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arXiv · 1211.0850

Hamiltonian formulation of reduced Vlasov-Maxwell equations

Cristel Chandre·Alain Brizard·Emanuele Tassi
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Abstract

The Hamiltonian formulation of the reduced Vlasov-Maxwell equations is expressed in terms of the macroscopic fields D and H. These macroscopic fields are themselves expressed in terms of the functional Lie-derivative generated by the functional S with the Poisson bracket [.,.] for the exact Vlasov-Maxwell equations. Hence, the polarization vector P= (D-E)/(4pi) and the magnetization vector M=(B-H)/(4pi) are defined in terms of the expressions 4pi P=[S,E]+... and 4pi M =-[S,B]+..., where lowest-order terms yield dipole contributions.

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Cristel Chandre, Alain Brizard, Emanuele Tassi. 2012-11-05. Hamiltonian formulation of reduced Vlasov-Maxwell equations. https://arxiv.org/abs/1211.0850

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