Higher-order Hamiltonian fluid reduction of Vlasov equation

Perin, Maxime; Chandre, Cristel; Morrison, Philip; Tassi, Emanuele

doi:10.1016/j.aop.2014.05.011

Cited by 19 publications

(18 citation statements)

References 33 publications

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“…(12) with where R and T are given by Eqs. (28)- (29). The dependence of the functions R and T in their arguments is not trivial.…”

Section: Model Without Normal Variablesmentioning

confidence: 99%

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Hamiltonian closures for fluid models with four moments by dimensional analysis

Perin¹,

Chandre²,

Morrison³

et al. 2015

J. Phys. A: Math. Theor.

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Abstract. Fluid reductions of the Vlasov-Ampère equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are identified. Two Hamiltonian models emerge, for which the explicit closures are given, along with their Poisson brackets and Casimir invariants.

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“…(12) with where R and T are given by Eqs. (28)- (29). The dependence of the functions R and T in their arguments is not trivial.…”

Section: Model Without Normal Variablesmentioning

confidence: 99%

“…Inserting this expression into the previous equations provides the necessary constraints a = 0 and ψ(ξ) = ψ 0 . As a consequence, this model does not have Casimir invariants of the entropy-type [29], i.e., of the form ρφ(S 2 , S 3 ) dx. Moreover, we can show in a similar way that Eq.…”

Section: Model Without Normal Variablesmentioning

confidence: 99%

Hamiltonian closures for fluid models with four moments by dimensional analysis

Perin¹,

Chandre²,

Morrison³

et al. 2015

J. Phys. A: Math. Theor.

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“…Linear closures, on the other hand, are those selected for drift and gyrokinetic models in the "δf approximation " [28,30]. Following this approach also a new Hamiltonian fluid model obtained from the Vlasov equation has been derived [31]. These results, however, concern fluid models retaining only a very low number of moments, more precisely two-moment models for Refs.…”

Section: Introductionmentioning

confidence: 98%

Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

Tassi

2015

Annals of Physics

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International audienceWe present an infinite family of Hamiltonian electromagnetic fluid models for plasmas, derived from drift-kinetic equations. An infinite hierarchy of fluid equations is obtained from a Hamiltonian drift-kinetic systems by taking moments of a generalized distribution function and using Hermite polynomials as weight functions of the velocity coordinate along the magnetic guide field. Each fluid model is then obtained by truncating the hierarchy to a finite number N + 1 of equations by means of a closure relation. We show that, for any positive N , a linear closure relation between the moment of order N + 1 and the moment of order N guarantees that the resulting fluid model possesses a Hamiltonian structure, thus respecting the Hamiltonian character of the parent drift-kinetic model. An orthogonal transformation is identified which maps the fluid moments to a new set of dynamical variables in terms of which the Poisson brackets of the fluid models become a direct sum and which unveils remarkable dynamical properties of the models in the tw

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“…It can be also observed in continuum simulations of the Vlasov equation and electromagnetic field, e.g., [9]. The emergence of dissipative phenomena from reversible equations is also observed when proposing closure relations in the Grad hierarchy, e.g., [10][11][12][13].…”

Section: Introductionmentioning

confidence: 83%

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

Pavelka

Klika

Grmela

2018

Entropy

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Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions, however, approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is not changed by the Vlasov equation. On the other hand, density and kinetic energy density, which are integrals of the distribution function, approach spatially homogeneous states strongly, which is accompanied by growth of the hydrodynamic entropy. Such a behavior can be seen when the Vlasov equation is reduced to the evolution equations for density and kinetic energy density by means of the Ehrenfest reduction.

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Higher-order Hamiltonian fluid reduction of Vlasov equation

Cited by 19 publications

References 33 publications

Hamiltonian closures for fluid models with four moments by dimensional analysis

Hamiltonian closures for fluid models with four moments by dimensional analysis

Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

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