Abstract. The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinitedimensional phase space. A nontrivial part of the formulation is the proof of Jacobi's identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.Comment: 11 pages, 2 figure
Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k < 1/λ i ), Hall (1/λ i < k < 1/λ e ), and electron inertia (k > 1/λ e ) regimes; k is the wavenumber and λ s = c/ω ps is the skin depth of species 's'. In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of −11/3 and −13/3 are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately −4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard 'dissipation' range paradigm.
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