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

Beginning with Boozer’s representation of magnetic fields with toroidal topology [Phys. Fluids 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 et 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 I(q,p,t), Lewis et al. derived those Hamiltonians for which I(q,p,t) is an invariant. In addition, for each of those Hamiltonians, they derived a function canonically conjugate to I(q,p,t) that is also an invariant. They appli...