VARIATIONAL FORMULATION FOR TWO-FLUID PLASMAS IN CLEBSCH VARIABLES
There is interest in developing variational principles in fluid and plasma dynamics within the Eulerian description to study nonlinear fluctuations. This description does not preserve a close similarity with a system of particles as the Lagrangian one does. The main difficulty is that the set of equations in the form originally given does not follow from a variational principle. An equivalent system which follows from a variational principle has to be found through transformations and different representations of the variables. Clebsch introduced Euler-like potential variables for the fluid velocity to derive the hydrodynamic equations for an ideal and incompressible fluid from a variational principle. Several studies have meanwhile appeared on the subject. Seliger and Whitham derived a variational principle for the equations of plasmas described by the two-fluid model, neglecting thermal motion. They used a combination of the potential representation for Maxwell's equations with the Clebsch potentials for the fluid equations. With the internal energy per unit mass as a function of the density and entropy, the scheme proposed in is now extended to two-fluid plasmas with finite pressure. A Hamiltonian description is introduced so that canonical (non-Poisson brackets can be defined in terms of the physical) fields. Gravitating two-fluid plasmas are also considered.
Bibliographic Reference: ZEITSCHRIFT FUER NATURFORSCHUNG, VOL. 39A (1984), PP. 9-12
Record Number: 1989122075200 / Last updated on: 1987-01-01
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