Hamiltonian Formulation of Two-Dimensional Gyroviscous MHD
نویسنده
چکیده
This work is concerned with the Hamiltonian field formulation of the equations that describe two-dimensional non-dissipative gyroviscous onefluid plasmas [I, 2, 3, 4J. These equations differ from the usual Eulerian form of ideal MHO by the inclusion of a non-entropy-producing stress tensor that arises from the finiteness of the ion gyroradius. The physics of this stress \ensor is important for modelling tokamak discharges [5J, and may be important for calculation of the MHO k-spectrum by means of the partition function [6, 7J. The Eulerian MHO equations in terms of their usual variables do not possess the form of a conventionaL Hamiltonian field-theory. Nonetheless, these equations were shown to be Hamiltonian in a generalized sense by incorporating a generalization of the Poisson bracket [8J. Generalized or noncanonical Poisson brackets possess the same algebraic properties as ordinary Poisson brackets, but the notion of canonical variables is abandoned and degeneracy is allowed. At present, noncanonieal Poisson brackets for all of the major non-dissipative plasma systems have been obtained. For review of the formalism and applications the reader is directed to [9]-[12]. This paper is organized as follows: in Sect. II the two-dimensional gyroviscous MHO equations are described. In Sect. III we briefly review some aspects of the noncanonical Hamiltonian formalism
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تاریخ انتشار 2007