Based on the self - consistent nonlinear theory of complex cavity gyrotron with gradual transition , a simulation code of self - consistent nonlinear beam - wave interaction has been made , in which the multiple modes interaction with an electron beam and the mode coupling are taken into account . the interaction between the electron beam and hsn - h521 rf field for third - harmonic gyrotron is simulated . the influences of the thickness and the velocity spread and the velocity ratio of the electron beam and the fluctuation of the magnetic field and the technologic errors of complex cavity on the multi - modes interaction with an electron beam are analyzed 二、在渐变复合腔回旋管多模自洽非线性理论的基础上，编制了高次谐波渐变复合腔回旋管多模注?波互作用自洽非线性模拟软件，并对8mm波段三次谐波渐变结构复合腔回旋管的注? ?波互作用进行了大量的自洽非线性数值模拟计算与研究，进而分析了电子注的厚度、速度零散、速度比值、磁场波动、腔体尺寸的加工误差等等多种因素对互作用效率的影响。
The linear theory of the coaxial disk - loaded cylindrical waveguide twt is built and the dispersion equation with an annular electron beam of this twt is obtained according to self - consistent field theory and the field matching method . the computation results of the hot dispersion equation indicate the relations between the electron beam parameters and the small signal gain 利用自洽场理论以及场的匹配方法，推导出此结构在小信号条件下的热色散方程，讨论了电子注参量和慢波系统几何参量与小信号增益和色散的关系。
The conventional linear theories describe the linear part of the interaction between beam and wave very well . however , when the interaction efficiency increases in a large scale , we should consider the nonlinear effects . in this case , we must take account for the modulation of the plasma density 我们认为大部分线性理论只是对场和电子注的线性部分进行了解释，尤其在效率增长幅度非常显著时，必须考虑非线性效应的影响，也就是说，必须考虑等离子体密度受到大功率微波调制形成等离子体密度栅的影响。
The mode competition is much improved . it may operated with a large electron beam radius , that means decreasing the space charge effects compared with a smaller radius beam with the same current , hence the rbwo may operated with a low axial guide magnetic field . besides , the rbwo with a sinusoidal corrugated coaxial structure is very easy to manufacture 波纹内导体rbwo具有一些突出优点:同轴结构中内导体的存在使系统的截止频率显著升高,使得系统尺寸可比普通波纹波导慢波系统大;具有很大的抑制模式竞争的能力和很高的功率容量;可以采用大半径电子注,在工作电流不变的情况下空间电荷效应大幅度降低,因而可以工作在低磁场状态;此种慢波结构内导体上的波纹易于加工。
