01-138 Philip J. Morrison

Hamiltonian description of Vlasov dynamics: action angle variables for the continuous spectrum (195K, PDF) Apr 6, 01

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Abstract. The linear Vlasov-Poisson system for homogeneous, stable equilibria is solved by means of a novel integral transform that is a generalization alization 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 Krein (energy) signature to a continuum eigenmode is given.

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