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

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Abstract

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.

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References

  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. 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)

    Article  ADS  Google Scholar 

  3. R. Lebert, W. Neff, D. Rothweiler, J. X-Ray Sci. Technol. 6, 2 (1996)

    Article  Google Scholar 

  4. V.A. Gribkov, A. Srivastava, P.C.K. Lee, V. Kudryashov, S. Lee, IEEE Trans. Plasma Sci. 30, 1331–1338 (2002)

    Article  ADS  Google Scholar 

  5. Rishi. Verma, P. Lee, S. Lee, S.V. Springham, T.L. Tan, R.S. Rawat, M. Krishnan, Appl. Phys. Lett. 93, 101501 (2008)

    Article  ADS  Google Scholar 

  6. M.G. Haines. Plasma Phys. Control. Fusion 53, 093001 (2011). doi:10.1088/0741-3335/53/9/093001

  7. J.W. Shearer, Phys. Fluids 19, 1426 (1976). doi:10.1063/1.861627

    Article  ADS  Google Scholar 

  8. V. Vikhrev. Pis’ma Zh Elsp Teor Fiz 27(2), 104–107 (1978)

    Google Scholar 

  9. K.N. Koshelev, Yu.V. Sidelnikov, Nucl. Instrum. Methods Phys. Res. B9, 204–205 (1985)

    Google Scholar 

  10. R. Pease, Procs. Phys. Soc. 70, 11 (1957)

    Article  ADS  MATH  Google Scholar 

  11. S. Braginskii, Zh. Eksp. Teor. Fiz. 33, 645 (1957)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  13. Lee S. Radiative Dense Plasma Focus Computation Package: RADPF

  14. http://www.plasmafocus.net (2011)

  15. S. Lee, in Radiations in Plasmas Vol II, ed. by B. McNamara (World Scientific, Singapore, 1984) pp. 978–987

  16. T.Y. Tou, S. Lee, K.H. Kwek, IEEE Trans. Plasma Sci. 17, 311–315 (1989)

    Article  ADS  Google Scholar 

  17. S. Lee, IEEE Trans. Plasma Sci. 19, 5 (1991)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  19. S. Lee, A. Serban, IEEE Trans. Plasma Sci. 24, 1101–1105 (1996)

    Article  ADS  Google Scholar 

  20. A. Jalil bin. Development and studies of a small plasma focus, Ph.D. Dissertation; Universiti Teknologi Malaysia, Malaysia, 1990

  21. D.E. Potter, Nucl. Fusion 18, 813–823 (1978)

    Article  ADS  Google Scholar 

  22. S. Bing, Plasma dynamics and X-ray emission of the plasma focus (Nanyang Technological University, Singapore, Ph.D. dissertation, 2000)

    Google Scholar 

  23. A. Serban, S. Lee, J. Plasma Phys. 60, 3–15 (1998)

    Article  ADS  Google Scholar 

  24. M.H. Liu, X.P. Feng, S.V. Springham, S. Lee. IEEE Trans. Plasma Sci., 26, 135 (1998)

    Google Scholar 

  25. S. Lee, Twelve years of UNU/ICTP PFFa review. Abdus Salam ICTP, Trieste IC/98/231, p 5–34, (1998)

  26. S.V. Springham, S. Lee, M.S. Rafique. Plasma Phys. Control. Fusion, 42, 1023 (2000)

    Google Scholar 

  27. Lee S. (2010) [Online]. Available: http://ckplee.myplace.nie.edu.sg/plasmaphysics/

  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)

    Article  ADS  Google Scholar 

  29. V. Siahpoush, M.A. Tafreshi, S. Sobhanian, S. Khorram, Plasma Phys. Control. Fusion 47, 1065–1075 (2005)

    Article  ADS  Google Scholar 

  30. S. Lee, S.H. Saw, J. Fusion Energ. 27, 292–295 (2008)

    Article  Google Scholar 

  31. S. Lee, Plasma Phys. Control. Fusion 50(105), 005 (2008)

    Google Scholar 

  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. S. Lee, S.H. Saw, Appl. Phys. Lett. 92(021), 503 (2008)

    Article  Google Scholar 

  34. S. Lee, P. Lee, S.H. Saw, R.S. Rawat, Plasma Phys. Control. Fusion 50, 065012 (2008)

    Article  ADS  Google Scholar 

  35. S. Lee, Appl. Phys. Lett. 95, 151503 (2009)

    Article  ADS  Google Scholar 

  36. S. Lee, S.H. Saw, L. Soto, S.P. Moo, S.V. Springham, Plasma Phys. Control. Fusion 51, 075006 (2009)

    Article  ADS  Google Scholar 

  37. S. Lee, S.H. Saw, P. Lee, R.S. Rawat, Plasma Phys. Control. Fusion 51, 105013 (2009)

    Article  ADS  Google Scholar 

  38. M. Akel, Sh. Al-Hawat, S.H. Saw, S. Lee, J. Fusion Energy 29, 223–231 (2010)

    Article  Google Scholar 

  39. S. Lee, R.S. Rawat, P. Lee, S.H. Saw, J. Appl. Phys. 106, 023309 (2009)

    Article  ADS  Google Scholar 

  40. S.H. Saw, P.C.K. Lee, R.S. Rawat, S. Lee, IEEE Trans. Plasma Sci. 37, 1276 (2009)

    Article  ADS  Google Scholar 

  41. S.P. Chow, S. Lee, B.C. Tan, J. Plasma Phys. 8, 21–31 (1973)

    Article  ADS  Google Scholar 

  42. M. Favre, S. Lee, S.P. Moo, C.S. Wong, Plasma Sources Sci. Technol. 1, 122 (1992)

    Article  ADS  Google Scholar 

  43. McWhirter in Plasma diagnostic techniques ed. by R. Huddelstone, S.L. Leonard (Academic Press, New York, 1965)

  44. http://physics.nist.gov/PhysRefData/Elements/

  45. S. Lee, Aust. J. Phys. 35, 391 (1983)

    Google Scholar 

  46. K. Koshelev, N. Pereira, J. Appl. Phys. 69, 21–44 (1991)

    Article  ADS  Google Scholar 

  47. A.E. Robson. Phys. Fluid B3, 1481 (1991)

  48. N.A.D. Khattak Anomalous Heating (LHDI). http://www.plasmafocus.net/IPFS/modelpackage/File3Appendix.pdf (2011)

  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)

    Article  ADS  Google Scholar 

  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. Sh. Al-Hawat, M. Akel, S. Lee, S.H. Saw, J. Fusion Energ. 31, 13–20 (2012)

    Article  Google Scholar 

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Lee, S., Saw, S.H. & Ali, J. Numerical Experiments on Radiative Cooling and Collapse in Plasma Focus Operated in Krypton. J Fusion Energ 32, 42–49 (2013). https://doi.org/10.1007/s10894-012-9522-8

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