Representation of magnetic fields with toroidal topology in terms of field-line invariants

Journal Article · Thu Nov 01 04:00:00 EST 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859379· OSTI ID:6055392

Lewis, H R ^[1]

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1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA)

Beginning with Boozer's representation of magnetic fields with toroidal topology (Phys. Fluids {bold 26}, 1288 (1983)), a general formalism is presented for the representation of any magnetic field with toroidal topology in terms of field-line invariants. The formalism is an application to the magnetic field case of results developed recently by Lewis {ital et} {ital al}. (submitted for publication to J. Phys. A) for arbitrary time-dependent Hamiltonian systems with one degree of freedom. Every magnetic field with toroidal topology can be associated with time-dependent Hamiltonian systems with one degree of freedom and every time-dependent Hamiltonian system with one degree of freedom can be associated with magnetic fields with toroidal topology. In the Hamiltonian context, given any particular function {ital I}({ital q},{ital p},{ital t}), Lewis {ital et} {ital al}. derived those Hamiltonians for which {ital I}({ital q},{ital p},{ital t}) is an invariant. In addition, for each of those Hamiltonians, they derived a function canonically conjugate to {ital I}({ital q},{ital p},{ital t}) that is also an invariant. They applied this result to the case where {ital I}({ital q},{ital p},{ital t}) is expressed as a function of two canonically conjugate functions. This general Hamiltonian formalism provides a basis for representing magnetic fields with toroidal topology in terms of field-line invariants. The magnetic fields usually contain plasma with flow and anisotropic pressure. A class of fields with or without rotational symmetry is identified for which there are magnetic surfaces. The formalism is developed for application to the case of vacuum magnetic fields.

• OSTI ID: 6055392
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:11; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

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ANNULAR SPACE
CANONICAL TRANSFORMATIONS
CLOSED CONFIGURATIONS
CONFIGURATION
FUNCTIONS
HAMILTONIANS
INVARIANCE PRINCIPLES
MAGNETIC FIELD CONFIGURATIONS
MAGNETIC FIELDS
MAGNETIC FLUX
MAGNETIC SURFACES
MATHEMATICAL OPERATORS
PLASMA
PLASMA DRIFT
PLASMA PRESSURE
QUANTUM OPERATORS
SPACE
TIME DEPENDENCE
TOROIDAL CONFIGURATION
TRANSFORMATIONS
VACUUM SYSTEMS