[en] In this paper, we show certain formulas for double series involving hyperbolic functions which come from the well-known transformation formula, namely Jacobi’s identity for the classical theta function. These can be regarded as relevant analogues of formulas given in the previous papers.

[en] The first section of this paper explores the consequences of the hypothesis that ZETA has produced a pinched discharge stabilized by a trapped axial field. The second section considers what happens if the stability condition is violated. The third section discusses the transport coefficients, which have a vital role in the heating of the discharge and in preserving the stable configuration

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[en] ZETA is an experimental apparatus for studying the pinched ring discharge as a possible method of producing controlled thermonuclear power. The principle of this method is that the self-magnetic field of the discharge current isolates the plasma from the walls of the discharge tube. The present paper reports the principal mechanical and electrical parameters, the performance as an electrical circuit, and our present knowledge of the physical characteristics of the plasma

[en] The Zeta method for the calibration of fission-track dating against other radiometric dating techniques has been described by Hurford and Green (1983). In this paper, the data for the Zeta calibration were obtained using 4π -Conversion Procedure (Suzuki et. al., 1984). The preliminary Zeta value determined from this work was found to be 224.52 ± 38.73, showing significant difference from values obtained by workers elsewhere using equivalent standard glass dosimeter. Factors that might have contributed to such discrepancy are discussed. From this study and work done by other fission-track workers, it is obvious that a wide range of Zeta values are in common use. However consistency in track-counting remains the prime factor for getting reliable ages for unknown samples

[en] It is well known both in early Z-pinch experiments and more recently in plasma focus experiments that highly accelerated ion beams are formed, this being inferred from the axial centre-of-mass motion of the neutrons produced by nuclear reactions. Two acceleration mechanisms are discussed here. The first, proposed in ref. 1, concerns the acceleration of ions across an electrostatic sheath adjacent to the anode, this sheath having a thickness less than an ion Larmor radius but greater than an electron Larmor radius. The electrons in the sheath, being magnetised, have a cExB/B₂ drift through which the Jsub(r)Bsub(THETA) force is provided to satisfy momentum conservation. The second is a new mechanism arising from the occurrence of a violent m=0 instability, and relies on large ion Larmor radius effects. It is shown that the inclusion of the Hall terms and finite ion Larmor radius (FLR) terms in the MHD equations removes the mirror symmetry each side of an m=0 neck. A detailed consideration of particle orbits during the formation of the highly compressed neck shows that on the cathode side of the neck an energetic ion beam is formed close to the axis, whilst on the anode side an equal and opposite momentum is distributed among a larger number of ions throughout the cross-section. (orig.)

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[en] A seven-chord infrared interferometer is used to study plasma density fluctuations during the formation phase in the ZT-40 toroidal pinch device. The mean quantities are found to depend systematically on the level of magnetic shear in the pinch discharge, in a manner which suggests that the density disturbances are elongated structures oriented parallel to the local magnetic field. The spatial correlation results are compared with earlier work on the Zeta device. (author)

[en] A detailed description of the ongoing high density Z-pinch experiments at Los Alamos is given. A review of past dense experiments is included. A model for a dense Z pinch as a high-Q, low yield, reactor system is presented. (orig.)