相对论返波管注-波作用不稳定区的研究

 以环形电子注驱动的、正弦型周期慢波结构的相对论返波管（RBWO）为模型，理论推导出RBWO慢波结构的色散方程，画出了不包括和包括电子注的色散曲线，然后采用在复平面上绘制等高线图进行逼近的方法对注-波作用不稳定区工作频率的实部和虚部进行了求解，绘出了完整的包括电子注的慢波结构色散关系曲线，并估算了微波的时间增长率和能量转换效率。研究得出：当a（电子注电流参数）较大时，电磁波与慢电荷波的相互作用是不稳定的；而在a较小时，注-波相互作用具有明显的三波作用的特点；微波增长是通过注-波不稳定作用引起的；随着a的增大，微波时间增长率先增大后减小，在a为0.02时有最大值1.37，此时的能量转换效率为19%；增大电子注半径或慢波结构的波纹深度都可以增强注-波不稳定作用。

Study on the region of instable beam-wave interaction in a relativistic backward wave oscillator

A theoretical research was developed for relativistic backward wave oscillators(RBWO) composed of a thin annular electron beam guided by a strong magnetic field through a slow wave structure(SWS) consisting of a cylindrical waveguide with a sinusoidally varying wall radius.Firstly,the analytic expressions of dispersion relations were derived from Swegle's analytic theory of RBWO.Then one code written by Matlab was used to solve the dispersion equations.Through drawing contour lines in the complex plane,the whole dispersion curves of SWS with electron beams were obtained and detailed study on the region of instable beam-wave interaction was carried out.The microwave growth rate and energy efficiency were calculated too.The simulation results illustrate that this interaction,which leads to microwave growth,occurs between the SBSCW and the electromagnetic wave when α(parameter of electron beams) is large,and there is obvious three-wave effect when α is a bit small.The microwave growth rate has the maximal value of 1.37,and the energy efficiency is 19% when α is 0.02.Beam-wave interaction will be inetnsified when the electron current,the beam radius or the depth of rippled wall increase.