| 电子束聚焦系统模型的周期性 |
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| 引用本文： | 陈丽娟,鲁世平.电子束聚焦系统模型的周期性[J].应用数学和力学,2019,40(2):181-188. |
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| 作者姓名： | 陈丽娟 鲁世平 |
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| 作者单位： | 南京信息工程大学 数学与统计学院, 南京 210044 |
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| 基金项目： | 国家自然科学基金(11271197) |
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| 摘 要： | 行波管电子束聚焦理论在物理、生物、电子等科学领域中的应用非常广泛.为了控制电子束的运动轨迹,使其有效地聚焦目标,利用重合度理论中的延拓定理对电子束聚焦系统数学模型的周期解的存在性进行了研究,得到了该模型在一定条件下存在周期正解的结论.同时分析了模型系数取值范围的可行性,对行波管的设计具有一定的指导意义.
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| 关 键 词： | 电子束聚焦系统 奇性 周期正解 重合度理论 |
| 收稿时间： | 2018-03-26 |
Periodicity of the Model for Electron Beam Focusing Systems |
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| CHEN Lijuan,LU Shiping.Periodicity of the Model for Electron Beam Focusing Systems[J].Applied Mathematics and Mechanics,2019,40(2):181-188. |
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| Authors: | CHEN Lijuan LU Shiping |
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| Affiliation: | School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044,P.R.China |
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| Abstract: | The electron beam focusing system theories are widely applied in the fields of physics, biology, electronics and so on. To control the movement track of the electron beam to be focused on the object effectively, the existence of periodic solutions was discussed based on the electron beam focusing system model with Mawhin’s coincidence degree theory. The existence of positive periodic solutions to the model was obtained under specific conditions, and the feasibility of the ranges of the parameters in the model was analyzed. The study provides a theoretical basis for the design of traveling-wave tubes. |
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| Keywords: | electron beam focusing system singularity positive periodic solution coincidence degree theory |
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