Hamiltonian Description of Vlasov Dynamics: Action-Angle Variables for the Continuous Spectrum
نویسنده
چکیده
The linear Vlasov-Poisson system for homogeneous, stable equilibria is solved by means of a novel integral transform that is a generalization of the Hilbert transform. The integral transform provides a means for describing the dynamics of the continuous spectrum that is well-known to occur in this system. The results are interpreted in the context of Hamiltonian systems theory, where it is shown that the integral transform defines a canonical transformation to action-angle variables for this infinite degree-of-freedom system. A means for attaching Krĕin (energy) signature to a continuum eigenmode is given.
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