Lifting of the Vlasov-Maxwell bracket by Lie-transform method
Abstract
The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation (`lift') of the Vlasov-Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to provide an explicit pathway to the Hamiltonian formulations for the guiding-centre and gyrokinetic Vlasov-Maxwell equations, which have found important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov-Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.
- Publication:
-
Journal of Plasma Physics
- Pub Date:
- December 2016
- DOI:
- 10.1017/S0022377816001161
- arXiv:
- arXiv:1606.06652
- Bibcode:
- 2016JPlPh..82f9008B
- Keywords:
-
- magnetized plasmas;
- plasma dynamics;
- Physics - Plasma Physics;
- Mathematical Physics
- E-Print:
- 39 pages