VAN DER POL MODEL OF A CHERENKOV MASER

A non-linear analysis of a Cherenkov maser is presented. The system co nsists of a ring configuration of a cylindrical waveguide filled with a dielectric material. A single transverse-magnetic mode is assumed to propagate in the system. A low-density pencil electron beam travels i n part of the ring, confined by a strong axial magnetic field. Using t he single-particle description for the beam and the wave equation for the held, we obtain a set of two coupled non-linear differential equat ions describing the slowly varying amplitude and phase of the electrom agnetic mode. The gain per path is assumed to be small and the spatial growth of the field is neglected. The resulting time dependent amplit ude includes the exponential gain of the linear stage and the saturati on to its maximum value. The time dependent frequency is also calculat ed. The two equations are combined to a single Van der Pol equation wi th a non-linear restoring force. This description demonstrates the sim ilarities and differences between the Cherenkov maser and other lasing systems.