3D simulations of fluctuation spectra in the hall-MHD plasma

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence

Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants, which are the magnetic helicity and the generalized helicity. Exact relations are derived for homogeneous (nonisotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with nonzero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e., the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations, while the magnetic helicity cascade is linked to the right polarized fluctuations.

Structure-function hierarchies and von Kármán-Howarth relations for turbulence in magnetohydrodynamical equations

We generalize the method of A. M. Polyakov, [ Phys. Rev. E 52 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension [ Eur. Phys. J. B 9 725 (1999)], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Kármán-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.

Multiscaling in Hall-magnetohydrodynamic turbulence: insights from a shell model

We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of three-dimensional Hall-magnetohydrodynamic, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.

Global scale-invariant dissipation in collisionless plasma turbulence

A higher-order multiscale analysis of the dissipation range of collisionless plasma turbulence is presented using in situ high-frequency magnetic field measurements from the Cluster spacecraft in a stationary interval of fast ambient solar wind. The observations, spanning five decades in temporal scales, show a crossover from multifractal intermittent turbulence in the inertial range to non-Gaussian monoscaling in the dissipation range. This presents a strong observational constraint on theories of dissipation mechanisms in turbulent collisionless plasmas.