Whistlerization and anisotropy in two-dimensional electron magnetohydrodynamic turbulence

Abstract

A detailed numerical simulation to understand the turbulent state of the decaying two-dimensional electron magnetohydrodynamics is presented. It is observed that the evolved spectrum is comprised of a collection of random eddies and a gas of whistler waves, the latter constituting the normal oscillatory modes of such a model. The whistlerization of the turbulent spectra has been quantified by novel diagnostics. In this work, results are presented only in the regime where the spatial excitation scales are longer than the electron skin depth. Simulations suggest that spectra at short scales are comparatively more whistlerized. The long scale field merely acts as the ambient field along which whistler waves propagate. It is also observed that, in the presence of an external magnetic field, the power spectrum acquires a distinct directional dependence. This anisotropy is dominant at short scales. It is shown that such an anisotropy at short scales results from a cascade mechanism governed by the interacting whistlers waves.

Hall cascades versus instabilities in neutron star magnetic fields

“…None of the fully nonlinear calculations, of ourselves or numerous other authors (Biskamp et al 1996(Biskamp et al , 1999Dastgeer et al 2000;Dastgeer & Zank 2003;Cho & Lazarian 2004;Shaikh & Zank 2005;Cho & Lazarian 2009), which have a broad variety of different initial conditions including sufficiently strong magnetic fields, have ever found anything other than a standard Hall cascade. Cumming et al (2004) also consider the possibility of a Hall instability, and its relevance for the evolution of neutron star magnetic fields.…”

“…As derived by Goldreich & Reisenegger (1992), the equation governing the magnetic field under the influence of both the Hall effect and Ohmic diffusion is…”

“…(1) theoretically and numerically, in both the original spherical-shell geometry (Hollerbach & Rüdiger 2002Cumming et al 2004;Pons & Geppert 2007), and the cartesian box geometries (Biskamp et al 1996(Biskamp et al , 1999Dastgeer et al 2000;Dastgeer & Zank 2003;Cho & Lazarian 2004;Shaikh & Zank 2005;Cho & Lazarian 2009) usually used in turbulence studies (because they allow much higher resolutions than more complicated geometries). The studies in box geometries in particular all found spectra that are similar to the classical 5/3 Kolmogorov spectrum, as well as changes in slope that were interpreted as a dissipative cutoff.…”

Spectral properties of decaying turbulence in electron magnetohydrodynamics

“…Previous numerical studies of 2 1 2 D decaying EMHD turbulence 8,9,12 have focused on investigating the spectral properties of the energy. These studies have shown that the energy spectrum follows a k Ϫ7/3 decay law for kd e Ͻ1 and k Ϫ5/3 for kd e Ͼ1.…”

“…7 Special interest in EMHD has arisen recently to study plasma turbulence. [8][9][10][11][12] Turbulence in a magnetized plasma is in general strongly anisotropic. The scale lengths of the perturbation along the strong field are typically much longer than the scale lengths in the perpendicular plane.…”