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## Study of three-dimensional nonlinear backward-wave interaction model and numerical simulation for helical traveling wave tube

Hu Yu-Lu, Hu Quan, Zhu Xiao-Fang, Li Bin, Qiu Hai-Jian, Gao Luan-Feng
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• #### 摘要

建立了三维非线性返波互作用模型，用于精确分析大功率螺旋线行波管中返波振荡非线性过程问题，并提出了计算返波振荡功率的方法及磁场抑制手段.该理论模型包括三维线路场方程、三维运动方程以及三维空间电荷场.首先比较三维模型与原有一维模型之间的差异，发现一维空间电荷场的径向交流电流分布模型与三维模型的差异是导致振荡频率偏大及起振长度缩短的主要原因.然后计算返波饱和输出功率大小并揭示返波饱和功率和振荡频率与互作用长度的关系，并探讨了磁场对返波振荡的抑制影响.最后以某一毫米波行波管为例，实验对比了一维与三维模型计算的振荡频率与热测的差异，其中三维模型的相对误差小于4.8%.

#### Abstract

The wide band high power traveling wave tubes (TWTs) employed in radar, communication systems, etc. are always facing the backward wave oscillation (BWO) problem. However, it takes much time and computer resource to simulate BWO by the large electromagnetic software. Thus, several parametric models are developed to solve the problem faster. Most of those models do not discuss the saturated oscillation power. In this paper, a three-dimensional (3D) nonlinear backward-wave interaction model is presented, by which the BWO phenomenon can be accurately studied in TWTs and the oscillation power is also analyzed. This model is established with the equation of 3D excitation fields combined with 3D motion equations and 3D space charge force. The oscillation frequencies and the start-oscillation lengths are calculated by one-dimensional (1D) and 3D models, respectively, and they are carefully compared in the cases of with and without the space charge force, indicating that the space charge force in 1D model is much weaker than in 3D model. The reason for that is the model of current density for space charge model in 1D model is supposed to be proportional to particle radius, but the one in 3D model is almost uniform, which is indicated by 3D beam trace distribution analysis. The BWO saturated powers and the oscillation frequencies are studied by this nonlinear 3D backward-wave interaction model. The simulation results show that the BWO saturated power increases as the beam-wave interaction length extends before many trajectories intercept the helix. While the oscillation frequencies decrease, the large saturated power supplies more energy to the beam at the very beginning in beam-wave interaction starting region. Then the BWO suppression induced by the magnetic field effect of the beam ripple is also under consideration. As the magnetic force increases, not only some cross area of interaction beam is suppressed, but also the interaction impedance of -1 space harmonic decreases. So increasing magnetic field strength can obviously reduce BWO, while the effect on forward wave interaction should be balanced. Finally, a Ka-band tube is used to validate the 1D and 3D nonlinear backward-wave interaction models. The BWO frequencies at different voltages are compared among the experimental results and the calculations by 1D and 3D models. The results from the 3D model in the test voltage range are 4.8% lower than the experimental data, while the difference from the results of the 1D model is 6.7%. The 3D model seems to be more accurate than the 1D model.

#### 作者及机构信息

###### 通信作者: 胡玉禄, yuluhu@uestc.edu.cn ; 胡玉禄, yuluhu@uestc.edu.cn ;
• 基金项目: 国家自然科学基金（批准号：61201003，61301054）资助的课题.

#### Authors and contacts

###### Corresponding author: Hu Yu-Lu, yuluhu@uestc.edu.cn ; , yuluhu@uestc.edu.cn ;
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61201003, 61301054).

#### 参考文献

 [1] Pierce J R 1950 Traveling-Wave Tubes (New York:Van Nostrand) pp1-248 [2] Gilmour A S J 1994 Principles of Traveling Wave Tubes (Norwood:Artechhouse) pp94-132 [3] Chernin D P, Antonsen T M J, Levush B, Whaley D R 2001 IEEE trans. Electron Devices 48 3 [4] Hao B L, Xiao L, Liu P K, Li G C, Jiang Y, Yi H X, Zhou W 2009 Acta Phys. Sin. 58 3118 (in Chinese)[郝保良, 肖刘, 刘濮鲲, 李国超, 姜勇, 易红霞, 周伟2009物理学报58 3118] [5] Hu Y L, Yang Z H, Li J Q, Li B, Gao P, Jin X L 2009 Acta Phys. Sin. 58 6665 (in Chinese)[胡玉禄, 杨中海, 李建清, 李斌, 高鹏, 金晓林2009物理学报58 6665] [6] Heffner H 1954 Proc. IRE 42 930 [7] Johnson H R 1955 Proc. IRE 43 684 [8] Belyavskiy E D, Goncharov I A, Martynyuk A E, Svirid V A, Khotiaintsev S N 2001 IEEE trans. Electron Devices 48 1727 [9] Belyavskiy E D, Chasnyk V I, Khotiaintsev S N 2006 IEEE trans. Electron Devices 53 2830 [10] Antonsen T M J, Safier P, Chernin D P, Levush B 2002 IEEE trans. Plasma Sci. 30 1089 [11] Chernin D P, Antonsen T M J, Levush B 2003 IEEE trans. Electron Devices 50 2540 [12] Gong Y B, Duan Z Y, Wang Y M, Wei Y Y, Wang W X 2011 IEEE trans. Electron Devices 58 1556 [13] Hu Y L, Yang Z H, Li B, Li J Q, Huang T, Jin X L 2010 Acta Phys. Sin. 59 5439 (in Chinese)[胡玉禄, 杨中海, 李斌, 李建清, 黄桃, 金晓林2010物理学报59 5439] [14] Hu Y L, Yang Z H, Li J Q, Li B 2011 IEEE trans. Electron Devices 58 1562

#### 施引文献

•  [1] Pierce J R 1950 Traveling-Wave Tubes (New York:Van Nostrand) pp1-248 [2] Gilmour A S J 1994 Principles of Traveling Wave Tubes (Norwood:Artechhouse) pp94-132 [3] Chernin D P, Antonsen T M J, Levush B, Whaley D R 2001 IEEE trans. Electron Devices 48 3 [4] Hao B L, Xiao L, Liu P K, Li G C, Jiang Y, Yi H X, Zhou W 2009 Acta Phys. Sin. 58 3118 (in Chinese)[郝保良, 肖刘, 刘濮鲲, 李国超, 姜勇, 易红霞, 周伟2009物理学报58 3118] [5] Hu Y L, Yang Z H, Li J Q, Li B, Gao P, Jin X L 2009 Acta Phys. Sin. 58 6665 (in Chinese)[胡玉禄, 杨中海, 李建清, 李斌, 高鹏, 金晓林2009物理学报58 6665] [6] Heffner H 1954 Proc. IRE 42 930 [7] Johnson H R 1955 Proc. IRE 43 684 [8] Belyavskiy E D, Goncharov I A, Martynyuk A E, Svirid V A, Khotiaintsev S N 2001 IEEE trans. Electron Devices 48 1727 [9] Belyavskiy E D, Chasnyk V I, Khotiaintsev S N 2006 IEEE trans. Electron Devices 53 2830 [10] Antonsen T M J, Safier P, Chernin D P, Levush B 2002 IEEE trans. Plasma Sci. 30 1089 [11] Chernin D P, Antonsen T M J, Levush B 2003 IEEE trans. Electron Devices 50 2540 [12] Gong Y B, Duan Z Y, Wang Y M, Wei Y Y, Wang W X 2011 IEEE trans. Electron Devices 58 1556 [13] Hu Y L, Yang Z H, Li B, Li J Q, Huang T, Jin X L 2010 Acta Phys. Sin. 59 5439 (in Chinese)[胡玉禄, 杨中海, 李斌, 李建清, 黄桃, 金晓林2010物理学报59 5439] [14] Hu Y L, Yang Z H, Li J Q, Li B 2011 IEEE trans. Electron Devices 58 1562
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##### 出版历程
• 收稿日期:  2016-05-31
• 修回日期:  2016-09-12
• 刊出日期:  2017-01-20

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