Scaling the Shear-flow Stabilized Z-pinch to Reactor Conditions

We present a conceptual design along with scaling calculations for a pulsed fusion reactor based on the shear-flow-stabilized Z-pinch device. Experiments performed on the ZaP device [1], at the University of Washington, have demonstrated stable operation for durations of 20 usec at $\sim$100kA discharge current for pinches that are $\sim$1 cm in diameter and 100 cm long. The inverse of the pinch diameter and plasma energy density scale strongly with pinch current and calculations show that maintaining stabilization durations of $\sim$7 usec for increased discharge current ($\sim$15x) in a shortened pinch (10 cm) results in a pinch diameter of $\sim$200 um and plasma conditions that approach those needed to support significant fusion burn and energy gain (Ti$\sim$30keV, density$\sim$3e26/m$^{3}$, ntau$\sim$1.4e20 sec/m$^{3}$). Compelling features of the concept include operation at modest discharge current (1.5 MA) and voltage (40kV) along with direct adoption of liquid metals for at least one electrode---technological capabilities that have been proven in existing, commercial, pulse power devices such as large ignitrons.\\[4pt] [1] U. Shumlak, et. al., Nucl. Fusion 49 (2009) 075039.