A compressible Hamiltonian electromagnetic gyrofluid model

Waelbroeck, F. L.; Tassi, Emanuele

doi:10.1016/j.cnsns.2011.04.015

Cited by 32 publications

(77 citation statements)

References 36 publications

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“…From such model we have then derived a gyrofluid model, which, by construction, also possesses a Hamiltonian structure. The resulting model corresponds to a known model [14] for magnetic reconnection. The derivation, however, is new and shows, by taking advantage of the results of Ref.…”

Section: Discussionmentioning

confidence: 99%

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Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

Tassi

2014

J. Phys.: Conf. Ser.

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Abstract. We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and driftkinetic systems. IntroductionFluid models represent a widespread and effective tool for investigating important phenomena in fusion plasmas such as instabilities, turbulence and reconnection events. Indeed, fluid models offer a considerable advantage, in terms of required computational resources, with respect to kinetic models. On the other hand, compared to these, they obviously suffer from limitations in the range of scales and frequencies of the phenomena that they can describe. The derivation of sophisticated fluid models aiming at partially remedying such limitations is an active line of research since a long time. An essential part of the problem is related to the closure adopted to truncate the fluid hierarchy of equations obtained by taking moments of a parent kinetic model. A considerable effort, directed also toward applications to space plasma turbulence, has been carried out to derive fluid and gyrofluid models (see, e.g. Refs. [1][2][3][4][5][6][7][8]) by taking moments of

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Section: Discussionmentioning

confidence: 99%

“…We remark that the Hamiltonian closure (14) does not depend on first order parallel moments, which is a consequence of having chosen a Maxwellian with zero mean flow as equilibrium distribution function [11].…”

Section: Derivation Of the Hamiltonian Gyrofluid Modelmentioning

confidence: 99%

Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

Tassi

2014

J. Phys.: Conf. Ser.

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“…Indeed, neglecting ion temperature fluctuations, one retrieves the four-field model of Ref. [111]. If, in addition, one neglects parallel ion dynamics and magnetic curvature, the three-field model of Ref.…”

Section: Gyrofluid Models With Isothermal Electronsmentioning

confidence: 99%

“…In Ref. [111], a four-field model was presented, which accounts also for parallel ion dynamics and magnetic curvature. Finally, Ref.…”

Section: Gyrofluid Models With Isothermal Electronsmentioning

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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“…(3) to simplify the gyro-averaging operator. References [12,17,18] discuss more general two-fluid and gyrofluid models in the context of magnetic reconnection.…”

Section: Magnetized Low-β Plasma Modelmentioning

confidence: 99%

An Explosive Scaling Law for Nonlinear Magnetic Reconnection and Its Insensitivity to Microscopic Scales

Hirota

2017

Plasma and Fusion Research

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The nonlinear phase of magnetic reconnection is investigated by numerically solving a gyrofluid model. The scaling law for the explosive reconnection rate, which has been recently derived for an ideal two-fluid model [Hirota et al., Phys. Plasmas 22, 052114 (2015)], is found to consistently hold when either the ion-sound gyroradius ρ S or the ion gyroradius ρ i is comparable to the electron skin depth d e , even in the presence of finite resistivity η. In this explosive phase, a local X-shaped current layer is spontaneously generated, in which the reconnection speed is closely related to the macroscopic shape of the layer and is almost independent of the layer width. The reconnection speed is therefore insensitive to the size of the microscopic scales, ρ S , ρ i , d e and η. On the other hand, in the cold plasma limit, where ρ S = ρ i = 0, the intermittent acceleration of the reconnection speed is caused by the plasmoid instability. This also seems to be explosive on average, but the rate always falls below the explosive scaling law. The reconnection time extrapolated from this scaling law is shown to be fast enough to explain the time scale of solar flares.

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A compressible Hamiltonian electromagnetic gyrofluid model

Cited by 32 publications

References 36 publications

Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

Hamiltonian closures in fluid models for plasmas

An Explosive Scaling Law for Nonlinear Magnetic Reconnection and Its Insensitivity to Microscopic Scales

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