Nonquasineutral model of an equilibrium Z-pinch

A fundamentally new approach is proposed for describing Z-pinches when the pinch current is gov-erned to a large extent by strong charge separation, which gives rise to a radial electric field in the nonquasineutral core of the pinch. In the central pinch region with a characteristic radius of about \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$r_0 \sim \sqrt {J_0 /en_e c}$$ \end{document}, part of the total pinch current J0<J, is carried by the drifting electrons and the remaining current is carried by ions moving at the velocity viz∼c(2eZJ/mic3) in the peripheral region with a radial size of c/ωpi. In the nonquasineutral core of a Z-pinch, the radial ion “temperature” is on the order of ZeJ0/c. The time during which the non-quasineutral region exists is limited by Coulomb collisions between the ions oscillating in the radial direction and the electrons. Since the magnetic field is not frozen in the ions, no sausage instability can occur in the non-quasineutral core of the Z-pinch. In the equilibrium state under discussion, the ratio of the radial charge-separation electric field E0 to the atomic field Ea may be as large as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$E_0 /E_a \sim 137^2 (a_0 \omega _{pe} /c)\sqrt {J/J_{Ae} }$$ \end{document}, where a0 is the Bohr radius.