# Hamiltonian formulations for perturbed dissipationless plasma equations

Abstract : The Hamiltonian formulations for the perturbed Vlasov-Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative $\partial{\cal F}/\partial\epsilon \equiv [{\cal F}, {\cal S}]$ of an arbitrary functional ${\cal F}[\vb{\psi}]$ of the Vlasov-Maxwell fields $\vb{\psi} = (f,{\bf E},{\bf B})$ or the ideal MHD fields $\vb{\psi} = (\rho,{\bf u},s,{\bf B})$, which are assumed to depend continuously on the (dimensionless) perturbation parameter $\epsilon$. Here, $[\;,\;]$ denotes the functional Poisson bracket for each set of plasma equations and the perturbation {\it action} functional ${\cal S}$ is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces the framework for the application of functional Lie-transform perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov-Maxwell and ideal MHD perturbation theories.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02932384
Contributor : Cristel Chandre <>
Submitted on : Monday, September 7, 2020 - 5:09:08 PM
Last modification on : Tuesday, September 8, 2020 - 3:29:34 AM

### Identifiers

• HAL Id : hal-02932384, version 1
• ARXIV : 2009.02225

### Citation

Alain Brizard, Cristel Chandre. Hamiltonian formulations for perturbed dissipationless plasma equations. 2020. ⟨hal-02932384⟩

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