Spectral Dynamics of a Free-Electron Maser with a Step-Tapered Undulator

The spectral behavior of a high-power, high-gain free-electron maser (FEM) is investigated. The maser has a step-tapered undulator consisting of two sections with different strengths and lengths and equal periodicities. The sections are separated by a field-free gap. The configuration is enclosed within a low quality cavity. The millimeter wave beam is guided within a rectangular corrugated waveguide. The purpose of this undulator setup is to enhance the efficiency at high output power. The associated high gain in the Linear as well as in the nonlinear regime provides a unique oscillator. The spectral dynamics of this device is analyzed with a multipass, multifrequency code. The radiation field of the code is described as a sum over discrete frequency components. The linear gain curve of the step-tapered undulator is not the sum of the curves of two single undulators and has a completely different spectrum. The gain of the FEM is so high that nonlinear interaction occurs within a few passes. In the fully nonlinear regime the gain is still relatively high. The power spectrum evolves towards a state in which the power at the resonance of the second undulator section is suppressed. In the final state, where the frequency spectrum hardly changes from pass to pass, the power spectrum exhibits two peaks at frequencies that are determined by the first section of the undulator. The main peak is related to its resonance frequency, while the second peak is a lower sideband. The dependence of the sideband on the gap length, the relative polarization of both sections, and the reflection coefficient is investigated.