电子束聚焦系统模型的周期性
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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.
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.
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.
引文
[1]MENDEL J T,OUATE C F,YOCOM W H.Electron beam focusing with periodic permanent magnet fields[J].Proceedings of the IRE,1954,42(5):800-810.
[2]CLOGSTON A M,HEFFNER H.Focusing of an electron beam by periodic fields[J].Journal of Applied Physics,1954,25(4):436-447.
[3]MENDEL J T.Magnetic focusing of electron beams[J].Proceedings of the IRE,1955,43(3):327-331.
[4]CHANG K K N.Beam focusing by periodic and complementary fields[J].Proceedings of the IRE,1955,43(1):62-71.
[5]HARKER K J.The periodic electron beam focusing with partially shielded cathode[J].Trans IRE,1955,4:29-35.
[6]RICHARD T.Emittance and the design of beam formation,transport,and collection systems in periodically focussed T W T's[J].IEEE Transactions on Electron Devices,1987,34(2):473-485.
[7]LU S P,KONG F C.Periodic solutions for a kind of prescribed mean curvature Lienard equation with a singularity and a deviating argument[J].A dvances in Difference Equations,2015,2015:151.DO I:10.1186/s13662-015-0474-y.
[8]HAKL R,TORRES P J,ZAMORA M.Periodic solutions of singular second order differential equations:the repulsive case[J].Topol Methods N onlinear A nal,2012,39(1):199-220.
[9]REN J L,CHENGZ B,STEFAN S.Positive periodic solution for Brillouin electron beam focusing system[J].Discrete and C ontinuous Dynamical Systems,2011,16:385-392.
[10]TORRES P J.Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system[J].Mathematical Methods in the A pplied Sciences,2000,23(13):1139-1143.
[11]KORY C L.Three-dimensional simulations of PPM focused helical traveling-wave tubes[D].PhDT hesis.C leveland,O H:C leveland State U niversity,2000.
[12]章美月,刘文斌,张建军.电子束聚焦系统模型正椭圆周期解的存在性[J].中国矿业大学学报,2007,36(6):864-868.(Z HAN G M eiyue,LIU W enbin,Z HAN G Jianjun.Existence of positive elliptic periodic solutions for the electron beam focusing system model[J].Journal of C hina University of Mining&T echnology,2007,36(6):864-868.(in C hinese))
[13]陈丽娟,鲁世平.地球磁层电磁场中粒子引导中心漂移运动模型的周期轨[J].物理学报,2014,63(19):190202.(CHEN Lijuan,LU Shiping.The periodic problem of drift motion of the guidance center in the earth's magnetosphere electromagnetic field[J].A cta Physica Sinica,2014,63(19):190202.(in Chinese))
[14]陈丽娟,鲁世平,徐晶.海-气耦合气候系统非线性扰动模式的周期正解[J].应用数学和力学,2017,38(4):469-476.(C HEN Lijuan,LU Shiping,XU Jing.Positive periodic solutions to the nonlinear disturbed model for sea-air coupling climate systems[J].A pplied Mathematics and Mechanics,2017,38(4):469-476.(in C hinese))
[15]GAINES R E,MAWHIN J L.Coincidence Degree,and Nonlinear Differential Equations[M].Berlin:Springer,1977.
[16]何国柱.永久磁铁周期性聚焦电子束[J].物理学报,1959,15(10):535-549.(HE Guozhu.Electron beam focusing w ith periodic magnet structures[J].A cta Physica Sinica,1959,15(10):535-549.(in Chinese))
[2]CLOGSTON A M,HEFFNER H.Focusing of an electron beam by periodic fields[J].Journal of Applied Physics,1954,25(4):436-447.
[3]MENDEL J T.Magnetic focusing of electron beams[J].Proceedings of the IRE,1955,43(3):327-331.
[4]CHANG K K N.Beam focusing by periodic and complementary fields[J].Proceedings of the IRE,1955,43(1):62-71.
[5]HARKER K J.The periodic electron beam focusing with partially shielded cathode[J].Trans IRE,1955,4:29-35.
[6]RICHARD T.Emittance and the design of beam formation,transport,and collection systems in periodically focussed T W T's[J].IEEE Transactions on Electron Devices,1987,34(2):473-485.
[7]LU S P,KONG F C.Periodic solutions for a kind of prescribed mean curvature Lienard equation with a singularity and a deviating argument[J].A dvances in Difference Equations,2015,2015:151.DO I:10.1186/s13662-015-0474-y.
[8]HAKL R,TORRES P J,ZAMORA M.Periodic solutions of singular second order differential equations:the repulsive case[J].Topol Methods N onlinear A nal,2012,39(1):199-220.
[9]REN J L,CHENGZ B,STEFAN S.Positive periodic solution for Brillouin electron beam focusing system[J].Discrete and C ontinuous Dynamical Systems,2011,16:385-392.
[10]TORRES P J.Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system[J].Mathematical Methods in the A pplied Sciences,2000,23(13):1139-1143.
[11]KORY C L.Three-dimensional simulations of PPM focused helical traveling-wave tubes[D].PhDT hesis.C leveland,O H:C leveland State U niversity,2000.
[12]章美月,刘文斌,张建军.电子束聚焦系统模型正椭圆周期解的存在性[J].中国矿业大学学报,2007,36(6):864-868.(Z HAN G M eiyue,LIU W enbin,Z HAN G Jianjun.Existence of positive elliptic periodic solutions for the electron beam focusing system model[J].Journal of C hina University of Mining&T echnology,2007,36(6):864-868.(in C hinese))
[13]陈丽娟,鲁世平.地球磁层电磁场中粒子引导中心漂移运动模型的周期轨[J].物理学报,2014,63(19):190202.(CHEN Lijuan,LU Shiping.The periodic problem of drift motion of the guidance center in the earth's magnetosphere electromagnetic field[J].A cta Physica Sinica,2014,63(19):190202.(in Chinese))
[14]陈丽娟,鲁世平,徐晶.海-气耦合气候系统非线性扰动模式的周期正解[J].应用数学和力学,2017,38(4):469-476.(C HEN Lijuan,LU Shiping,XU Jing.Positive periodic solutions to the nonlinear disturbed model for sea-air coupling climate systems[J].A pplied Mathematics and Mechanics,2017,38(4):469-476.(in C hinese))
[15]GAINES R E,MAWHIN J L.Coincidence Degree,and Nonlinear Differential Equations[M].Berlin:Springer,1977.
[16]何国柱.永久磁铁周期性聚焦电子束[J].物理学报,1959,15(10):535-549.(HE Guozhu.Electron beam focusing w ith periodic magnet structures[J].A cta Physica Sinica,1959,15(10):535-549.(in Chinese))