Canonical Coordinates or “Generalized Magnetic Coordinates”

Abstract

As an extension to the subject of flux coordinates, we discuss concisely the more general topic of canonical coordinates for magnetic fields. The word canonical derives from the Hamiltonian character of the magnetic field, which will be demonstrated presently. Canonical coordinates for B, and the canonical representation of B exist even if there are no flux surfaces. Flux coordinates, on the contrary, only exist in the presence of magnetic surfaces. The canonical coordinates are sometimes called “generalized magnetic coordinates”. It must be understood, however, that this is not a synonym for flux coordinates. The reason for the name “generalized magnetic coordinates” is the superficial resemblance of the B-field representation in canonical coordinates and flux coordinates.