A REMARK ON THE HAMILTONIAN FORM OF THE MAGNETIC-FIELD-LINE EQUATIONS

It is frequently assumed that a solenoidal vector field u in a simple toroid may be represented in the form of u = delpsi X delphi + delchi x deltheta with appropriate toroidal angle phi, poloidal angle theta, and two fluxes phi and chi. This expression allows one to write the field-line equations in a Hamiltonian form [Phys. Fluids 26, 1288 (1983)]. It is proved on a rigorous mathematical basis that every solenoidal field in an arbitrary smooth simple toroidal domain can be written in the above form.