Periodic permanent magnet focusing of an annular electron beam and its application to a 250 MW ubitron free-electron maser

Abstract

Stable electron beam flow is shown to exist for an annular electron beam within a coaxial periodic permanent magnet wiggler and transmission line with zero guide field. When the beam is properly centered near the magnetic minimum of the wiggler, a condition exists where the magnetic radial force balances the space-charge repulsion of the beam. The stability condition relating the electron beam current to the magnetic field strength in terms of the plasma frequency, wiggler cyclotron frequency and relativistic Lorentz factor is ω2p=(γ/2)Ω2w, which is the same stability condition found for Brillouin flow in a uniform magnetic field and for focused beam flow along periodic dipole magnetic fields. The radial scallop of an annular electron beam satisfying this condition can be extremely low. Although this propagation technique can be utilized for any high power coaxial linear-beam device, it is most appropriate for free electron masers. Using parameters satisfying the stability condition, a 500 kV, 1 kA, TE01 ubitron free-electron maser design is presented that is predicted to generate 250 MW at 11.4 GHz.