Nonlinear analysis of the Cerenkov maser

Abstract

The nonlinear evolution of the Cerenkov maser amplifier is investigated numerically for a configuration that consists of an energetic electron beam propagating through a dielectric-lined cylindrical waveguide. An axial guide magnetic field is included in the formulation in order to improve beam confinement. A set of coupled nonlinear differential equations is derived in three dimensions that governs the evolution of both the electromagnetic field and the trajectories of an ensemble of electrons. The system is assumed to be azimuthally symmetric, and the electromagnetic field is represented as a superposition of the TM0n modes of the vacuum waveguide. The initial conditions are chosen to model the simultaneous injection of either a solid or annular electron beam, and an electromagnetic wave of arbitrary input power. Thermal effects are treated under the assumption that the beam is initially monoenergetic but exhibits a pitch angle spread; however, the subsequent evolution of the beam is treated in a self-consistent manner. This class of distribution is appropriate to the treatment of diode-produced beams and describes a beam with an initial axial energy spread. This is the crucial determinant in the efficiency, since saturation occurs by means of an axial bunching mechanism that results in the phase trapping of the beam. The specific parameters used in the numerical analysis correspond to experiments conducted at Dartmouth College [J. Appl. Phys. 58, 627 (1985)], and good agreement is found between theory and experiment.

Linear permittivity tapering in a Cerenkov microwave source with a pre-bunched beam

“…Following the procedure previously shown, 6,7 it is possible to write the following equations describing the evolution of the amplitude and phase of the electromagnetic wave in terms of the beam current:…”

“…The system will therefore amplify microwave signals at that frequency which are present as noise or are deliberately introduced into the structure. [4][5][6] The picture is more complicated when the beam initially contains density perturbations such as the steep rise in current at the head of a pulsed beam. 7 These perturbations excite the structure's TM modes over a range of frequencies, not just the design operating frequency.…”

A Cherenkov free electron laser with high peak power

“…To estimate the performance of the Cherenkov FEL in the far infrared and millimeter wavelength region, nonlinear calculations were performed using a three dimensional model [5]. The parameters used in the calculations reflect the design parameters for the Cherenkov FEL under construction.…”

Simulation analysis of rectangular dielectric-loaded traveling wave amplifiers for THz sources

“…A lot of attention has been paid to investigation on dielectric-loaded traveling-wave tubes (TWT), mostly with a cylindrical configuration [13][14][15][16], while the rectangular configuration is catching less interest. A rectangular structure may have some potential advantages; for example, rf input/output couplers may have a larger bandwidth because a symmetric excitation can be made to match the rf fields of operating mode, and dielectric slabs are easier to fabricate, especially for short wavelength applications.…”