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Self-similar solutions for imploding z-pinch shells in magnetized plasmas

Published online by Cambridge University Press:  01 June 2009

Y. M. SHTEMLER  and
M. MOND
Y. M. SHTEMLER
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel (shtemler@bgu.ac.il, mond@bgu.ac.il, mondmichael@gmail.com)
M. MOND
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel (shtemler@bgu.ac.il, mond@bgu.ac.il, mondmichael@gmail.com)
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Abstract

Imploding z-pinch shells with total currents that are proportional to some power of time are investigated. Time-space separable self-similar solutions with cylindrical symmetry are explicitly obtained. The problem is treated asymptotically in high thermal conductivity within the model of magnetized resistive plasmas, while the ionization and radiation processes are ignored.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 3 , June 2009 , pp. 373 - 387
Copyright
Copyright © Cambridge University Press 2009

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References

Bud'ko, A. B., Kravchenko, Yu. and Uby, L. 1994 Exact solutions of the dissipative screw-pinch problem. Plasma Phys. Control. Fusion 36, 833–853.Google Scholar
Coppins, M., Culverwell, I. D. and Haines, M. G. 1988 Time dependent Z-pinch equilibria. Phys. Fluids 31, 2688–2694.Google Scholar
Coppins, M., Chittenden, J. P. and Culverwell, I. D. 1992 Self-similar Z-pinch equilibria in the unmagnetized regime, and their role in pinch evolution. J. Phys. D: Appl. Phys. 25, 178–187.CrossRefGoogle Scholar
Davara, G., Gregorian, L., Kroupp, E. and Maron, Y. 1998 Spectroscopic determination of the magnetic-field distribution in an imploding plasma. Phys. Plasmas 5, 1068–1076.Google Scholar
Deeba, F., Ahmed, K., Haseeb, M. Q. and Mirza, A. M. 2005 Finite-effect on the dynamics of double gas-puff staged pinch. Phys. Scr. 72, 399–403.CrossRefGoogle Scholar
Gregorian, L., Bernshtam, V. A., Kroupp, E., Davara, G. and Maron, Y. 2003 Use of emission-line intensities for a self-consistent determination of the particle densities in a transient plasma. Phys. Rev. E 67, 016404.Google Scholar
Gregorian, L., Kroupp, E., Davara, G., Fisher, V. I., Starobinets, A., Bernshtam, V. A., Fisher, A. and Maron, Y. 2005a Electron density and ionization dynamics in an imploding z-pinch plasma. Phys. Plasmas 12, 092704.CrossRefGoogle Scholar
Gregorian, L., Kroupp, E., Davara, G., Starobinets, A., Fisher, V. I., Bernshtam, V. A., Ralchenko, Yu. V., Maron, Y., Fisher, A. and Hoffmann, D. H. H. 2005b Electron-temperature and energy-flow history in an imploding plasma. Phys. Rev. E 71, 056402.Google Scholar
Kroupp, E., Osin, D., Starobinets, A., Fisher, V., Bernshtam, V., Maron, Y., Uschmann, I., Forster, E., Fisher, A. and Deeney, C. 2007 Ion-Kinetic-Energy Measurements and Energy Balance in a Z-Pinch Phys. Rev. Lett. 98, 115001.Google Scholar
Kruskal, M. and Schwarzchild, M. 1954 Some instabilities of completely ionized plasma. Proc. Royal Soc. London A 223, 348–360.Google Scholar
Lifshits, E. M. and Pitaevskii, L. P. 1981 Physical Kinetics. Oxford: Pergamon Press.Google Scholar
Ryutov, D. D., Derzon, M. S. and Matzen, M. K. 2000 The physics of fast Z pinches. Rev. Mod. Phys. 72, 167–223.Google Scholar
Shtemler, Y. M. and Mond, M. 2005 Asymptotic self-similar solutions for thermally isolated Z-pinches. J. Plasma Phys. 71, 267–287.Google Scholar
Shtemler, Y. M. and Mond, M. 2006 Nonlinear evolution of perturbations in Hall MHD Z-pinch plasmas. J. Plasma Phys. 72, 699–710.Google Scholar