  The generalized Debye source representation of time-harmonic electromagnetic
fields yields well-conditioned second-kind integral equations for a variety of
boundary value problems, including the problems of scattering from perfect
electric conductors and dielectric bodies. Furthermore, these representations,
and resulting integral equations, are fully stable in the static limit as
$\omega \to 0$ in multiply connected geometries. In this paper, we present the
first high-order accurate solver based on this representation for bodies of
revolution. The resulting solver uses a Nystr\"om discretization of a
one-dimensional generating curve and high-order integral equation methods for
applying and inverting surface differentials. The accuracy and speed of the
solvers are demonstrated in several numerical examples.
