螺旋线行波管欧拉非线性注波互作用理论

An Analytic Model for Eulerian Large-Signal Beam-Wave Interaction Theory of Helix Traveling Wave Tubes

如何获得螺旋线行波管的欧拉非线性解析解是研究其非线性特性产生物理机制的关键。本文采用逐次逼近法,详细推导了螺旋线行波管的欧拉非线性注波互作用解析解,获得了电场与电子相位的解析关系,并将逐次逼近解析解与拉格朗日理论以及传统的欧拉理论进行对比。仿真中采用了一支C波段和一支Ku波段的螺旋线行波管(均匀螺距分布),仿真结果表明:在非线性区,四阶逐次逼近解析解与拉格朗日理论具有很好的一致性,并且精度高于一阶、二阶以及三阶的逐次逼近解析解。同时,还发现四阶逐次逼近解析解能够呈现出由电子超越引起的饱和现象,而传统的欧拉理论是无法对此饱和现象进行描述的。此外,四阶逐次逼近解析解比现有的方法更加简捷,因此可以进行解析研究处理,以便研究行波管非线性互作用物理机制。研究表明四阶逐次逼近解析解优于现有的研究。

Determining how to achieve an analytic solution of Eulerian large-signal beam-wave interaction model of a traveling wave tube is a key point to study nonlinear effects.In this paper,we detailed derived the analytic solutions of an Eulerian large-signal beam-wave interaction theory of a helix traveling wave tube by the method of successive approximation.The analytic relationship between electric field and electron phase is also found.Then,the successive analytic solutions are compared to Lagrangian theory and traditional Eulerian models.C-and Ku-bands helix traveling wave tubes based on a single pitch section are included in the simulation.It is found that the fourth order analytic solution agrees well with Lagrangian theory and gains more accuracy than the first,second or third order analytic solution in nonlinear region.The saturation effects caused by electron overtaking cannot be found by traditional Eulerian analysis,but can be described by the fourth order analytic solution.Moreover,the fourth order analytic solution is simpler than existing approaches,and thus allow analytical progress.The study confirms that the fourth order analytic solution can outperform previous proposals.