Action principles for extended magnetohydrodynamic models

Charidakos, Ioannis Keramidas; Lingam, Manasvi; Morrison, Philip; White, Ryan; Wurm, Alexander

doi:10.1063/1.4896336

Cited by 40 publications

(51 citation statements)

References 40 publications

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“…The form of Eq. (22) ensures that the condition ∇ · B = 0 holds, while the existence of the term ∇Υ in Eq. (23) allows for compressibility of the flow (provided the function Υ(x, y) is not harmonic).…”

Section: A Translationally Symmetric Poisson Bracketmentioning

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: A Translationally Symmetric Poisson Bracketmentioning

confidence: 99%

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

2017

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“…For instance, if we consider a domain where extended MHD is applicable, a third term must be included in the above formula that will be proportional to the square of the electron skin depth in normalized units [95][96][97][98]. Similarly, when Finite Larmor Radius (FLR) are important, they can be incorporated into the above formula by adding gyroaveraged contributions [99][100][101].…”

Section: The Choice Of Constraintsmentioning

confidence: 99%

A maximum entropy principle for inferring the distribution of 3D plasmoids

Lingam

Comisso

2018

Physics of Plasmas

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The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux and helicity exhibit a power-law behavior with exponents of −4/3, −2, −3 and −2 respectively for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v = |v|, is shown to be flat for v → 0, and becomes a power law with an exponent of −7/3 for v → ∞. Most of these results are nearly independent of the free parameters involved in this specific problem. A preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.

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“…In obtaining the above two equations, we observe that a barotropic pressure was implicitly assumed; for a nonbarotropic treatment, we refer the reader to Keramidas Charidakos et al [7], D'Avignon et al [10]. In the above expressions, note that…”

Section: Preliminary Model Considerationsmentioning

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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Action principles for extended magnetohydrodynamic models

Cited by 40 publications

References 40 publications

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

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

A maximum entropy principle for inferring the distribution of 3D plasmoids

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

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