Nonlinear Hall MHD and electrostatic ion-cyclotron stationary waves: a Hamiltonian-geometric viewpoint

Some supplementary results and interpretations on the theory of Hall MHD solitons (McKenzie and Doyle 2002 Phys. Plasmas 9, 55) are presented. It is shown that the Hall MHD soliton reduces, in the appropriate limit, to an electrostatic ion-cyclotron soliton. R is also shown how the dynamical equations governing the Hall MHD soliton can be obtained frorn a Hamiltonian H. Soliton solutions correspond to H = 0, periodic solutions to H < 0 and rotation-type solutions to H > 0. Possible applications are discussed. A non-canonical Hamiltonian picture is developed and compared to the well-known example of a free rigid body.