Staged Z Pinch.

PHYSICS OF PLASMAS VOLUME 8, NUMBER 2 FEBRUARY 2001 Staged Z pinch for controlled fusion P. Ney and H. U. Rahman Institute of Geophysics and Planetary Physics, University of California, Riverside, California 92521 F. J. Wessel and N. Rostoker Department of Physics, University of California, Irvine, California 92717 共Received 11 January 2000; accepted 8 November 2000兲 A staged Z pinch is considered in which an annular plasma shell made of a high Z material like Kr implodes onto a coaxial plasma target made of a low Z material like deuterium or a deuterium– tritium mixture. The target plasma could be made either by exploding a cryogenically extruded fiber or by filling the annular shell with a gas puff or a plasma puff. Modeling is performed with a two-dimensional 共2D兲 radiation-MHD 共magnetohydrodynamic兲 code. A parameter study is made to determine the sensitivity of this configuration to initial conditions of the shell and the target plasmas. An axial magnetic field is essential for a stable implosion and efficient energy coupling to the final load. Using a 50–50 mixture of deuterium–tritium as a target plasma, the fusion energy gain is optimized by adjusting the initial parameters. The calculations are based on the parameters of the University of California Irvine Z-pinch facility which has a maximum energy storage of 50 kJ. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1339230兴 I. INTRODUCTION column becomes unstable in its final phase of implosion dur- ing stagnation, because of the rapid growth of magnetohy- drodynamic 共MHD兲 instabilities. These instabilities are usu- ally unavoidable in conventional Z pinches and have been observed in almost every Z pinch experiment. The most dan- gerous modes of MHD instabilities are the sausage (m⫽0) mode and the kink (m⫽1) mode that can virtually destroy the uniformity of the cylindrical plasma column. The upper limit on the growth time of these instabilities is the Alfve´n time scale ␶ A ⬇a/ v A , where a is the radius of the plasma column and v A is the Alfve´n velocity. Unless the stagnation time of the pinch is faster than the Alfve´n time scale, these instabilities will certainly appear and disrupt the pinch. Trap- ping an axial magnetic field inside the plasma column will develop an outward magnetic pressure which will hinder the growth of the sausage instability. On the other hand, an azi- muthal magnetic field outside the pinch with a trapped axial magnetic field inside the pinch can lead to a sheared mag- netic field profile that can easily stop the growth of the RT- instability provided it is maintained during the implosion. As a disadvantage, the trapping of a magnetic field inside the plasma column leads to a softer pinch. However, the axial magnetic field alone does not stabilize the kink or higher m modes, but these modes usually have a much higher growth time as compared to the stagnation time of a staged Z pinch. The chances of developing these modes in a fast pinch are very low. The staged Z pinch in general 13,14 corresponds to a wide range of configurations, e.g., Z–Z pinch, Z– ␪ pinch, 15 com- posite pinch, 16 nested wire array, 3 puff on puff, etc. All these configurations usually involve similar types of physical mechanisms for coupling energy from one load to another. Experiments have shown that these pinches are relatively stable and provide much better coupling of energy to the final load. In this paper we focus on one of the simplest of The conventional Z pinch consists of a simple cylindri- cal load which implodes due to a self generated azimuthal magnetic field produced by an axial current through the load. The current profile is usually in a pulsed form with a char- acteristic rise time determined by the circuit parameters. Al- though the Z pinch provides a mechanism for the direct con- version of electrical energy into thermal energy of the plasma, energy coupling is not very effective. This is prima- rily due to radiation losses and the unstable nature of the imploding plasma column. Both these effects become worse in machines which have relatively slow rising current pro- files. A new class of machine with an extremely fast current rise time (dI/dt⬇10 14 A/s), e.g., PBFAZ, 1 Saturn, 2 etc., has been developed to overcome some of these problems. Recent results have shown remarkable improvement, both in energy coupling and the stability of the imploding Z-pinch plasma column. In particular, on a 20 MA Z facility at Sandia Na- tional Laboratories, tungsten wire array implosions have generated x-ray powers of up to 280 TW 3 with a total radi- ated energy of 1.75 MJ, which was ⬇58% of the total input electrical energy. Modeling performed by the same code used in the present study has attributed this enhanced level of energy coupling to a lower level of growth of Rayleigh– Taylor instability. Z pinches are inherently unstable mainly due to Rayleigh–Taylor 共RT兲 instability which appears during the run-in phase of the pinch. The reason for the growth of this instability is the development of a steep density gradient across an accelerating interface between the plasma and the magnetic field. There are several ways to control or at least mitigate some of the most dangerous modes associated with RT-type instabilities. 4–12 Some of these methods have been successfully implemented on several facilities. Even if by some mechanism the RT-instability is controlled, the plasma 1070-664X/2001/8(2)/616/9/$18.00 © 2001 American Institute of Physics