Journal of Fusion Energy

, Volume 36, Issue 1, pp 25–39 | Cite as

Physical and Numerical Model for Calculation of Ensembles of Trajectories of Dust Particles in a Tokamak

Original Research


The calculation of the trajectories and main physical parameters (e.g. mass, temperature, electric potential) of an ensemble of several representative dust particles has recently emerged as an important problem in the physics of tokamaks, with the aim of studying their role as a source of impurities in a thermonuclear plasma and their effects in the interaction with the first wall. The physical problem despite its apparent simple goals, is fraught with difficulties related to various subtle physical processes and requires the development of specific accurate numerical tools. In this work, the key physics aspects of the problem of dust tracking in a high temperature tokamak plasma are addressed from the concrete point of view of developing adequate and consistent numerical tools for their treatment. The basic elements and the rationale of the numerical code DUST-TRACKing (DUSTTRACK) developed for it are outlined. To describe the performance and potential of DUSTTRACK, a “realistic” output of the code is finally showed.


DUSTTRACK Nuclear-fusion Tokamak Dust 



This work has been carried out at the Istituto di Fisica del Plasma IFP-CNR. The views and opinions expressed herein do not necessarily respect those of IFP-CNR.


  1. 1.
    G. Federici, H. Wuerz, G. Janeschitz, R. Tivey, Fusion Eng. Des. 61–62, 81 (2002)CrossRefGoogle Scholar
  2. 2.
    J.P. Sharpe, D.A. Petti, H.-W. Bartels, Fusion Eng. Des. 63–64, 153 (2002)CrossRefGoogle Scholar
  3. 3.
    S.I. Krasheninnikov, R.D. Smirnov, D.L. Rudakov, Plasma Phys. Control. Fusion 53(8), 083001 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    S. Ratynskaia, L. Vignitchouk, P. Tolias, I. Bykov, H. Bergsåker, A. Litnovsky, N. den Harder, E. Lazzaro, Nucl. Fusion 53(12), 123002 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    M. Sertoli, J.C. Flannegan, A. Cackett, E. Hodille, P. de Vries, I.H. Coffey, B. Sieglin, S. Marsen, S. Brezinsek, G.F. Matthews, J.W. Coenen, JET-EFDA Contributors. Phys. Scr. T159, 014014 (2014)Google Scholar
  6. 6.
    M. Sertoli, J.C. Flanagan, M. Bacharis, O. Kardaun, A. Jarvinen, G.F. Matthews, S. Brezinsek, D. Harting, A. Cackett, E. Hodille, I.H. Coffey, E. Lazzaro, T. Pütterich, J. Nucl. Mater. 463, 837 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    J.C. Flanagan, M. Sertoli, M. Bacharis, G.F. Matthews, P.C. de Vries, A. Widdowson, I.H. Coffey, G. Arnoux, B. Sieglin, S. Brezinsek, J.W. Coenen, S. Marsen, T. Craciunescu, A. Murari, D. Harting, A. Cackett, E. Hodille, Plasma Phys. Control. Fusion 57(1), 014037 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    S.J. Piet, A. Costley, G. Federici, F. Heckendorn, R. Little, in 17th IEEE/NPSS Symposium on Fusion Engineering, vol. 1, (1997), pp. 167–170Google Scholar
  9. 9.
    V. Rohde, M. Balden, T. Lunt, The ASDEX Upgrade Team, Phys. Scr. T138, 014024 (2009)Google Scholar
  10. 10.
    AYu. Pigarov, S.I. Krasheninnikov, T.K. Soboleva, T.D. Rognlien, Phys. Plasmas 12(12), 122508 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    R.D. Smirnov, A.Y. Pigarov, M. Rosenberg, S.I. Krasheninnikov, D.A. Mendis, Plasma Phys. Control. Fusion 49(4), 347 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    M. Bacharis, M. Coppins, J.E. Allen, Phys. Rev. E 82, 026403 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    M. Bacharis, M. Coppins, J.E. Allen, Phys. Plasmas 17(4), 042505 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    E. Lazzaro, I. Proverbio, F. Nespoli, S. Ratynskaia, C. Castaldo, U. de Angelis, M. De Angeli, J.-P. Banon, L. Vignitchouk, Plasma Phys. Control. Fusion 54(12), 124043 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    L. Vignitchouk, P. Tolias, S. Ratynskaia, Plasma Phys. Control. Fusion 56(9), 095005 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    S. Ratynskaia, P. Tolias, A. Shalpegin, L. Vignitchouk, M. De Angeli, I. Bykov, K. Bystrov, S. Bardin, F. Brochard, D. Ripamonti, N. den Harder, G. De Temmerman, J. Nucl. Mater. 463, 877 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    A. Uccello, G. Gervasini, F. Ghezzi, E. Lazzaro, M. Bacharis, J. Flanagan, G. Matthews, A. Järvinen, M. Sertoli, J.E.T. Contributors, Phys. Plasmas 23, 102506 (2016)ADSCrossRefGoogle Scholar
  18. 18.
  19. 19.
    R. Simonini, G. Corrigan, G. Radford, J. Spence, A. Taroni, Contrib. Plasma Phys. 34(2–3), 368 (1994)ADSCrossRefGoogle Scholar
  20. 20.
    A.E. Jaervinen, M. Groth, M. Airila, P. Belo, M. Beurskens, S. Brezinsek, M. Clever, G. Corrigan, S. Devaux, P. Drewelow, T. Eich, C. Giroud, D. Harting, A. Huber, S. Jachmich, K. Lawson, B. Lipschultz, G. Maddison, C. Maggi, T. Makkonen, C. Marchetto, S. Marsen, G.F. Matthews, A.G. Meigs, D. Moulton, M.F. Stamp, S. Wiesen, M. Wischmeier, JET-EFDA Collaborators. J. Nucl. Mater. 463, 135 (2015)Google Scholar
  21. 21.
    P. Stangeby, The Plasma Boundary of Magnetic Fusion Devices (Taylor & Francis Group, New York, 2000)CrossRefGoogle Scholar
  22. 22.
    A. Baron-Wiechec, E. Fortuna-Zaleśna, J. Grzonka, M. Rubel, A. Widdowson, C. Ayres, J.P. Coad, C. Hardie, K. Heinola, G.F. Matthews, Nucl. Fusion 55(11), 113033 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    J.E. Allen, Phys. Scr. 45(5), 497 (1992)ADSCrossRefGoogle Scholar
  24. 24.
    P.K. Shukla, A.A. Mamun, Introduction to Dusty Plasma Physics. Series in Plasma Physics and Fluid Dynamics (CRC Press, Boca Raton, 2001)CrossRefGoogle Scholar
  25. 25.
    S. Dushman, Rev. Mod. Phys. 2, 381 (1930)ADSCrossRefGoogle Scholar
  26. 26.
    A.H.W. Beck, Thermionic Valves (Cambridge University Press, Cambridge, 2015)Google Scholar
  27. 27.
    R.A. Langley, J. Bohdansky, W. Eckstein, P. Mioduszewski, J. Roth, E. Taglauer, E.W. Thomas, H. Verbeek, K.L. Wilson, Nucl. Fusion 24(S1), S9 (1984)CrossRefGoogle Scholar
  28. 28.
    E.W. Thomas, (IAEA, Vienna, 1984), p. 94Google Scholar
  29. 29.
    M.S. Chung, T.E. Everhart, J. Appl. Phys. 45(2), 707 (1974)ADSCrossRefGoogle Scholar
  30. 30.
    ITER Technical Basis, ITER EDA Documentation Series No 24 (IAEA, Vienna, 2002)Google Scholar
  31. 31.
    R. Marek, J. Straub, Int. J. Heat Mass Tranf. 44(1), 39 (2001)CrossRefGoogle Scholar
  32. 32.
    A.T. Dinsdale, Calphad 15(4), 317 (1991)CrossRefGoogle Scholar
  33. 33.
    D.R. Lide, CRC Handbook of Chemistry and Physics, vol. 80 (Taylor & Francis, London, 1999)Google Scholar
  34. 34.
    T.E. Stringer, Nucl. Fusion 12(6), 689 (1972)CrossRefGoogle Scholar
  35. 35.
    I.H. Hutchinson, Plasma Phys. Control. Fusion 48(2), 185 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    S.A. Khrapak, A.V. Ivlev, S.K. Zhdanov, G.E. Morfill, Phys. Plasmas 12(4), 042308 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    C. Thornton, Z. Ning, Powder Technol. 99(2), 154 (1998)CrossRefGoogle Scholar
  38. 38.
    W. Goldsmith, Impact: The Theory and Physical Behaviour of Colliding Solids (E. Arnold, London, 1960)MATHGoogle Scholar
  39. 39.
    X. Li, P.F. Dunn, R.M. Brach, Aerosol Sci. Technol. 33(4), 376 (2000)CrossRefGoogle Scholar
  40. 40.
    R. Bridson, R. Fedkiw, J. Anderson, ACM Trans. Graph. 21(3), 594 (2002)CrossRefGoogle Scholar
  41. 41.
    M.C. van Beek, C.C.M. Rindt, J.G. Wijers, A.A. van Steenhoven, Powder Technol. 165(2), 53 (2006)CrossRefGoogle Scholar
  42. 42.
    S.V. Klinkov, V.F. Kosarev, M. Rein, Aerosp. Sci. Technol. 9(7), 582 (2005)CrossRefGoogle Scholar
  43. 43.
    D. Shepard, in Proceedings of the 1968 23rd ACM National Conference (ACM, New York, NY, 1968), pp. 517–524Google Scholar
  44. 44.
    G.F. Counsell, J.W. Connor, S.K. Erents, A.R. Field, S.J. Fielding, B. La Bombard, K.M. Morel, J. Nucl. Mater. 266–269, 91 (1999)CrossRefGoogle Scholar
  45. 45.
    P.N. Brown, A.C. Hindmarsh, L.R. Petzold, SIAM J. Sci. Comput. 15, 1467 (1994)CrossRefGoogle Scholar
  46. 46.
    L.R. Petzold, Scientific Computing (Montreal, Quebec, 1982) (IMACS, New Brunswick, NJ, 1983)Google Scholar
  47. 47.
    S. Nordbeck, B. Rystedt, BIT 7(1), 39 (1967)CrossRefGoogle Scholar
  48. 48.
    S.W. Sloan, Adv. Eng. Softw. (1978) 7(1), 45 (1985)CrossRefGoogle Scholar
  49. 49.
  50. 50.
    G.F. Matthews, J. Nucl. Mater. 438, Supplement, S2 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Gabriele Gervasini
    • 1
  • Enzo Lazzaro
    • 1
  • Andrea Uccello
    • 1
  1. 1.Istituto di Fisica del Plasma IFP-CNRMilanItaly

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