Action-angle variables for the ideal-MHD continuous spectrum

Hirota, Makoto; Tokuda, Shinji; Fukumoto, Yasuhide*

Energy of eigenmodes (or wave energy) in ideal magnetohydrodynamics (MHD) is formulated in the Hamiltonian context. It is shown that the wave energy is transformed into the normal form (i.e. the action variable multiplied by the eigenfrequency) not only for point spectra but also for the Alfvn and slow continuous spectra. These continuous spectra partially correspond to the negative energy wave in the presence of the plasma flow of the order of the Alfvn speed. Coupling of negative and positive energy waves causes linear instability as is common with Hamiltonian systems of finite degree of freedom. However, the generalization of this Hamiltonian picture to the case with continuous spectrum is still nontrivial. Some investigations on this problem are made for slab or cylindrical plasmas with flow.