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Two-Dimensional Magnetohydrodynamic Model for the Dense Plasma Focus of A Z Pinch

  • V. F. D’yachenko
  • V. S. Imshennik
Part of the Reviews of Plasma Physics book series (ROPP)

Abstract

Earlier analysis of the transient plasma compression in a Z pinch makes use of the one-dimensional approximation [1]. All the MHD properties are assumed to be functions of the cylindrical radius r and the time t. The incoporation of dissipative processes on the basis of the classical transport theory yields a detailed description of the focusing effects of the collapse of the shock wave and the current sheet and also makes it possible to find the maximum plasma temperature and density near the pinch axis. A comparison of the quantiative results of the one-dimensional theory with the experimental results in a noncylindrical Z pinch leads to an important conclusion: The high velocity with which the plasma collapses to the axis, and the associated high temperature, are reached experimentally as a result of a mechanism which ejects plasma from the region in which the plasma parameters reach their maximum values. This comparison shows that the typical ejection involves at least 90% of the mass per unit length of the plasma. This conclusion implies substantial deviations from the cylindrical symmetry assumed in the formulation of the one-dimensional problem. These deviations were observed in the very earliest experiments and were in fact deliberately produced by Filippov et al. [2] in order to raise the parameters of the compressed plasma and to increase the neutron yield. The term “noncylindrical Z pinch” was applied to these experiments even before theoretical work on the problem began. The conclusion noted above — that a substantial fraction of the plasma mass is ejected from the region in which the current sheet approaches the axis most closely — is interpreted more accurately as a reflection of the essential nature of the process rather than simply as evidence that the pinch is non-cylindrical. Experimentally, it is difficult to measure the ejected mass, although indirect conclusions regarding this effect (the observation of an axial plasma jet) were reached a long time ago [3]. Accordingly, a better theoretical description of the actual processes that occur in a noncylindrical Z pinch means that it is necessary to go beyond the one-dimensional MHD theory.

Keywords

Current Sheet Joule Heating Calculation Point Plasma Focus Neighboring Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • V. F. D’yachenko
  • V. S. Imshennik

There are no affiliations available

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