Nernst and Ettinghausen effects in the dense Z-pinch: their impact upon equilibria and runaway electrons

Abstract

The effects of the Nerst term in Ohm's law and Ettinghausen heat flow are examined for the dense Z-pinch. The Ettinghausen term causes radial electron heat flow in the direction of j V-product B whereas the Nernst term redistributes the axial current density according to the radial electron temperature gradient. The effects of these two terms on Z-pinch equilibria are the eradication of both the surface peak in current and the associated surface maximum in electron temperature. In dense Z-pinches formed from solid fibres in vacuum, the plasma density must fall to zero at the edge. This means that near the edge the equilibration timescale exceeds the ohmic heating timescale and the electron and ion temperatures become decoupled. Two temperature simulations of such pinches show the electron temperature apparently becoming extremely large near the pinch surface. However, inclusion of the Ettinghausen and Nernst terms eradicates this problem. Therefore these terms are important in determining whether the threshold conditions for the onset of micro-instabilities are exceeded in the surface plasma of fibre Z-pinches. The Nernst and Ettinghausen effects arise from the velocity dependence of the collision frequency. The electrons in the energetic tail of the distribution function flow preferentially radially inwards due to an Ez/Btheta drift and, upon reaching the axis, become demagnetized and are free to run away with singular orbits about the local field null. The generation of electron beams by this mechanism will be particularly prevalent if runaway is assisted by a very low density on axis such as an in gas-puff pinches.