Journal of Fusion Energy

, Volume 32, Issue 1, pp 42–49 | Cite as

Numerical Experiments on Radiative Cooling and Collapse in Plasma Focus Operated in Krypton

  • S. Lee
  • S. H. Saw
  • Jalil Ali
Original Research


The Plasma Focus has wide-ranging applications due to its intense radiation of SXR, XR, electron and ion beams and fusion neutrons when operated in deuterium. The 5-phase Lee Model code has been developed for the focus operated in various gases including D, D–T, He, Ne, N, O, Ar, Kr and Xe. Radiation-coupled motion is included in the modelling. In this paper we look at the effect of radiation cooling and radiation collapse in krypton. The Pease–Braginskii current is that current flowing in a hydrogen pinch which is just large enough for the Bremsstrahlung to balance Joule heating. This radiation-cooled threshold current for a hydrogen pinch is 1.6 MA. It is known that in gases undergoing line radiation strongly the radiation-cooled threshold current is considerably lowered. We show that the equations of the Lee Model code may be used to compute this lowering. The code also shows the effect of radiation cooling leading to radiative collapse. Numerical experiments based on experimentally fitted model parameters are run to demonstrate a regime in which radiation collapse is observed in Kr at a pinch current of 50–100 kA.


Plasma focus Plasma focus modeling Radiative cooling Radiative collapse Plasma focus radiation 


  1. 1.
    A. Bernard, H. Bruzzone, P. Choi, H. Chuaqui, V. Gribkov, J. Herrera, K. Hirano, A. Krejci, S. Lee, C. Luo, F. Mezzetti, M. Sadowski, H. Schmidt, K. Ware, C.S. Wong, V. Zoita, Moscow J. Phys. Soc. 8, 93–170 (1998)Google Scholar
  2. 2.
    S. Lee, P. Lee, G. Zhang, X. Feng, V.A. Gribkov, M. Liu, A. Serban, T. Wong, IEEE Trans. Plasma Sci. 26, 1119–1126 (1998)ADSCrossRefGoogle Scholar
  3. 3.
    R. Lebert, W. Neff, D. Rothweiler, J. X-Ray Sci. Technol. 6, 2 (1996)CrossRefGoogle Scholar
  4. 4.
    V.A. Gribkov, A. Srivastava, P.C.K. Lee, V. Kudryashov, S. Lee, IEEE Trans. Plasma Sci. 30, 1331–1338 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Rishi. Verma, P. Lee, S. Lee, S.V. Springham, T.L. Tan, R.S. Rawat, M. Krishnan, Appl. Phys. Lett. 93, 101501 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    M.G. Haines. Plasma Phys. Control. Fusion 53, 093001 (2011). doi: 10.1088/0741-3335/53/9/093001
  7. 7.
    J.W. Shearer, Phys. Fluids 19, 1426 (1976). doi: 10.1063/1.861627 ADSCrossRefGoogle Scholar
  8. 8.
    V. Vikhrev. Pis’ma Zh Elsp Teor Fiz 27(2), 104–107 (1978)Google Scholar
  9. 9.
    K.N. Koshelev, Yu.V. Sidelnikov, Nucl. Instrum. Methods Phys. Res. B9, 204–205 (1985)Google Scholar
  10. 10.
    R. Pease, Procs. Phys. Soc. 70, 11 (1957)ADSMATHCrossRefGoogle Scholar
  11. 11.
    S. Braginskii, Zh. Eksp. Teor. Fiz. 33, 645 (1957)Google Scholar
  12. 12.
    K.N. Koshelev, V.I. Krauz, N.G. Reshetniak, R.G. Salukvadze Yu, V. Sidelnikov, E.Yu. Khautiev, J. Phys. D Appl. Phys. 21, 1827 (1988)ADSCrossRefGoogle Scholar
  13. 13.
    Lee S. Radiative Dense Plasma Focus Computation Package: RADPFGoogle Scholar
  14. 14.
  15. 15.
    S. Lee, in Radiations in Plasmas Vol II, ed. by B. McNamara (World Scientific, Singapore, 1984) pp. 978–987Google Scholar
  16. 16.
    T.Y. Tou, S. Lee, K.H. Kwek, IEEE Trans. Plasma Sci. 17, 311–315 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    S. Lee, IEEE Trans. Plasma Sci. 19, 5 (1991)CrossRefGoogle Scholar
  18. 18.
    S. Lee, T.Y. Tou, S.P. Moo, M.A. Eissa, A.V. Gholap, K.H. Kwek, S. Mulyodrono, A.J. Smith, S. Suryadi, W. Usada, M. Zakaullah, Am. J. Phys. 56, 62–68 (1988)ADSCrossRefGoogle Scholar
  19. 19.
    S. Lee, A. Serban, IEEE Trans. Plasma Sci. 24, 1101–1105 (1996)ADSCrossRefGoogle Scholar
  20. 20.
    A. Jalil bin. Development and studies of a small plasma focus, Ph.D. Dissertation; Universiti Teknologi Malaysia, Malaysia, 1990Google Scholar
  21. 21.
    D.E. Potter, Nucl. Fusion 18, 813–823 (1978)ADSCrossRefGoogle Scholar
  22. 22.
    S. Bing, Plasma dynamics and X-ray emission of the plasma focus (Nanyang Technological University, Singapore, Ph.D. dissertation, 2000)Google Scholar
  23. 23.
    A. Serban, S. Lee, J. Plasma Phys. 60, 3–15 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    M.H. Liu, X.P. Feng, S.V. Springham, S. Lee. IEEE Trans. Plasma Sci., 26, 135 (1998)Google Scholar
  25. 25.
    S. Lee, Twelve years of UNU/ICTP PFFa review. Abdus Salam ICTP, Trieste IC/98/231, p 5–34, (1998)Google Scholar
  26. 26.
    S.V. Springham, S. Lee, M.S. Rafique. Plasma Phys. Control. Fusion, 42, 1023 (2000)Google Scholar
  27. 27.
    Lee S. (2010) [Online]. Available:
  28. 28.
    D. Wong, P. Lee, T. Zhang, A. Patran, T.L. Tan, R.S. Rawat, S. Lee, Plasma Sources Sci. Technol. 16, 116–123 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    V. Siahpoush, M.A. Tafreshi, S. Sobhanian, S. Khorram, Plasma Phys. Control. Fusion 47, 1065–1075 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    S. Lee, S.H. Saw, J. Fusion Energ. 27, 292–295 (2008)CrossRefGoogle Scholar
  31. 31.
    S. Lee, Plasma Phys. Control. Fusion 50(105), 005 (2008)Google Scholar
  32. 32.
    S. Lee, S.H. Saw, P.C.K. Lee, R.S. Rawat, H. Schmidt, Appl. Phys. Lett. 92(111), 501 (2008)Google Scholar
  33. 33.
    S. Lee, S.H. Saw, Appl. Phys. Lett. 92(021), 503 (2008)CrossRefGoogle Scholar
  34. 34.
    S. Lee, P. Lee, S.H. Saw, R.S. Rawat, Plasma Phys. Control. Fusion 50, 065012 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    S. Lee, Appl. Phys. Lett. 95, 151503 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    S. Lee, S.H. Saw, L. Soto, S.P. Moo, S.V. Springham, Plasma Phys. Control. Fusion 51, 075006 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    S. Lee, S.H. Saw, P. Lee, R.S. Rawat, Plasma Phys. Control. Fusion 51, 105013 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    M. Akel, Sh. Al-Hawat, S.H. Saw, S. Lee, J. Fusion Energy 29, 223–231 (2010)CrossRefGoogle Scholar
  39. 39.
    S. Lee, R.S. Rawat, P. Lee, S.H. Saw, J. Appl. Phys. 106, 023309 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    S.H. Saw, P.C.K. Lee, R.S. Rawat, S. Lee, IEEE Trans. Plasma Sci. 37, 1276 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    S.P. Chow, S. Lee, B.C. Tan, J. Plasma Phys. 8, 21–31 (1973)ADSCrossRefGoogle Scholar
  42. 42.
    M. Favre, S. Lee, S.P. Moo, C.S. Wong, Plasma Sources Sci. Technol. 1, 122 (1992)ADSCrossRefGoogle Scholar
  43. 43.
    McWhirter in Plasma diagnostic techniques ed. by R. Huddelstone, S.L. Leonard (Academic Press, New York, 1965)Google Scholar
  44. 44.
  45. 45.
    S. Lee, Aust. J. Phys. 35, 391 (1983)Google Scholar
  46. 46.
    K. Koshelev, N. Pereira, J. Appl. Phys. 69, 21–44 (1991)ADSCrossRefGoogle Scholar
  47. 47.
    A.E. Robson. Phys. Fluid B3, 1481 (1991)Google Scholar
  48. 48.
    N.A.D. Khattak Anomalous Heating (LHDI). (2011)
  49. 49.
    S.H. Saw, S. Lee, F. Roy, P.L. Chong, V. Vengadeswaran, A.S.M. Sidik, Y.W. Leong, A. Singh, Rev. Sci. Instrum. 81, 053505 (2010)ADSCrossRefGoogle Scholar
  50. 50.
    S. Lee, S.H. Saw, R.S. Rawat, P. Lee, R. Verma, A. Talebitaher, S.M. Hassan, A.E. Abdou, I. Mohamed, M. Amgad, H. Torreblanca, Sh. Al Hawat, M. Akel, P.L. Chong, F. Roy, A. Singh, D. Wong, K. Devi. J. Fusion Energy (2011) Online First 27 July. doi: 10.1007/s10894-011-9456-6
  51. 51.
    Sh. Al-Hawat, M. Akel, S. Lee, S.H. Saw, J. Fusion Energ. 31, 13–20 (2012) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.INTI International UniversityNilaiMalaysia
  2. 2.Institute for Plasma Focus StudiesChadstoneAustralia
  3. 3.Institute of Advanced Photonic Science, Nanotechnology Research Alliance, Universiti Teknologi MalaysiaJohor BaruMalaysia

Personalised recommendations