Self-similar z-pinch equilibria in the unmagnetized regime, and their role in pinch evolution

New self-similar time-dependence z-pinch equilibria, valid for an unmagnetized plasma, are described. They assume a current rising as I ∝ t1/3, and thus exactly satisfy pressure balance. It is shown that these equilibria have a maximum radius, and that the equilibrium profiles differ considerably from well known magnetized plasma self-similar solutions. One-dimensional simulations show that, although the latter act as attractors, the existence of two distinct classes of self-similar equilibria ensures, firstly, that convergence to the magnetized plasma self-similar state is not perfect, and, secondly, that the transition to the magnetized regime is accompanied by an increase in pinch radius. Variations of the value of the Coulomb logarithm also give rise to a slow expansion of the pinch. (author)