A GENERALIZATION OF THE TAYLOR CONSTRAINT TO THE ADVECTION OF AXISYMMETRICAL POLOIDAL MAGNETIC-FIELDS

The range of inverted-open-triangle LAMBDA (u LAMBDA B) is determined for an axisymmetric poloidal incompressible B and incompressible u, by solving inverted-open-triangle LAMBDA (u LAMBDA B) = inverted-open-triangle LAMBDA v for u, assumed to be confined to within a surface of revolution. Two constraints on v are shown to be necessary for the existence of solutions, viz that the integral of c-phi/\B\ must vanish on each flux surface, and that the integral of v1 around any closed field line must vanish. The construction of the general solution proves that the constraints are sufficient conditions, providing also that the second derivative, with respect to the poloidal flux function, of the volume contained by flux surfaces does not vanish. The general solution is stated for the homogeneous case, v = 0. For the particular case of poloidal v, an integral property of the solution u is established.