State of the Art Simulations of High Intense Particle Beams in Complicated Accelerator Structures

  • A. Adelmann
  • R. Jeltsch
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


As a part of our research activities aimed at a detailed understanding of space charge effects in ring cyclotrons and in the corresponding injection beam lines at the Paul Scherrer Institut, we are currently developing a three dimensional space charge simulation code. Using the collision less Vlasov Maxwell equation as base model, we show how to solve this set of highly nonlinear equations in the light of accelerator simulations. We assume that we deal with low energy but high intensity beams only. Basically we use a split operator technique H = H 1 + H 2 enriched with the ability to impose complicated boundary conditions.

For the first term H 1, in H above, we use Lie Algebraic methods combined with Differential Algebraic (DA) methods to solve the single particle motion part of our problem.

Algorithms for solving kinetic equations can be roughly speaking divided into two groups, corresponding to the Lagrangian and Euler description of the phase space dynamics. We will use a parallel FFT based particle mesh approach and a Barnes Hut tree based field solver for our purposes. The efficient and accurate treatment of the space charge term H 2 relies on the fact that one has a fast and accurate Poisson solver available, doing better than O(n 2), where n characterizes the problem size. In order to minimize numerical noise, the ratio between number of macro particles N p, and real number of particles in the beam pulse is a critical issue. With our approach we try to make this ratio close to one, in order to minimize numerical impurities. In today’s view of modern software engineering, extensibility, maintainability and re-usability are key issues, in addition to accuracy and stability. We show how to tackle the challenge of building a modern problem solving environment, by using the object oriented framework approach, hence combining two leading edge C++ class libraries, namely CLASSIC (Class Library for Acceleration System Simulation and Control) from CERN and POOMA (Parallel Object Oriented Methods and Applications) from advanced computing lab (ACL) in Los Alamos.


Space Charge Space Charge Effect Local Reference System Split Operator Technique Differential Algebraic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gluckstern, R.L. (1994) Phys. Rev. Lett., 73, p. 1247.CrossRefGoogle Scholar
  2. 2.
    Qiang, J. and Ryne, R.D. (2000) Phys. Rev. ST. Accel. Beams 3, 064201.Google Scholar
  3. 3.
    Forest, E. et al. (1991) Phys. Lett.,A 158, p.99.Google Scholar
  4. 4.
    Forest, E. (1998) Beam Dynamics A new Attitude and Framework. Volume 8 The Physics and Technology of Particle and Proton Beams, Harword Academic Publishers.Google Scholar
  5. 5.
    Yoshida, H. (1990) Phys. Lett.,A 150, p.262.Google Scholar
  6. 6.
    Hockney, R.W. and Eastwood, J.W. (1988) Computer Simulation Using Particles. Adam Hilger, New York.zbMATHCrossRefGoogle Scholar
  7. 7.
    Birdsall, C.K. and Langdon, A.B. (1985) Plasma Physics Via Computer Simulation. McGraw-Hill Book Company, NY.Google Scholar
  8. 8.
    Qiang, J. and Ryne, R. High Performance Particle-In-Cell Simulation in a Proton Linac. To be submitted to PRST-AB.Google Scholar
  9. 9.
    Science 285, no. 5431, p.1194 (1999).Google Scholar
  10. 10.
    Science 285, no. 5432, p.1342 (1999).Google Scholar
  11. 11.
    Science 286, no. 5437, p.28 (1999).Google Scholar
  12. 12.
    Science 286, no. 5448, p.2239 (1999).Google Scholar
  13. 13.
    Science 285, no. 5436, p.2048 (1999).Google Scholar
  14. 14.
    Fitze, H.R. et. al. Upgrade Concepts of the PSI Accelerator RF Systems for a Projected 3mA Operation. to be submitted to the Cyclotrons 2001 conference.Google Scholar
  15. 15.
    Stammbach, T. et. al. The PSI 2mA Beam & Future Applications. to be submitted to the Cyclotrons 2001 conference.Google Scholar
  16. 16.
    Cern Courier Vol. 40, Number 10 (2000), p. 8.Google Scholar
  17. 17.
    Stammbach, T. et al. (1994) Proc. lth Int. Conf. on Accelerator Driven Transmutation Technologies. AIP Conf. Proc., 346, p. 228.Google Scholar
  18. 18.
    Stammbach, T. et al. (1996) Proc. 2th Int. Conf. on Accelerator Driven Transmutation Technologies. Upsale Univ., p. 1013.Google Scholar
  19. 19.
    Dragt, A.J. (1996) Summary of the Working Group on Maps. Particle Accelerator, Vol. 54, 55 Number 2-4, 1 - 4.Google Scholar
  20. 20.
    Iselin, F.C. (1996) The Classic Project. Particle Accelerator, Vol. 54, 55 Number 2-4, 1 - 4.Google Scholar
  21. 21.
    Dragt, A.J. (1998) Lie Methods for Nonlinear Dynamics with Application to Accelerator Physics. Lecture Notes, Center for Theoretical Physics, University of Maryland.Google Scholar
  22. 22.
    Berz, M. (1999) Modern Map Methods in Particle Beam Physics. Advances in Imaging and Electorn Physics,Volume 108, Academic Press.Google Scholar
  23. 23.
    Sanz-Serna, J.M. and Calvo, M.P. (1994) Numerical Hamiltonian Problems. Applied Mathematics and Mathematical Computation, 7,Chapman and Hall.Google Scholar
  24. 24.
    Ryne, R.D. private communications.Google Scholar
  25. 25.
    Dragt, A.J. et al. ( 1998 Draft) Marylie 3.0 User’s manual. Center for Theoretical Physics, University of Maryland.Google Scholar
  26. 26.
    URL:, canonical MAD resource pageGoogle Scholar
  27. 27.
    Brown, K.L. et al. (1980) TRANSPORT a computer program for designing cahrged particle beam transport systems. CERN YELLOW REPORTS 80 - 04.Google Scholar
  28. 28.
    Cummings, J.C. and Humphrey, W.F. (1997) Parallel Particle Simulations using the POOMA Framework. 8th SIAM Conf. Parallel Processing for Scientific Computing.Google Scholar
  29. 29.
    Montague, B.W. (1995) Basic Hamiltonian mechanics. CERN Yellow Report, 95 - 06 Vol. 1.Google Scholar
  30. 30.
    Willeke,F. (1995) Modern Tools for Partilce Tracking. CERN Yellow Report, 95 - 06 Vol. 1.Google Scholar
  31. 31.
    URL: Scholar
  32. 32.
    Adam, S. TRANSENG, a double precision TRANSPORT engine. unpublished Google Scholar
  33. 33.
    Gamma, E. et al. (1995) Design Patterns. Addison Wesley.Google Scholar
  34. 34.
    Ryne, R.D. (1995) Finding matched rms envelopes in rf linacs: A Hamiltonian approach. e-Print archive, acc-phys/9502001.Google Scholar
  35. 35.
    Pelz, R.B. (1997) Parallel FFTs. In Parallel Numerical Algorithms, D.E Keyes, A. Sameh, V. Venkatakrishnan, Kluwer Academic Publishers.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. Adelmann
    • 1
  • R. Jeltsch
    • 2
  1. 1.Paul Scherrer InstitutSwitzerland
  2. 2.Seminar for Applied MathematicsETH ZurichSwitzerland

Personalised recommendations