Inertial magnetohydrodynamics

Lingam, Manasvi; Morrison, Philip; Tassi, Emanuele

doi:10.1016/j.physleta.2014.12.008

Cited by 27 publications

(46 citation statements)

References 43 publications

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“…In the inertial MHD limit d i → 0 the parameters λ ± = (−d i ± d 2 i + 4d 2 e )/(2d 2 e ) go to ±d −1 e and hence lim di→0 µ ± = ∓d e , which leads to the following form for the Casimir invariants: follows similarly. An interesting property of IMHD is that the wellknown MHD cross helicity is also a Casimir for IMHD if B → B * [6], that is…”

Section: E Inertial Mhd Limitmentioning

confidence: 99%

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

2017

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The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the three-dimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebsch-like forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energy-Casimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into Grad-Shafranov-Bernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ion-flow from electromagnetic surfaces.

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Section: E Inertial Mhd Limitmentioning

confidence: 99%

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

2017

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“…This may appear counterintuitive, but we observe that d i and d e must be perceived as independent variables. The resultant model has sometimes been referred to as IMHD [71,74], because it encompasses electron inertia but not the Hall term.…”

Section: Mhd Hallmentioning

confidence: 99%

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

2017

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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.

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“…(5) are Hall terms. For definiteness, in this work we focus on the investigation of magnetic reconnection in the thermal-inertial regime, which correspond to the situation in which the thermal-inertial terms are larger than the Hall terms [33][34][35][36]. For an electron-ion plasma, assuming that the Hall terms are of the same order, the thermal-inertial regime can be achieved if the condition ∆µJB ξh ne U J…”

Section: Model Equationsmentioning

confidence: 99%

Collisionless magnetic reconnection in curved spacetime and the effect of black hole rotation

Comisso

Asenjo

2018

Phys. Rev. D

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Magnetic reconnection in curved spacetime is studied by adopting a general relativistic magnetohydrodynamic model that retains collisionless effects for both electron-ion and pair plasmas. A simple generalization of the standard Sweet-Parker model allows us to obtain the first order effects of the gravitational field of a rotating black hole. It is shown that the black hole rotation acts as to increase the length of azimuthal reconnection layers, per se leading to a decrease of the reconnection rate. However, when coupled to collisionless thermal-inertial effects, the net reconnection rate is enhanced with respect to what would happen in a purely collisional plasma due to a broadening of the reconnection layer. These findings identify an underlying interaction between gravity and collisionless magnetic reconnection in the vicinity of compact objects.

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Inertial magnetohydrodynamics

Cited by 27 publications

References 43 publications

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Collisionless magnetic reconnection in curved spacetime and the effect of black hole rotation

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