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Numerical method to study the stability of periodic solutions of particle motion in nonlinear magnetic fields; Chislennyj metod issledovaniya ustojchivosti periodicheskikh reshenij dvizheniya chastits v nelinejnykh magnitnykh polyakh

Technical Report:

Abstract

The equations of betatron oscillations in nonlinear magnetic fields belong to the Lyapunov systems having a number of periodic solutions. Using the matrix methods developed for studying periodic linear systems one can construct the algorithm for searching these solutions and studying their stability in order to determined the region of stable motion. The present note describes the method of numeric search for the periodic solutions of two-dimensional betatron motion, using the nonlinear element in thin-lens approximation. To illustrate the technique, the results on calculating the pattern on the phase plane close to the line and node of the sum third-order resonance are presented. 5 refs.; 5 figs.
Authors:
Publication Date:
Dec 31, 1992
Product Type:
Technical Report
Report Number:
IFVE-UNK-92-22
Reference Number:
SCA: 430200; PA: AIX-25:006423; EDB-94:014545; ERA-19:007221; NTS-94:015091; SN: 94001126433
Resource Relation:
Other Information: PBD: 1992
Subject:
43 PARTICLE ACCELERATORS; ACCELERATORS; BEAM DYNAMICS; STORAGE RINGS; EQUATIONS OF MOTION; MAGNETIC FIELDS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PARTICLE BEAMS; RESONANCE; STABILITY; TRAJECTORIES; 430200; BEAM DYNAMICS, FIELD CALCULATIONS, AND ION OPTICS
OSTI ID:
10113392
Research Organizations:
Gosudarstvennyj Komitet po Ispol`zovaniyu Atomnoj Ehnergii SSSR, Serpukhov (Russian Federation). Inst. Fiziki Vysokikh Ehnergij
Country of Origin:
Russian Federation
Language:
Russian
Other Identifying Numbers:
Other: ON: DE94610740; TRN: RU9305263006423
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
11 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Fedotov, Yu S. Numerical method to study the stability of periodic solutions of particle motion in nonlinear magnetic fields; Chislennyj metod issledovaniya ustojchivosti periodicheskikh reshenij dvizheniya chastits v nelinejnykh magnitnykh polyakh. Russian Federation: N. p., 1992. Web.
Fedotov, Yu S. Numerical method to study the stability of periodic solutions of particle motion in nonlinear magnetic fields; Chislennyj metod issledovaniya ustojchivosti periodicheskikh reshenij dvizheniya chastits v nelinejnykh magnitnykh polyakh. Russian Federation.
Fedotov, Yu S. 1992. "Numerical method to study the stability of periodic solutions of particle motion in nonlinear magnetic fields; Chislennyj metod issledovaniya ustojchivosti periodicheskikh reshenij dvizheniya chastits v nelinejnykh magnitnykh polyakh." Russian Federation.
@misc{etde_10113392,
title = {Numerical method to study the stability of periodic solutions of particle motion in nonlinear magnetic fields; Chislennyj metod issledovaniya ustojchivosti periodicheskikh reshenij dvizheniya chastits v nelinejnykh magnitnykh polyakh}
author = {Fedotov, Yu S}
abstractNote = {The equations of betatron oscillations in nonlinear magnetic fields belong to the Lyapunov systems having a number of periodic solutions. Using the matrix methods developed for studying periodic linear systems one can construct the algorithm for searching these solutions and studying their stability in order to determined the region of stable motion. The present note describes the method of numeric search for the periodic solutions of two-dimensional betatron motion, using the nonlinear element in thin-lens approximation. To illustrate the technique, the results on calculating the pattern on the phase plane close to the line and node of the sum third-order resonance are presented. 5 refs.; 5 figs.}
place = {Russian Federation}
year = {1992}
month = {Dec}
}