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arXiv · 2410.05745

Hamiltonian structure of single-helicity, incompressible magnetohydrodynamics and application to magnetorotational instability

M. Furukawa·M. Hirota
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Abstract

A four-field reduced model of single helicity, incompressible MHD is derived in cylindrical geometry. An appropriate set of noncanonical variables is found, and the Hamiltonian, the Lie-Poisson bracket and the Casimir invariants are clarified. Detailed proofs of properties of the Lie-Poisson bracket, (i) antisymmetry, (ii) Leibniz rule, and (iii) Jacobi identity, are given. Two applications are presented: the first is that the local dispersion relation of axisymmetric magnetohydrodynamics (MRI) is properly reproduced, and the second is that linear stability analyses including negative-energy MRI were successfully performed.

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M. Furukawa, M. Hirota. 2024-10-08. Hamiltonian structure of single-helicity, incompressible magnetohydrodynamics and application to magnetorotational instability. https://arxiv.org/abs/2410.05745

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