Noncanonical Hamiltonian mechanics and its application of magnetic field line flow

Journal Article · Mon Oct 31 23:00:00 EST 1983 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(83)90313-5· OSTI ID:5265337

Cary, J R; Littlejohn, R G

A noncanonical Hamiltonian theory of dynamical systems is presented and applied to magnetic field line flow. The theory allows all of the theorems of Hamiltonian mechanics (most importantly, Noether's theorem, relating symmetries and invariants) to be applied to the magnetic field line system. The theory is not restricted to any particular geometry. An elementary derivation of noncanonical Hamiltonian perturbation theory, based on Lie transforms, is also presented. As an example, the perturbation theory is applied to magnetic field line flow in nearly azimuthally symmetric geometry. Other applications are to the adiabatic motion of charged particles.

• Research Organization: Institute for Fusion Studies, University of Texas, Austin, Texas 78712
• DOE Contract Number: FG05-80ET53088
• OSTI ID: 5265337
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 151:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657007* -- Electricity & Magnetism-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADIABATIC PROCESSES
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
PERTURBATION THEORY
QUANTUM OPERATORS
VARIATIONAL METHODS