Scaling Laws for Plasma Focus Machines from Numerical Experiments

S. H. SAW, S. LEE

.

DOI: 10.4236/epe.2010.21010                

Abstract

Numerical experiments carried out systematically using the Lee Model code unveil insightful and practical wide-ranging scaling laws for plasma focus machines for nuclear fusion energy as well as other applications. An essential feature of the numerical experiments is the fitting of a measured current waveform to the computed waveform to calibrate the model for the particular machine, thus providing a reliable and rigorous determination of the all-important pinch current. The thermodynamics and radiation properties of the resulting plasma are then reliably determined. This paper provides an overview of the recently published scaling laws for neutron (Yn) and neon soft x-ray, SXR (Ysxr) yields: Yn = 3.2x1011 Ipinch4.5; Yn = 1.8x1010 Ipeak3.8; Ipeak (0.3 to 5.7), Ipinch (0.2 to 2.4) in MA. Yn~E02.0 at tens of kJ to Yn~E00.84 at MJ level (up to 25MJ) and Ysxr = 8.3x103 Ipinch3.6; Ysxr = 6x102 Ipeak3.2; Ipeak (0.1 to 2.4), Ipinch (0.07 to1.3) in MA. Ysxr~E01.6 (kJ range) to Ysxr~E00.8 (towards MJ).

Keywords

dense plasma focus, plasma focus scaling laws, neutron scaling laws, soft x-ray scaling laws, plasma focus modeling, Lee model code

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Lee, “Twelve years of UNU/ICTP PFF-A review,” IC/ 98/231 Abdus Salam ICTP, Miramare, Trieste, pp. 5–34, ICTP Open Access Archive, 1998, http://eprints.ictp.it/31/.
[2]	Y. Kato and S. H. Be, Applied Physics Letters, No. 48, pp. 686, 1986
[3]	E. P. Bogolyubov, V. D. Bochkov, V. A. Veretennikov, L. T. Vekhoreva, V. A. Gribkov, A. V. Dubrovskii, P. Ivanov Yu, A. I. Isakov, O. N. Krokhin, P. Lee, S. Lee, V. Ya Nikulin, A. Serban, P. V. Silin, X. Feng, and G. X. Zhang, “A powerful soft x-ray source for x-ray lithography based on plasma focusing,” Physica Scripta, Vol. 57, pp. 488– 494, 1998.
[4]	S. Lee, P. Lee, G. Zhang, X. Feng, V. A. Gribkov, L. Mahe, A. Serban, and T. K. S. Wong, IEEE Transactions on Plasma Science, No. 26, pp. 1119, 1998.
[5]	N. V. Filippov, T. I. Filippova, M. A. Karakin, V. I. Krauz, V. P. Tykshaev, V. P. Vinogradov, Y. P. Bakulin, V. V. Timofeev, V. F. Zinchenko, J. R. Brzosko, and J. S. Brzosko, IEEE Transactions on Plasma Science, No. 24, pp. 1215– 1223, 1996.
[6]	N. V. Filippov, T. I. Filippova, I. V. Khutoretskaia, V. V. Mialton, and V. P. Vinogradov, “Megajoule scale plasma focus as efficient X-ray source,” Physics Letters A, Vol. 211, No. 3, pp. 168–171, 1996.
[7]	Institute for Plasma Focus Studies, http://www.plasmafocus.net.
[8]	Internet Workshop on Plasma Focus Numerical Experiments (IPFS-IBC1), April 14–May 19, 2008, http://www.plasmafocus.net/IPFS/Papers/IWPCAkeynote2ResultsofInternet-basedWorkshop.doc.
[9]	S. Lee, “Radiative dense plasma focus computation package: RADPF,” http://www.intimal.edu.my/school/fas/UFLF/File1RADPF.htm, http://www.plasmafocus.net/IPFS/modelpackage/File1RA DPF.htm.
[10]	S. Lee, R. S. Rawat, P. Lee, and S. H. Saw, “Soft x-ray yield from NX2 plasma focus-correlation with plasma pinch parameters,” (to be published).
[11]	S. Lee and S. H. Saw, “Neutron scaling laws from numerical experiments,” Journal of Fusion Energy, No. 27, pp. 292–295, 2008.
[12]	S. Lee, “Current and neutron scaling for megajoule plasma focus machine,” Plasma Physics and Controlled Fusion, No. 50, 105005, (14pp), 2008.
[13]	S. Lee, S. H. Saw, P. C. K. Lee, R. S. Rawat, and H. Schmidt, “Computing plasma focus pinch current from total current measurement,” Applied Physics Letters, No. 92, 111501, 2008.
[14]	S. Lee and S. H. Saw, “Pinch current limitation effect in plasma focus,” Applied Physics Letters, No. 92, 021503, 2008.
[15]	S. Lee, P. Lee, S. H. Saw, and Rawat R S, “Numerical experiments on plasma focus pinch current limitation,” Plasma Physics and Controlled Fusion, No. 50, 065012 (8pp), 2008.
[16]	S. Lee, “Plasma focus model yielding trajectory and structure” in Radiations in Plasmas, B. McNamara, ed., World Scientific Publishing Co, Singapore, ISBN 9971- 966-37-9, Vol. 2, pp. 978–987, 1984.
[17]	S. Lee, et al, “A simple facility for the teaching of plasma dynamics and plasma nuclear fusion,” American Journal of Physics, No. 56, pp. 62–68, 1988.
[18]	T. Y. Tou, S. Lee, and K. H. Kwek, “Non perturbing plasma focus measurements in the run-down phase,” IEEE Transactions on Plasma Science, No. 17, pp. 311– 315, 1989.
[19]	S. Lee, “A sequential plasma focus,” IEEE Transactions on Plasma Science, Vol. 19, No. 12, pp. 912–919, 1991.
[20]	J. B. Ali, “Development and studies of a small Plasma focus,” PhD thesis, Universiti Teknologi Malaysia, Malaysia, 1990.
[21]	D. E. Potter, “The formation of high density z-pinches,” Nuclear Fusion, Vol. 18, pp. 813–823, 1978.
[22]	S. Lee and A. Serban, “Dimensions and lifetime of the plasma focus pinch,” IEEE Transactions on Plasma Science, Vol. 24, No. 3, pp. 1101–1105, 1996.
[23]	M. H. Liu, “Soft X-rays from compact plasma focus,” PhD thesis, NIE, Nanyang Technological University, Singapore, 2006, ICTP Open Access Archive: http://eprints.ictp.it/327/.
[24]	S. Bing, “Plasma dynamics and x-ray emission of the plasma focus,” PhD Thesis, NIE, Nanyang Technological University, Singapore, 2000, ICTP Open Access Archive: http://eprints.ictp.it/99/.
[25]	A. Serban and S. Lee, “Experiments on speed-enhanced neutron yield from a small plasma focus,” Journal of Plasma Physics, Vol. 60, Part 1, pp. 3–15, 1998.
[26]	M. H. Liu, X. P. Feng, S. V. Springham, and S. Lee, “Soft x-ray measurement in a small plasma focus operated in neon,” IEEE Transactions on Plasma Science, No. 26, pp. 135–140, 1998.
[27]	D. Wong, P. Lee, T. Zhang, A. Patran, T. L. Tan, R. S. Rawat, and S. Lee, “An improved radiative plasma focus model calibrated for neon-filled NX2 using a tapered anode,” Plasma Sources Science and Technology, No. 16, pp. 116–123, 2007.
[28]	S. Lee, 2000–2007, http://ckplee.myplace.nie.edu.sg/plas- maphysics/.
[29]	S. Lee, 2005, ICTP Open Access Archive: http://eprints. ictp.it/85/.
[30]	M. A. Mohammadi, S. Sobhanian, C. S. Wong, S. Lee, P. Lee, and R. S. Rawat, “The effect of anode shape on neon soft x-ray emissions and current sheath configuration in plasma focus device,” Journal of Physics D: Applied Physics, 42, 2009, 045203 (10pp).
[31]	Springham S V, Lee S and Rafique M S, “Correlated deuteron energy spectra and neutron yield for a 3 kJ plasma focus,” Plasma Physics Controlled Fusion, Vol. 42, pp. 1023–1032, 2000.
[32]	S. Lee, P. Lee, G. Zhang, X. Feng, V. A. Gribkov, M. Liu, A. Serban, and T. Wong “High rep rate high performance plasma focus as a powerful radiation source,” IEEE Transactions on Plasma Science, Vol. 26, No. 4, pp. 1119– 1126, 1998.
[33]	V. Siahpoush, M. A. Tafreshi, S. Sobhanian, and S. Khorram, “Adaptation of Sing Lee’s model to the Filippov type plasma focus geometry,” Plasma Physics Controlled Fusion, No. 47, pp. 1065–1072, 2005.
[34]	V. A. Gribkov, A. Banaszak, B. Bienkowska, A. V. Dubrovsky, I. Ivanova-Stanik, L. Jakubowski, L. Karpinski, R. A. Miklaszewski, M. Paduch, M. J. Sadowski, M. Scholz, A. Szydlowski, and K. Tomaszewski, “Plasma dynamics in the PF-1000 device under full-scale energy storage: II, Fast electron and ion characteristics versus neutron emission parameters and gun optimization perspectives,” Journal of Physics D: Applied Physics, No. 40, pp. 3592–3607, 2007.
[35]	J. D. Huba, Plasma Formulary page, No. 44, 2006.
[36]	S. Lee, S. H. Saw, P. Lee, and R. S. Rawat, “Numerical experiments on plasma focus neon soft x-ray scaling,” Plasma Physics and Controlled Fusion, No. 51, 105013 (8pp), 2009, Available at http://stacks.iop.org/PPCF/51/105013.
[37]	D. C. Gates, Proceedings of the 2nd International Conference on Energy Storage, Compression and Switching, Venice, No. 2, pp. 3239, Plenum Press, New York, 1983.
[38]	S. Lee, “Neutron yield saturation in plasma focus-A fundamental cause,” Applied Physics Letters, No. 95, 151503, First online 15 October 2009.
[39]	S. H. Saw, “Experimental studies of a current-stepped pinch,” PhD Thesis Universiti Malaya, Malaysia, 1991.
[40]	S. Lee, “A current-stepping technique to enhance pinch compression,” Journal of Physics D: Applied Physics, No. 17, pp. 733–739, 1984.