Axisymmetric magnetic fields and fluid motions

Abstract

The equations of hydromagnetics appropriate for an incompressible inviscid fluid of finite electrical conductivity are considered in case the magnetic fields and the fluid motions have symmetry about an axis By using a known theorem that a solenoidal vector field can be expressed as a superposition of a poloidal and a toroidal field, the equations are reduced to four equations for four governing scalars. In the limiting case of infinite electrical conductivity, a general relation is derived which includes, as special cases, the known theorems on force-free fields, isorotation, and conditions for hydrostatic equilibrium. Some integral relations which follow from the four equations are also derived.