Hybrid kinetic-MHD simulations in general geometry

Kim, Charlson C.; Sovinec, C. R.; Parker, Scott

doi:10.1016/j.cpc.2004.06.059

Cited by 25 publications

(48 citation statements)

References 9 publications

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“…in the current-coupling scheme (28)- (31), so that Lorentz forces in (28) are replaced by a relative pressure term. Notice that the static equilibria of the above equations (62)-(64) coincide with those of the hybrid model in [23,43] (for hot particles undergoing Vlasov dynamics), provided the equilibrium Vlasov distribution (usually denoted by f 0 ) is isotropic in the velocity coordinate, i.e. K 0 = v f 0 d 3 v = 0.…”

Section: Formulation Of the Modelmentioning

confidence: 91%

Euler-Poincaré formulation of hybrid plasma models

Holm

Tronci

2012

Communications in Mathematical Sciences

106

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Abstract. Three different hybrid Vlasov-fluid systems are derived by applying reduction by symmetry to Hamilton's variational principle. In particular, the discussion focuses on the EulerPoincaré formulation of three major hybrid MHD models, which are compared in the same framework. These are the current-coupling scheme and two different variants of the pressure-coupling scheme. The Kelvin-Noether theorem is presented explicitly for each scheme, together with the Poincaré invariants for its hot particle trajectories. Extensions of Ertel's relation for the potential vorticity and for its gradient are also found in each case, as well as new expressions of cross helicity invariants.

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Section: Formulation Of the Modelmentioning

confidence: 91%

Euler-Poincaré formulation of hybrid plasma models

Holm

Tronci

2012

Communications in Mathematical Sciences

106

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“…As follows from Eq. (19), the inequality (21) implies that one of the conditions for stability is that the equilibrium flow be sub-Alfvénic. Condition (22) is a sufficient condition for stability, but a more in-depth analysis would show that the line bending term can add a positive contribution.…”

Section: Energy-casimir Stability Via the Second Variationmentioning

confidence: 99%

Energy-Casimir stability of hybrid Vlasov-MHD models

Tronci

Tassi

Morrison

2015

J. Phys. A: Math. Theor.

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Different variants of hybrid kinetic-fluid models are considered for describing the interaction of a bulk fluid plasma obeying MHD and an energetic component obeying a kinetic theory. Upon using the Vlasov kinetic theory for energetic particles, two planar Vlasov-MHD models are compared in terms of their stability properties. This is made possible by the Hamiltonian structures underlying the considered hybrid systems, whose infinite number of invariants makes the energy-Casimir method effective for determining stability. Equilibrium equations for the models are obtained from a variational principle and in particular a generalized hybrid Grad-Shafranov equation follows for one of the considered models. The stability conditions are then derived and discussed with particular emphasis on kinetic particle effects on classical MHD stability.

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“…, which emphasizes the various kinetic energy contributions. A natural consequence of this kinetic equation is that its zero-th moment n satisfies the simple advection relation ∂ t n + div(n U ) = 0, so that the total density D = ρ + n satisfies the equation ∂ t D + div(D U ) = 0, as it appears in [21].…”

Section: Second Pressure-coupling Schemementioning

confidence: 99%

Hamiltonian approach to hybrid plasma models

Tronci¹

2010

J. Phys. A: Math. Theor.

130

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The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.

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Hybrid kinetic-MHD simulations in general geometry

Cited by 25 publications

References 9 publications

Euler-Poincaré formulation of hybrid plasma models

Euler-Poincaré formulation of hybrid plasma models

Energy-Casimir stability of hybrid Vlasov-MHD models

Hamiltonian approach to hybrid plasma models

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