本文采用实际的圆柱腔回旋管模型,由电子的相对论运动方程导出描述电子与波非线性相互作用的振动方程和慢变耦合方程组,并在均匀磁场与线性递增磁场两种工作条件下,对电子与波的互作用过程进行了数值模拟。画出了电子相轨迹图和相空间分布,阐明了不同工作磁场下回旋管中电子与波的非线性相互作用过程和电子群聚特点。 In this paper, the actual cylindrical cavity gyroscope model is used to derive the equations of vibration and the slow-coupling equations describing the nonlinear interaction of electrons and waves from the electron’s relativistic equation of motion. Under both the uniform magnetic field and linear increasing magnetic field, The electron-wave interaction is numerically simulated. The trajectories of electrons and the distribution of phase space are drawn, and the nonlinear interaction between electrons and waves and the characteristics of electron clustering in different working magnetic fields are clarified.