Three-Dimensional Particle-in-Cell and Electromagnetic Simulations

  • Alan Mankofsky
  • Adam T. Drobot
Conference paper

Abstract

In computational plasma physics the development of simulation techniques and their application has followed an evolution which has been determined, in part, by the cost, speed, and availability of computers. The ever increasing power of modern supercomputers has allowed a progression from modeling of one-dimensional simple problems to two-dimensional simulations which involve complicated geometry and multiple physical processes. One- and two-dimensional PIC codes have become standard research tools and have been applied to an extremely broad set of basic physics and engineering problems. Fully three-dimensional plasma and field models have the obvious attraction that they can deal with problems that are inherently three-dimensional and cannot be analyzed in lower dimensionality, problems in which the dimensionality is suspected to have a role, and design problems in which three-dimensional concepts are a possible option if risk can be assessed through computation or analysis. Until recently the use of general three-dimensional plasma codes, while conceptually attractive, was simply not affordable or highly impractical, requiring very long running times and excessive memory or auxiliary storage.

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References

  1. 1.
    A. Mankofsky, L. Seftor, C.-L. Chang, A. A. Mondelli, A. T. Drobot, J. Moura, S. T. Brandon, D. E. Nielsen, Jr., “Three-Dimensional PIC Simulations and Mixed Geometry Calculations Using ARGUS, ” Proceedings of the 12th Conference on the Numerical Simulation of Plasmas, San Francisco, CA, Sept. 20–23, 1987, Paper PM18.Google Scholar
  2. 2.
    D.B. Seidel, M. L. Kiefer, R. S. Coats, A. L. Siegel, J. P. Quintez, “QUICKSILVER—A 3-D, Electromagnetic PIC Code, ”Proceedings of the 12th Conference on the Numerical Simulation of Plasmas, San Francisco, CA, Sept. 20–23, 1987, Paper PT24.Google Scholar
  3. 3.
    B. Goplen, L. Ludeking, J. McDonald, G. Warren, R. Worl, “SOS User’s Manual, ” Mission Research Corporation Report MRC/WDC-R-158, Alexandria, VA, 1989.Google Scholar
  4. 4.
    T. Weiland, “On the Numerical Solution of Maxwell’s Equations and Applications in the Field of Accelerator Physics, ” Particle Accelerators 75 p. 245–292, 1984; and T. Weiland, “On the Unique Numerical Solution of Maxwellian Eigenvalue Problems in Three Dimensions, ” Particle Accelerators 17 p. 227–242, 1985.Google Scholar
  5. 5.
    M. N. Campbell, B. B. Godfrey, D. J. Sullivan, “IVORY User’s Manual, ” Mission Research Corporation Report AMRC-R-454, Albuquerque, NM, 1983.Google Scholar
  6. 6.
    B. B. Godfrey, D. R. Welch, “The IPROP Three-Dimensional Beam Propagation Code, ” Proceedings of the 12th Conference on the Numerical Simulation of Plasmas, San Francisco, CA, Sept. 20–23, 1987, Paper CM1.Google Scholar
  7. 7.
    O. Buneman, C. W. Barnes, J. C. Green, D. E. Nielsen, Jr., “Principles and Capabilities of 3-D, E-M Particle Simulations, ” J. Comp. Phys. 38, p. 1, 1980; and S. Y. Kim, H. Okuda, “Guiding Center Magnetostatic Particle Simulation Model in Three Dimensions,” J. Comp. Phys. 65 (1) p. 215, 1986.Google Scholar
  8. 8.
    A. Friedman, R. N. Sudan, J. Denavit, “A Linearized 3D Hybrid Code for Stability Studies of Field-Reversed Ion Rings, ” J. Comp. Phys. 40 (1) p. 1, 1981.Google Scholar
  9. 9.
    E. J. Horowitz, “QN3D: A Three Dimensional Quasi-Neutral Hybrid Particle-in-Cell Code with Applications to the Tilt Mode Instability in Field Reversed Configurations,” Lawrence Livermore National Laboratory Report UCRL-53808, Livermore, CA, 1987; and E. J. Horowitz, Don E. Shumaker, and David Anderson, J. Comp. Phys. 84 (2), 1989.Google Scholar
  10. 10.
    Berni Alder, Sidney Fembach, Manuel Rotenberg Eds., Chapter 1, and 4–8, in Methods of Computational Physics; Plasma Physics, Volume 9, Academic Press, New York, 1970.Google Scholar
  11. 11.
    Jay P. Boris, Ramy A. Shanny Eds. Proceedings of the Fourth Conference on Numerical Simulation of Plasmas, Nov. 2–3, 1970, Naval Research Laboratory, Washington, DC, 1971.Google Scholar
  12. 12.
    Berni Alder, Sidney Fernbach, Manuel Rotenberg Eds., Chapters 8–10, in Methods of Computational Physics: Controlled Fusion, Volume 16, Academic Press, New York, 1976.Google Scholar
  13. 13.
    R.W. Hockney, J.W. Eastwood Computer Simulation Using Particles, McGraw-Hill, New York, 1981.Google Scholar
  14. 14.
    J.M. Dawson, A.T. Lin, in Handbook of Plasma Physics, Volume 2, A. A. Galeev and R.N. Sudan Eds., North-Holland, Amsterdam, 1984.Google Scholar
  15. 15.
    Charles K. Birdsall, A. Bruce Langdon, Plasma Physics via Computer Simulations, McGraw-Hill, New York, 1985.Google Scholar
  16. 16.
    Jeremiah U. Brackbill, Bruce I. Cohen Eds., Chapters 8–11 in Multiple Time Scales, Academic Press, New York, 1985.Google Scholar
  17. 17.
    Maha Ashour-Abdalla, Daryl Ann Dutton Eds., Space Plasma Simulations, D. Reidel, Boston, 1985.Google Scholar
  18. 18.
    B. Lembege, J.W. Eastwood Eds., Proceedings of the Third International School on Numerical Simulation of Space Plasmas, Beaulieu-sur-Mer, France, June 22–27, 1987, North-Holland, Amsterdam, 1988.Google Scholar
  19. 19.
    J.U. Brackbill, J.J. Monaghan Eds., Proceedings of the Workshop on Particle Methods in Fluid Dynamics and Plasma Physics, Los Alamos, NM, April 13–15, 1987, North-Holland, Amsterdam, 1988.Google Scholar
  20. 20.
    William L. Kruer, Chapter 2, “Computer Simulation of Plasmas Using Particle Codes, ” in The Physics of Laser Plasma Interaction, Frontiers in Physics Series No. 73, Addison-Wesley, New York, 1988.Google Scholar
  21. 21.
    Toshiko Tajima, Computational Plasma Physics: With Applications to Fusion and Astrophysics, Addison-Wesley, New York, 1989.Google Scholar
  22. 22.
    P. T. Kirsten, G. S. Kino, W. E. Walters, in Space Charge Flow, McGraw Hill, New York, 1967.Google Scholar
  23. 23.
    W. B. Herrmannsfeldt, “Electron Trajectory Program, ” Stanford Linear Accelerator Center Report SLAC-226, 1979.Google Scholar
  24. 24.
    J. E. Boers, “Digital Computer Simulation of High-Current, Relativistic, and Field Emission Electron Tubes, ” Record of the IIth Symposium on Electron, Ion and Laser Beam Technology, R. F. M. Thornley, Ed., San Francisco Press, p. 527, 1971.Google Scholar
  25. 25.
    Kenneth Eppley, “Algorithms for the Self-Consistent Simulation of High Power Klystrons, ” Proceedings of the Linear Accelerator and Beam Optics Code Workshop, San Diego, CA, January 1988.Google Scholar
  26. 26.
    D. W. Hewett, C. W. Nielson, “A Multidimensional Quasineutral Plasma Simulation Model, ” J. Comp. Phys. 29, p. 219 (1978).MATHCrossRefGoogle Scholar
  27. 27.
    Rodney J. Mason, “Implicit Moment PIC-Hybrid Simulation of Collisional Plasmas, ” J. Comp. Phys. 51 (3) p. 484, 1983.MATHCrossRefGoogle Scholar
  28. 28.
    A. Mankofsky, R. N. Sudan, J. Denavit, “Hybrid Simulation of Ion Beams in Background Plasma, ” J. Comp. Phys. 70 (1), 1987.Google Scholar
  29. 29.
    Robert B. Wilhelmso, Jones H. Erickson, “Direct Solutions for Poisson’s Equation in Three Dimensions,” J. Comp. Phys. 25, p. 319, 1977; and also Clive Temperton, “Direct Methods for the Solution of the Discrete Poisson Equation: Some Comparisons,” J. Comp. Phys. 31, p. 1, 1979.Google Scholar
  30. 30.
    P. J. Roache, Chapter 3 in Computational Fluid Dynamics, Hermosa Press, Albuquerque, NM, 1976.Google Scholar
  31. 31.
    Stephen F. McCormick, Ed., Multigrid Methods, SIAM, Philadelphia, PA, 1987.MATHGoogle Scholar
  32. 32.
    B. E. McDonald, “The Chebyshev Method for Solving Nonself-Adjoint Elliptic Equations on a Vector Computer,” J. Comp. Phys. 35, p. 147, 1980.MATHCrossRefGoogle Scholar
  33. 33.
    Kazuyoshi Miki, Toshiyuki Takagi, “Numerical Solution of Poisson’s Equation with Arbitrary Shaped Boundaries Using a Domain Decomposition and Overlapping Technique,” J. Comp. Phys. 67, p. 263, 1986; and J. H. Whealton, R. W. McGaffey, P. S. Meszaros, “A Finite Difference 3-D Poisson-Vlasov Algorithm for Ions Extracted from a Plasma,” J. Comp. Phys. 63 (1) p. 20, 1986.Google Scholar
  34. 34.
    G. A. Bird, Chapter 7 in Molecular Gas Dynamics, Clarendon Press, Oxford, England, 1976.Google Scholar
  35. 35.
    A. Mankofsky, J. L. Seftor, C.-L. Chang, K. Ko, A. A. Mondelli, A. T. Drobot, J. Moura, W. Aimonetti, S. T. Brandon, D. E. Nielsen, Jr., K. M. Dyer, “Domain Decomposition and Particle Pushing for Multiprocessing Computers,” Computer Physics Communications 48, p. 155, 1988.Google Scholar
  36. 36.
    J. Tuchmantel, CERN Report RF 85–4, Geneva, Switzerland, July 1985: see also T. Weiland, Particle Accelerators 17 p. 227, 1985.Google Scholar
  37. 37.
    See for example C.-L. Chang, T. M. Antonsen, Jr., E. Ott, A. T. Drobot, Phys. Fluids 27, p. 2545 (1984).Google Scholar
  38. 38.
    J. Swegle, E. Ott, Phys. Fluids 24, p. 1821, 1981.MATHCrossRefGoogle Scholar
  39. 39.
    S. Humphries, Jr., Nuclear Fusion 20, p. 1549, 1980.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Alan Mankofsky
  • Adam T. Drobot

There are no affiliations available

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