Van der Pol model of a Cherenkov maser

M. Kleckner*, A. Ron, M. Botton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A non-linear analysis of a Cherenkov maser is presented. The system consists 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 in part of the ring, confined by a strong axial magnetic field. Using the single-particle description for the beam and the wave equation for the field, we obtain a set of two coupled non-linear differential equations describing the slowly varying amplitude and phase of the electromagnetic mode. The gain per path is assumed to be small and the spatial growth of the field is neglected. The resulting time dependent amplitude includes the exponential gain of the linear stage and the saturation to its maximum value. The time dependent frequency is also calculated. The two equations are combined to a single Van der Pol equation with a non-linear restoring force. This description demonstrates the similarities and differences between the Cherenkov maser and other lasing systems.

Original languageAmerican English
Pages (from-to)ABS27-ABS29
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number1-3
StatePublished - 11 Jun 1996
Externally publishedYes


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