Abstract
An analytic and numerical examination of the slow wave Cerenkov free electron maser is presented. We consider the steady state amplifier configuration as well as operation in the selfamplified spontaneous emission (SASE) regime. The linear theory is extended to include electron beams that have a parabolic radial density inhomogeneity. Closed form solutions for the dispersion relation and modal structure of the electromagnetic field are determined in this inhomogeneous case. To determine the steady state response, a macro-particle approach is used to develop a set of coupled nonlinear ordinary differential equations for the amplitude and phase of the electromagnetic wave, which are solved in conjunction with the particle dynamical equations to determine the response when the system is driven as an amplifier with a time harmonic source. We then consider the case in which a fast rise time electron beam is injected into a dielectric loaded waveguide. In this case, radiation is generated by SASE, with the instability seeded by the leading edge of the electron beam. A pulse of radiation is produced, slipping behind the leading edge of the beam due to the disparity between the group velocity of the radiation and the beam velocity. Short pulses of microwave radiationmore » are generated in the SASE regime and are investigated using particle-in-cell (PIC) simulations. The nonlinear dynamics are significantly more complicated in the transient SASE regime when compared with the steady state amplifier model due to the slippage of the radiation with respect to the beam. As strong self-bunching of the electron beam develops due to SASE, short pulses of superradiant emission develop with peak powers significantly larger than the predicted saturated power based on the steady state amplifier model. As these superradiant pulses grow, their pulse length decreases and forms a series of soliton-like pulses. Comparisons between the linear theory, macro-particle model, and PIC simulations are made in the appropriate regimes.« less
Highlights
It is well known that the passage of an electron beam through a slow wave structure can be used either to amplify or generate electromagnetic radiation
We have presented a comprehensive examination of the Cerenkov maser using three models of increasing complexity
The dispersion relation for this system was calculated as well as the modal structure of the electromagnetic field, with the solutions approaching the results of the limiting case of a uniform electron beam
Summary
It is well known that the passage of an electron beam through a slow wave structure can be used either to amplify or generate electromagnetic radiation. Joe et al [13] consider a dispersion analysis for finite width sheet beams propagating over a grating in a rectangular waveguide Their analysis includes hybrid modes and they examine convective instabilities of the forward waves and absolute instabilities. Lemons and Thode [15] consider both the linear and nonlinear regime of operation of the Cerenkov maser; their nonlinear analysis only provides an estimate of the saturation amplitude based on phase trapping of beam electrons. Freund [16] and Freund and Ganguly [17] develop a three-dimensional macroparticle model of the Cerenkov amplifier for weak beams based on models similar to those used for the analysis of gyrotrons and free electron lasers It has the advantage of reduced computational requirements due to the extraction of the fast behavior of the wave-particle dynamics. From the PIC simulations, the evolution of the SASE generated superradiant pulses are examined
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