the phase space distribution of ions can develop owing to thermal fluctuations, and that these holes can propagate and grow [Dupree, 1982]. In simulations these structures form owing to drifts between ion and electron species and owing to thermal fluctuations.…”

Conversion of poloidal flows into toroidal flows by phase space structures in trapped ion resonance driven turbulence

“…For this model, the Kubo number [30], which measures coherence of the turbulence, is Before starting a detailed analysis, we start by considering a simple case of a single structure in phase space density ( Fig.1). Here, we consider a hole structure [18,21] (a localized deficit) located at (x 0 , E 0 ) in phase space. x 0 is the radial position of the structure and…”

Ion temperature gradient driven turbulence with strong trapped ion resonance

“…At the nonlinear stage, as turbulent amplitude increases, an increasing number of resonant particles are trapped in waves. In this case, the system shows rich nonlinear behavior, such as the formation of BGK vortices, 1 phase space density holes, [2][3][4][5][6] pairs of clumps and holes, [7][8][9][10][11][12][13] and phase space density granulations. [14][15][16][17] More recently, state-of-the-art numerical scheme and computational power were applied to study simplified models, such as bump-on-tail 18 and ion-acoustic turbulence.…”