  This paper concerns kinematic helical dynamos in a spherical fluid body
surrounded by an insulator. In particular, we examine their behaviour in the
regime of large magnetic Reynolds number $\Rm$, for which dynamo action is
usually concentrated upon a simple resonant stream-surface. The dynamo
eigensolutions are computed numerically for two representative single-roll
flows using a compact spherical harmonic decomposition and fourth-order
finite-differences in radius. These solutions are then compared with the growth
rates and eigenfunctions of the Gilbert and Ponty (2000) large $\Rm$ asymptotic
theory. We find good agreement between the growth rates when $\Rm>10^4$, and
between the eigenfunctions when $\Rm>10^5$.
