The excitation of a relativistic electron beam, by means of a fast waveguide structure, is examined. Here the beam is injected into a modified waveguide, and interacts with the modes of the guide in such a way as to transform some of its energy into microwave radiation. This microwave generation device, called the Ubitron, is based upon a fast-wave excitation of a magnetically modulated relativistic electron beam. The beam is modulated by injecting it into a small spatially periodic magnetic field region within the guide. Analysis of this interaction shows that the slow space charge beam mode couples actively to the fast transverse electric guide mode. The result is parametric instability of the coupled modes. Synchronism between the doppler-shifted transverse travelling wave and the undulating electron beam results in a transfer of energy from the beam to the transverse field. The parametrically growing field can be a source of microwave radiation. The period magnetic field, together with the beam density, provide the coupling media between the unstable waves. The growth rate of the instability is shown to depend, in a nonlinear manner, on the product of the beam plasma frequency and the strength of the applied rippled magnetic field. The growth rate is obtained as a function of the system parameters.
