Geodesic
Modification of Hill's equation for the storage rings simplified models
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2012), pp. 60-65
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An approach suggested allows to describe charged particle dynamics for linear machines in a usual 3-dimensional space. In addition, a new type of differential equations with periodic coefficients and a large parameter is derived.
Keywords: magnetic system, lattice, differential equation, asymptotics. 
@article{VSPUI_2012_2_a6,
     author = {O. E. Shishanin},
     title = {Modification of {Hill's} equation for the storage rings simplified models},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {60--65},
     year = {2012},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_2_a6/}
}
TY  - JOUR
AU  - O. E. Shishanin
TI  - Modification of Hill's equation for the storage rings simplified models
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2012
SP  - 60
EP  - 65
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2012_2_a6/
LA  - ru
ID  - VSPUI_2012_2_a6
ER  - 
%0 Journal Article
%A O. E. Shishanin
%T Modification of Hill's equation for the storage rings simplified models
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2012
%P 60-65
%N 2
%U http://geodesic.mathdoc.fr/item/VSPUI_2012_2_a6/
%G ru
%F VSPUI_2012_2_a6
O. E. Shishanin. Modification of Hill's equation for the storage rings simplified models. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2012), pp. 60-65. http://geodesic.mathdoc.fr/item/VSPUI_2012_2_a6/

[1] Shishanin O. E., “Sinkhrotronnoe izluchenie elektrona v silnofokusiruyuschem magnitnom pole”, Zhurn. eksper. i teor. fiziki, 103:4 (1993), 1117–1126

[2] Shishanin O. E., “Sinkhrotronnoe izluchenie elektronov v periodicheskikh slabofokusiruyuschikh magnitnykh polyakh”, Zhurn. eksper. i teor. fiziki, 117:5 (2000), 835–843

[3] Shishanin O. E., “Vliyanie betatronnykh kolebanii na magnitotormoznoe izluchenie”, Zhurn. tekhn. fiziki, 68:11 (1998), 133–134

[4] Wiedemann H., “Design of low emittance storage rings”, Nucl. Inst. and Meth., A246:1-3 (1986), 4–11

[5] Wiedemann H., Particle Accelerator Physics. Basic Principle and Linear Beam Dynamics, Springer-Verlag, Berlin, 1993, 445 pp.

[6] Nayfen A. H., Introduction to Perturbation Techniques | MR

[7] Wasow W., Asymptotic expansion for ordinary differential equations

[8] Smirnov V. I., Kurs vysshei matematiki, v. 3, ch. 2, Izd. 10-e, stereotip., Nauka, M., 1969, 672 pp.

[9] Erdelyi A., Asymptotic expansion

[10] Whittaker E. T., Watson G. N., A course of modern analysis