Development of Numerical Simulation Codes and Application to Klystron Efficiency Enhancement(数値解析コードの開発及びその適用によるクライストロン高効率化の研究)
Development of Numerical Simulation Codes and Application to Klystron Efficiency Enhancement(数値解析コードの開発及びその適用によるクライストロン高効率化の研究)
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数值模拟代码的开发及其在速调管效率提升中的应用
DOI：
10.11501/3135469
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发表时间：
1998
影响因子：
3.4
通讯作者：
Kai Masuda
中科院分区：
文献类型：
--
作者：
Kai Masuda
本文讨论了凹陷集热器的性能特点，以及旨在显著提高速调管效率的空心束。本文还介绍了一组二维数值代码的发展，以研究这两种方法。结果总结如下：(1)本研究开发了一种新的有限元特征模态求解器（KUEMS），旨在提高圆柱对称模态的计算精度。本文采用H r θ来代替现有规范中常用的θ H或θ rH来表示电磁场。本有限元公式的精度明显高于其他公式，特别是在基模态的本征频率上。它还可以使解相对于网格点的数量收敛得更平滑，提供了良好的外推性。（ii）还开发了用于计算速调管外部聚焦场的螺线管场求解器（KUSOS）。将有限元法和矩量法相结合，提出了一种新的混合方法，可以处理包括非线性介质在内的无界问题。数值计算结果与解析解吻合较好，不同画框的数值解无差异，计算得到的画框磁场具有较好的连续性。（三）通过修改现有的模拟代码，编制了两个单元内粒子模拟代码。一个是用于模拟静态场中的电子轨迹（KUAD2）。通过枪的性能与实验的比较证实了这一点，在- 2.3% ~ + 2.4%的相对误差内显示出良好的一致性。另一个是电子束与速调管腔（KUBLAI）相互作用的模拟。提出了一种改进的Newmark方法，以稳定同时计算电子运动和束致场时的数值不稳定性。本文还提出了一种计算腔电压的改进方法，该方法最终收敛于稳态解的速度比基本方法快。KUBLAI模拟与实验结果也进行了比较，结果表明，对于速调管的饱和输出功率，在- 4.9% ~ + 6.9%的相对误差范围内，结果非常吻合。（iv）利用本研究开发的验证码，对上述两种方法进行了速调管效率提高的研究。对消沉式集热器能量回收的理论极限进行了评价。研究发现，理论上，5级集热器可以将效率从60.5%的基本效率提高到80.3%，而增加一级和优化电位都不能进一步提高效率。然后，通过KUAD2模拟设计了一个5级压抑收集器，与没有压抑收集器的60.5%的效率相比，效率提高了71.3%，这是非常令人鼓舞的。空心梁也被发现比目前使用的实心梁效率更高。结果表明，在空心半径优化的情况下，在不抑制集热器的情况下，效率可提高67.0%。还发现，较大的空心比最佳往往导致相当低的效率。综上所述，本研究中新开发的模拟代码在大功率速调管设计中是有效的，并且，通过使用这些数值代码，无论是凹陷集电极还是空心梁，都可以在数值上显著提高效率。
This thesis discusses performance characteristics of depressed collectors, and hollow beams aiming at appreciable enhancements of klystron efficiencies. Also presented are developments of a set of 2-dimensional numerical codes to investigate these two approaches. The results are summarized as follows.(i) A new Finite Element eigenmode solver (KUEMS) has been developed in this study, aiming at improved accuracy in calculating cylindrically symmetric modes. Instead of θ H, or θ rH preferentially used so far in the existing codes, the quantity H r θ is newly used in this study to represent the electromagnetic fields. This present Finite Element formulation is found to result in remarkably higher accuracy than the other formulations, particularly, in the eigenfrequency of the fundamental mode. It is also found to result in smoother convergence of the solutions with respect to number of the mesh points, to provide good extrapolation property.(ii) Also developed was a solenoidal field solver (KUSOS) for calculating external focusing fields in klystrons. A new hybrid method is proposed, 112 which can deal with unbounded problems including nonlinear media by combining the Finite Element method and the Moment method. The numerical results show good agreements with the analytical solutions, no difference in the numerical solutions for different choices of the picture frames, and excellent continuity of the calculated magnetic fields on the picture frames.(iii) Two particle-in-cell simulation codes have been developed by modifying the existing codes. One is for simulations of electron trajectories in static fields (KUAD2). It was verified through comparisons of gun perveances with experiments, showing excellent agreements within–2.3%∼+ 2.4% relative errors. The other is for simulations of interactions between electron beams and klystron cavities (KUBLAI). A modified Newmark method is proposed to stabilize the numerical instability in calculating simultaneously both electron motions, and beam-induced fields. Also proposed is a modified method for calculating cavity voltages, which eventually shows faster convergence to the steady-state solutions than the basic method. Comparisons were also made between the KUBLAI simulations and experiments, showing excellent agreements within–4.9%∼+ 6.9% relative errors with respect to the saturated output powers of klystrons.(iv) By use of the verified codes developed in this study, the aforementioned two approaches were investigated for the klystron efficiency enhancements. Theoretical limit of the energy recovery with depressed collectors was evaluated. It is found that a 5-stage collector could, theoretically, enhance the efficiency up to 80.3% from the basic efficiency of 60.5%, and neither additional stages nor optimized potentials would enhance the 113 efficiency appreciably further. A 5-stage depressed collector was, then, designed through the KUAD2 simulations, leading to an enhanced efficiency of 71.3%, which is very encouraging compared with the 60.5% efficiency without depressed collectors. Hollow beams are found also to result in higher efficiencies than the currently used solid beam. It is found that, with an optimized hollow radius, an enhanced efficiency of 67.0% could be achieved without depressed collectors. It is also found that larger hollows than the optimum tend to result in rather lower efficiencies. In summary, the simulation codes newly developed in this study are found to be efficient in high-power klystron designing, and, also, by use of these numerical codes, either the depressed collectors, or the hollow beams are found, numerically, to result in appreciable efficiency enhancements of …