### 2.4 Axisymmetric formulation

The sunspot butterfly diagram, Hale’s polarity law, synoptic magnetograms, and the shape of the solar
corona at and around solar activity minimum jointly suggest that, to a tolerably good first
approximation, the large-scale solar magnetic field is axisymmetric about the Sun’s rotation axis, as
well as antisymmetric about the equatorial plane. Under these circumstances it is convenient
to express the large-scale field as the sum of a toroidal (i.e., longitudinal) component and a
poloidal component (i.e., contained in meridional planes), the latter being expressed in terms
of a toroidal vector potential. Working in spherical polar coordinates , one writes
Such a decomposition evidently satisfies the solenoidal constraint , and substitution into the
MHD induction equation produces two (coupled) evolution equations for and , the latter simply
given by the -component of Equation (1), and the former, under the Coulomb gauge , by