Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

Morrison, Philip; Lingam, Manasvi; Acevedo, Ramiro

doi:10.1063/1.4891321

Cited by 31 publications

(81 citation statements)

References 55 publications

(99 reference statements)

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“…Previous results concerning the inclusion of (ion) FLR effects in Hamiltonian reduced fluid models were presented in Morrison et al (1984); Hazeltine et al (1987); Dagnelund & Pavlenko (2005); Morrison et al (2014); Izacard et al (2011). It could in particular be of interest to investigate whether the idea of the gyromap transformation, adopted in Morrison et al (1984); Hazeltine et al (1987); Izacard et al (2011); Morrison et al (2014), together with the Hamiltonian structure of the model in the absence of FLR contributions, can help in building a Hamiltonian model including electron FLR effects. Further developments should also include numerical simulations to test the predictions for the turbulent energy spectra, and in particular to evaluate the role of coherent structures and analyze the difference between two-and three-dimensional geometries.…”

Section: Resultsmentioning

confidence: 99%

“…In the turbulent regime, RLF models could in particular provide an efficient tool to study the relative contributions of coherent structure disruptions and incoherent fluctuation cascades in the processes of dissipation and plasma heating (Parashar et al 2015), an important issue aimed at being addressed by the THOR satellite mission (Vaivads et al 2016).…”

Section: Resultsmentioning

confidence: 99%

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Electron-scale reduced fluid models with gyroviscous effects

2017

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Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on pressure balance or on the incompressibility of the electron fluid, they respectively capture kinetic Alfvén waves (KAWs) or whistler waves (WWs), and can provide suitable tools for reconnection and turbulence studies. Both isothermal regimes and Landau fluid closures permitting anisotropic pressure fluctuations are considered. For small values of the electron beta parameter β e , a perturbative computation of the gyroviscous force valid at scales comparable to the electron inertial length is performed at order O(β e ), which requires second-order contributions in a scale expansion. Comparisons with kinetic theory are performed in the linear regime. The spectrum of transverse magnetic fluctuations for strong and weak turbulence energy cascades is also phenomenologically predicted for both types of waves. In the case of moderate ion to electron temperature ratio, a new regime of KAW turbulence at scales smaller than the electron inertial length is obtained, where the magnetic energy spectrum decays like k −13/3 ⊥ , thus faster than the k −11/3 ⊥ spectrum of WW turbulence.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Electron-scale reduced fluid models with gyroviscous effects

2017

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“…A second consequence is that the energy-momentum tensor is rendered symmetric, which ensures that the angular momentum is conserved for this ansatz. If we further restrict ourselves to the specific case where B = B zẑ , we find that (13) yields the same magnetization equation employed in [32]. Hence, in this scenario, the magnetization is generated through the existence of a finite magnetic moment, which in turn emerges via P /B.…”

Section: The Hamiltonian Formulation Of Ferrofluidsmentioning

confidence: 76%

“…Firstly, we demonstrated that the (classical) magnetization arises from (15). It was shown in [32] that it plays a crucial role in modeling finite Larmor radius (FLR) corrections, and gives rise to the Braginskii gyroviscosity in the 2D limit. Secondly, we indicated that the MHD models with magnetization do not appear to conserve angular momentum, but they do conserve energy and momentum.…”

Section: Discussionmentioning

confidence: 98%

Dissipative effects in magnetohydrodynamical models with intrinsic magnetization

Lingam

2015

Communications in Nonlinear Science and Numerical Simulation

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“…In Ref. [58] the origin of the gyromap procedure from an action principle perspective is discussed. In Ref.…”

Section: B Adding Ion Finite Larmor Radius Effects While Preserving mentioning

confidence: 99%

Hamiltonian closures in fluid models for plasmas

Tassi

2017

Eur. Phys. J. D

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This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models.Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and connections with previously discussed fluid models are pointed out.

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Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

Cited by 31 publications

References 55 publications

Electron-scale reduced fluid models with gyroviscous effects

Electron-scale reduced fluid models with gyroviscous effects

Dissipative effects in magnetohydrodynamical models with intrinsic magnetization

Hamiltonian closures in fluid models for plasmas

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