Electron nonlinear dynamics in a compact accelerator based on the circular rotating TM110 mode

Abstract

The present study investigates the electron autoresonant acceleration using the rotating transverse magnetic mode TM110 microwave field within an inhomogeneous magnetostatic field. Differential equations governing the evolution of the phase shift between the electron’s angular position and the angle at which transferred power is maximized, the total electron energy, and the longitudinal electron velocity are derived. Magnetic field profiles required to sustain electron acceleration are determined. The results demonstrate that an electron injected along the cavity axis with an energy of 30keV can be accelerated up to approximately 200keV, using an electric field amplitude of 20kV/cm, a frequency of 8GHz, and a linear magnetic field profile. Additionally, we consider the case of electron acceleration under exact resonance conditions, and the corresponding magnetic field profile predicted by the model is obtained.The findings presented in this paper are valuable for the design of RF accelerators utilizing the circular rotating TM110 mode, particularly in applications such as x-ray sources for medical purposes, airport security, and various other fields.