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利用傅里叶级数展开,给出了一种求解梯形慢波结构表达式的方法。通过数值模拟,研究了级数展开次数对求解精度的影响。当级数为10阶时,线型拟合而成的结构与原结构吻合较好。利用此表达式数值求解了色散方程,得到两个最低阶模quasi-TEM模和A模。分析了为实现电子束与quasi-TEM模的-1次空间谐波相互作用慢波结构参数所需满足的条件,并指出利用此条件下纵向电场具有表面波的特点可实现横向模式选择。采用S参数理论研究有限长慢波结构的纵向谐振特性,提出在同轴慢波器件中加入同轴引出结构可减少所需慢波结构周期数,这不但使器件结构更为紧凑,还可避免纵模竞争从而提高器件效率、稳定产生微波频率。在此基础上设计了一种L波段同轴相对论返波振荡器,采用KARAT 2.5维全电磁粒子模拟程序研究了器件内束-波作用的物理过程。模拟结果表明,该器件具有径向尺寸小、束-波作用效率高的特点。在电子束能量700keV、电子束流11.5 kA的条件下,器件在频率1.6 GHz处获得较高的微波输出,饱和后微波的平均功率达2.60 GW,平均效率约为32.3%。
Using Fourier series expansion, a method to solve the structure of the trapezoidal slow-wave structure is given. Through numerical simulation, the influence of the number of series expansion on the accuracy of the solution is studied. When the series is 10 order, the linear fitting structure is in good agreement with the original structure. The dispersion equation is solved numerically using this expression, resulting in the two lowest-order modes, quasi-TEM mode and A-mode. The conditions for satisfying the -1-order space harmonic interaction between the electron beam and the quasi-TEM mode are analyzed. It is pointed out that the choice of the transverse mode can be achieved by using the characteristics that the longitudinal electric field has a surface wave under this condition. The S-parameter theory is used to study the longitudinal resonance characteristics of a finite-length slow-wave structure. It is proposed that adding a coaxial lead-out structure to a coaxial slow-wave device can reduce the number of required slow-wave structure periods. This not only makes the device structure more compact but also avoids Longitudinal modes compete to increase device efficiency and generate stable microwave frequencies. Based on this, a L-band coaxial relativistic back-wave oscillator was designed and the physical process of beam-to-wave interaction in the device was studied by using KARAT 2.5-dimensional full electromagnetic particle simulation program. Simulation results show that the device has the characteristics of small radial size and high beam-wave efficiency. At 700 keV electron beam energy and 11.5 kA electron beam current, the microwave device achieves a high microwave output at 1.6 GHz with an average power of 2.60 GW and an average efficiency of about 32.3%.