### 2.5 Boundary conditions and parity

The axisymmetric dynamo equations are to be solved in a meridional plane, i.e., and
, where the inner radial extent of the domain () need not necessarily extend all
the way to . It is usually assumed that the deep radiative interior can be treated as a
perfect conductor, so that is chosen a bit deeper than the lowest extent of the region where
dynamo action is taking place; the boundary condition at this depth is then simply ,
.
It is usually assumed that the Sun/star is surrounded by a vacuum, in which no electrical currents
can flow, i.e., ; for an axisymmetric B expressed via Equation (4), this requires

It is therefore necessary to smoothly match solutions to Equations (1, 5) on solutions to Equations (6) at
. Regularity of the solutions demands that and on the symmetry axis
( and in a meridional plane). This completes the specification of the boundary
conditions.
Formulated in this manner, the dynamo solution will spontaneously “pick” its own parity, i.e., its
symmetry with respect to the equatorial plane. An alternative approach, popular because it
can lead to significant savings in computing time, is to solve only in a meridional quadrant
() and impose solution parity via the boundary condition at the equatorial plane ():