Modeling Imbalanced Collisionless Alfvén Wave Turbulence with Nonlinear Diffusion Equations

Abstract

A pair of nonlinear diffusion equations in Fourier space is used to study the dynamics of strong Alfvénwave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is much larger than in the corresponding collisional regime described by the usual (or reduced) magnetohydrodynamics. The combined effect of high imbalance and ion Landau damping induces a steep energy spectrum for the transverse magnetic field at sub-ion scales. This spectrum is consistent with observations in highly Alfvenic regions of the SW, such as trailing edges, but does not take the form of a transition range continued at smaller scales by a shallower spectrum. This suggests that the observed spectra displaying such a transition result from the superposition of contributions originating from various streams with different degrees of imbalance. Furthermore, when imbalanced energy injection is supplemented at small scales in an already fully developed turbulence, for example under the effect of magnetic reconnection, a significant enhancement of the imbalance at all scales is observed.

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence

“…No correlation between spectral steepening and cross helicity was found, throwing the influence of alignment on ion-scale steepening further into doubt. Effects of damping on highly imbalanced turbulence may provide insight into the transition range [89]. Though we exclude intervals with coherent waves, the presence of intermittency may affect nonlinear interaction at ion scales [40,47,48,50,90].…”

Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence

“…In [118], it is shown that, in the forced case, there is an enhanced inverse transfer of kinetic energy to the large scales. The role of a (generalized) cross-helicity is studied in [119] (see also [120]). It can be seen as allowing for a smooth transition from MHD scales to kinetic scales.…”

Helical fluid and (Hall)-MHD turbulence: a brief review

“…Indeed, high-resolution spacecraft observations of solar-wind turbulence provide important data for constructing models of energy cascades in Hall-MHD and beyond, such as for instance statistical theories of extended MHD where both the Hall drift and the electron inertia are included to treat length and time scales comparable to the ion cyclotron frequency and/or the electron skin depth [90,118] (see also [119]). These formulations are expected to be useful for modelling inertial confinement by high-intensity lasers in the laboratory, as well as turbulenceplasma waves interactions.…”