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Electromagnetic waves with phase defects in the form of vortex lines combinedwith a constant magnetic field are shown to pin down cyclotron orbits (Landauorbits in the quantum mechanical setting) of charged particles at the locationof the vortex. This effect manifests itself in classical theory as a trappingof trajectories and in quantum theory as a Gaussian shape of the localized wavefunctions. Analytic solutions of the Lorentz equation in the classical case andof the Schr\"odinger or Dirac equations in the quantum case are exhibited thatgive precise criteria for the localization of the orbits. There is a range ofparameters where the localization is destroyed by the parametric resonance.Pinning of orbits allows for their controlled positioning -- they can betransported by the motion of the vortex lines.Comment: This version differs from the printed paper in having the full titles  of all referenced pape

Pinning and transport of cyclotron (Landau) orbits by electromagnetic vortices