Twist periodic solutions of the electron beam focusing system with unshielded cathode

被引：0

作者：

Liang, Zaitao ^{[1
]}

Zhou, Ziqing ^{[1
]}

Li, Shengjun ^{[2
,3
]}

机构：

[1] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China

[2] Hainan Univ, Sch Math & Stat, Haikou, Peoples R China

[3] Hainan Univ, Sch Sci, Haikou 570228, Hainan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 12期

关键词：

electron beam focusing system; Lyapunov stability; third-order approximation method; twist periodic solutions; STABILITY; EQUATION;

D O I：

10.1002/mma.10136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the electron beam focusing system guided by an axially symmetric periodic magnetic field with unshielded cathode. Based on the third-order approximation method and some quantitative methods, we establish two different sufficient conditions for the existence of twist periodic solutions of the system. Such twist periodic solutions are stable in the sense of Lyapunov. Some results in the literature are generalized and improved.

引用

页码：10507 / 10519

页数：13

共 22 条

[1]

[Anonymous], 1971, Asymptotic behavior and stability problems in ordinary differential equations

[2]

[Anonymous], 2008, Theory and Design of Charged Particle Beams

[3]

Bevc V., 1958, J BRIT I RADIO ENG, V18, P696

[4]

Chu JF, 2008, DISCRETE CONT DYN-A, V21, P1071

[5] Twist periodic solutions for differential equations with a combined attractive repulsive singularity [J].

Chu, Jifeng ;

Torres, Pedro J. ;

Wang, Feng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 437 (02) :1070-1083

[6] Twist periodic solutions of second order singular differential equations [J].

Chu, Jifeng ;

Li, Ming .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) :830-838

[7]

De Coster C., 2006, Two-Point Boundary Value Problems: Lower and Upper Solutions, V205

[8]

Harker K. J., 1955, IRE T ELECTRON DEV, V2, P13, DOI DOI 10.1109/T-ED.1955.14085

[9] Twist character of the least amplitude periodic solution of the forced pendulum [J].

Lei, JZ ;

Li, X ;

Yan, P ;

Zhang, MR .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (04) :844-867

[10]

Magnus W., 1966, HILLS EQUATIONS

← 1 2 3 →