  Microswimmers exhibit noisy circular motion due to asymmetric propulsion
mechanisms, their chiral body shape, or by hydrodynamic couplings in the
vicinity of surfaces. Here, we employ the Brownian circle swimmer model and
characterize theoretically the dynamics in terms of the directly measurable
intermediate scattering function. We derive the associated Fokker-Planck
equation for the conditional probabilities and provide an exact solution in
terms of generalizations of the Mathieu functions. Different spatiotemporal
regimes are identified reflecting the bare translational diffusion at large
wavenumbers, the persistent circular motion at intermediate wavenumbers and an
enhanced effective diffusion at small wavenumbers. In particular, the circular
motion of the particle manifests itself in characteristic oscillations at a
plateau of the intermediate scattering function for wavenumbers probing the
radius.
