On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Abstract

Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.

Electron-scale reduced fluid models with gyroviscous effects

“…The regime at scales smaller than d e has been extensively studied mostly for WWs, in the framework of EMHD (Biskamp et al 1996(Biskamp et al , 1999Galtier & Bhattacharjee 2003;Galtier & Meyrand 2015;Lyutikov 2013), of an incompressible bi-fluid model (Andrés et al 2014;Andrés et al 2016a,b) and of extended magnetohydrodynamics (XMHD) (Miloshevich et al 2017). Full particle-in-cell simulations of this regime were performed by Gary et al (2012) and Chang et al (2013).…”

Chirality, extended magnetohydrodynamics statistics and topological constraints for solar wind turbulence

“…For such a Galerkin truncated system, the Liouville theorem ensures an ultimate invariant probability measures describing the phase flows at the absolute equilibrium (AE) state (Lee 1952;Kraichnan 1973). The convenient and physical one is the canonical distribution ∼ exp{−αH − βHM − γHC} as used by Miloshevich, Lingam & Morrison (2017), closely following whose notations a := α, b := β/k, c := γ, f := k(βd 2 e + γdi)…”

“…We may apply the chiroids' AE for finer analysis of plasmas dynamics and the SWT. For clarity, we will follow Abdelhamid, Lingam & Mahajan (2016) and Miloshevich, Lingam & Morrison (2017) to discuss separate regimes respectively.…”

“…The first of Miloshevich, Lingam & Morrison (2017)'s Eqs. (69-71) reads in our notations for the 3D modal spectral density Zhu, Yang & Zhu (2014) also observed, the deep-sub-electronlimit spectrum is exactly in the same form of neutral fluid, which in general can only have the large-k pole indicating forward cascade and secondary OCSDS, and Miloshevich, Lingam & Morrison (2017) shows the qualitatively consistent spectra in their Fig.…”

“…At the deep sub-ion and even sub-electron scales, kinetic effects (e.g., Passot & Sulem 2015) enter and explanations resorting to gyrokinetic turbulence theory (see, e.g., Krommes 2012, and references therein) may be more complete, however, though Kolmogorov phenomenology and tentative statistical absolute equilibrium analyses have been performed for electrostatic cases (Plunk et al 2010;Zhu & Hammett 2010), general solid calculations would be formidable for clear illumination. Fluid models, especially extended magnetohydrodynamics (XMHD, see, e.g., Miloshevich, Lingam & Morrison 2017, and references therein), with the ion and electron skin depths, di and de, included to reflect the relevant physical ingredients, may present the major physics concerning the multiple scaling regimes, among others.…”