Transient self-amplified Cerenkov radiation with a short pulse electron beam

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 self-amplified 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 macroparticle 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 radiation 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 solitonlike pulses. Comparisons between the linear theory, macroparticle model, and PIC simulations are made in the appropriate regimes.

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:…”

“…[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. This drives the formation of a short-pulse wave packet.…”