The influence of temperature gradients on the distribution of axial current in a large current Z-pinch implosion

General algebraic expressions for the tensor electrical conductivity and heat conductivity are presented that are needed in one-dimensional (1-D) magnetohydrodynamic modeling of Z-pinch implosions. The expressions contain both the ionization state and the magnetic field dependence of these quantities and generalize Braginskii's results. The ionization dependence is important in any description of a Z-pinch's implosion dynamics, since substantial ionization occurs during the course of the implosion. The tensor character of the electrical conductivity implies that axial currents are generated by radial temperature gradients in the presence of a Z-pinch's magnetic field. We find that these currents make contributions to the full current distribution that are comparable to the electric field generated currents. The effect of these temperature gradients on the full current distribution in a 1-D Z-pinch implosion is calculated by using the derived formulas for the electrical resistivity. The implosion we model is similar to the one that was found in an analysis of time-resolved X-ray data to give a good representation of the temperature gradients generated in a 90-wire, aluminum shot on the Saturn generator at the Sandia National Laboratories. [Phys. Rev. E 56, 3540 (1997)]. In the calculation, we find that, on axis, gradient-driven currents limit total current flow near the front surface of the plasma, causing a much larger current to flow in the plasma interior than otherwise and reducing the temperature gradients that would be calculated in their absence. The gradient structure of the plasma is changed because the modified current distribution produces a different set of j/spl times/B forces, which act on the plasma. These nonlinear magnetic field effects persist during the plasma's expansion from the axis following peak compression.