A note on a Hamiltonian formulation of force‐free toroidal magnetic fields

Recently, a formalism was presented for representing magnetic fields with toroidal topology in terms of field‐line invariants [Phys. Fluids B 2, 2551 (1990)]. The representation of a field with a nonvanishing toroidal component depends on a transformation from toroidal coordinates to a set of variables consisting of a poloidal angle function, a toroidal flux function, and a toroidal angle function. A restricted class of such transformations was considered for vacuum fields. Here it is shown that this class of transformations for a vacuum or force‐free field always requires that the field be axisymmetric.