  We propose a numerical method for the solution of electromagnetic problems on
axisymmetric domains, based on a combination of a spectral Fourier
approximation in the azimuthal direction with an IsoGeometric Analysis (IGA)
approach in the radial and axial directions. This combination allows to blend
the flexibility and accuracy of IGA approaches with the advantages of a Fourier
representation on axisymmetric domains. It also allows to reduce significantly
the computational cost by decoupling of the computations required for each
Fourier mode. We prove that the discrete approximation spaces employed
functional space constitute a closed and exact de Rham sequence. Numerical
simulations of relevant benchmarks confirm the high order convergence and other
computational advantages of the proposed method.
