Geometry of plasma dynamics. I. Group of canonical diffeomorphisms
- Department of Mathematics, Yeditepe University, Atasehir, 34755 Istanbul (Turkey)
The dynamics of collisionless plasma described by the Poisson-Vlasov equations is connected to the Hamiltonian motions of particles and their symmetries. The group of canonical diffeomorphisms of particle phase space is described and adopted as the configuration space. The dual space of its Lie algebra of Hamiltonian vector fields is identified with the space of nonclosed one-forms. The Poisson equation is obtained as a constraint arising from the gauge symmetries of particle dynamics. Variational derivative constrained by the Poisson equation is used to obtain reduced dynamical equations. Usual Lie-Poisson reduction for the group of canonical diffeomorphisms gives the momentum-Vlasov equations. Plasma density is defined as the divergence of symplectic dual of momentum variables. This definition is also given a momentum map description associated with the action of additive group of functions of particle phase space. Equivalence of Hamiltonian functionals in momentum and density formulations is shown. As an alternative formulation in momentum variables, a canonical Hamiltonian system with a quadratic Hamiltonian functional is described. In the case that the groups of Hamiltonian and volume preserving diffeomorphisms coincide, a comparison of one-dimensional plasma and two-dimensional incompressible fluid is presented.
- OSTI ID:
- 21476540
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories
The Maxwell{endash}Vlasov equations in Euler{endash}Poincar{acute e} form
Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN-VLASOV EQUATION
CALCULATION METHODS
COLLISIONLESS PLASMA
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PLASMA
PLASMA DENSITY
POISSON EQUATION
QUANTUM OPERATORS
SPACE
SYMMETRY GROUPS
VARIATIONAL METHODS
VECTOR FIELDS