  We consider Maxwell eigenvalue problems on uncertain shapes with perfectly
conducting TESLA cavities being the driving example. Due to the shape
uncertainty the resulting eigenvalues and eigenmodes are also uncertain and it
is well known that the eigenvalues may exhibit crossings or bifurcations under
perturbation. We discuss how the shape uncertainties can be modelled using the
domain mapping approach and how the deformation mapping can be expressed as
coefficients in Maxwell's equations. Using derivatives of these coefficients
and derivatives of the eigenpairs, we follow a perturbation approach to compute
approximations of mean and covariance of the eigenpairs. For small
perturbations these approximations are faster and more accurate than sampling
or surrogate model strategies. For the implementation we use an approach based
on isogeometric analysis, which allows for straightforward modelling of the
domain deformations and computation of the required derivatives. Numerical
experiments for a three-dimensional 9-cell TESLA cavity are presented.
