Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

Nonlinear Poincare–Steklov equation and its solution in problems of electron optics

Keywords:

V.M. Sveshnikov – Dr.Sc. (Phys.-Math.), Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences; Professor, Novosibirsk State University. Е-mail: victor@lapasrv.sscc.ru


Poincare–Steklov equation is known from the solution of linear problems of mathematical physics by the domain decomposition method. In this paper, this equation is proposed to use for calculating the intensive charged particle beams in nonlinear self-consistent problem of electron optics. The algorithm for solving nonlinear Poincare–Steklov equation defines iterative process for solving the nonlinear problem of electron optics. The essence of the proposed approach is as follows. The computational domain is divided into two subdomains: the near-cathode and the main. In the near-cathode subdomain analytical solution is built and in the main subdomain solution is found numerically. Central question is crosslinking subdomains. To do this, Poincare–Steklov equation is written on the boundary of subdomains that is approximated by a system of nonlinear operator equations. Its solution is carried out by Broyden method. As follows from the numerical experiment, already in the fourth iteration the Broyden process is converged with acceptable accuracy for practical purposes.
References:

 

  1. Quarteroni A., Valli A.Domain decomposition methods for partial differential equations. Oxford: ClarendonPress. 1999.
  2. Sveshnikov V.M. Povyshenie tochnosti rascheta intensivnykh puchkov zarjazhennykh chastic // Prikladnaja fizika. 2004. № 1. S. 55–65.
  3. Sveshnikov V.M. Reshenie samosoglasovannykh zadach ehlektronnojj optiki metodom iteracijj po podoblastjam bez naleganija i smeny tipa granichnogo uslovija // Vychislitelnye tekhnologii. 2006. T.11. № 5. S. 77–91.
  4. Sveshnikov V. Increased-accuracy numerical modeling of electron-optical systems with space-charge // Nuclear Instruments and Methods in Physics Research A. 2011. № 645. P. 307–309.
  5. Syrovojj V.A. Vvedenie v teoriju intensivnykh puchkov zarjazhennykh chastic. M.: EHnergoatomizdat. 2004.
  6. Sveshnikov V.M. Postroenie prjamykh i iteracionnykh metodov dekompozicii // SibZHIM. 2009. T.12. № 3(39). S. 99–109.
  7. Sveshnikov V.M. Parallelnye prjamye i iteracionnye metody dekompozicii dlja reshenija kraevykh zadach na mnogoprocessornykh superEHVM // Vestnik KHersonskogo nacionalnogo tekhnicheskogo universiteta. 2009.T. 2(35). S. 398–402.
  8. Dehnis Dzh., SHnabel R. CHislennye metody bezuslovnojj optimizacii i reshenija nelinejjnykh uravnenijj. M.: Mir.1988.
  9. Sveshnikov V.M. Raschet prikatodnojj oblasti v ehlektronno-opticheskikh sistemakh, formirujushhikh intensivnye puchki zarjazhennykh chastic // Prikladnaja fizika. 2004. № 1. S. 50–55.
  10. Langmuir I., Blodjett K.B. Current limited by space charge between concentric spheres // Phys. Rev. 1924. V. 24. № 1. P. 49–59.

 

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio