Alpha particle heating and ignition in an equilibrium Z-pinch

Pulsed power driven Z-pinches offer a low cost route to the high energy density states of matter required for controlled thermonuclear fusion energy. The susceptibility of Z-pinches to magneto-hydrodynamic instabilities, however, has to date limited their application as a fusion energy source. In this work, we examine the fusion properties of a Z-pinch under conditions of equilibrium pressure balance and in the absence of the effects of MHD instability, in order assess whether in this hypothetical situation Z-pinches can provide a route to energy gain.

For the case of an Ohmically heated Z-pinch surrounded by vacuum and satisfying the Bennett relation, the plasma radius as a function of time can be determined using a simple energy balance model which considers compressional, Ohmic, and alpha particle heating as well as radiative and end losses. Results for a simple LCR circuit with a peak current of 4MA indicate that significant burn up fractions can be achieved fraction but highlight sensitivity to the fraction of alpha particle energy coupled back into the plasma and the level of anomalous resistivity, both of which prevent the onset of radiative collapse, but also reduce the fusion output by causing plasma expansion.

Using 1D extended MHD simulations coupled to a Monte-Carlo model of the magnetised alpha particles, we examine how the fraction of alpha energy deposited back into the plasma varies with the ratio of alpha Larmor radius to pinch radius. We also examine the effects of anomalous resistivity localised to the pinch surface and how this changes the shape of the plasma profiles.