Hamiltonian formulation of reduced Vlasov-Maxwell equations

Cristel Chandre (1, 2) , Alain Brizard (3) , Emanuele Tassi (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire
3 Saint Michael's College

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.

Domaines: Dynamique Chaotique [nlin.CD]; Physique des plasmas [physics.plasm-ph]

Cristel Chandre, Alain Brizard, Emanuele Tassi. Hamiltonian formulation of reduced Vlasov-Maxwell equations. 2012. ⟨hal-00748241⟩