Asymptotic self-similar solutions for thermally isolated Z-pinches

The dynamics of thermally-isolated Z-pinches carrying power law in time total currents (∼ t^S) in magnetized resistive plasmas is studied. Time-space separable self-similar solutions with cylindrical symmetry are considered. The non-dimensional variables are chosen in a way that makes the problem consistent with the moderately resistive magnetohydrodynamic (MHD) model. For S {=} -1/5 and Lundquist number Lu > 1.5 a non-equilibrium solution is obtained in addition to the conventional solutions for either exact, S {=} ±1/3, or asymptotic, Lu {=} ∞, equilibria (the latter is homogeneously valid for long times only if S > -1/5). The problem is treated asymptotically for high dimensionless thermal-conductivity, which is proportional to the square root of the ion/electron mass ratio. To obtain a closure condition for the leading-order isothermal solution, the first-order terms in the energy equation are invoked. Radial profiles are found explicitly which depend on S for equilibrium, and on Lu for non-equilibrium solutions. The multiplicity of the self-similar solutions is investigated.