Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

TL;DR

This paper derives asymptotic scaling laws for the stagnation conditions of Z-pinch implosions, providing theoretical insights into how key plasma parameters depend on target design in ideal, instability-free scenarios.

Contribution

It introduces new asymptotic scaling laws for hydrodynamic and performance metrics of Z-pinch implosions in the high aspect ratio limit, enhancing understanding of their in-flight dynamics.

Findings

Derived scaling laws for density, temperature, and pressure at stagnation.

Quantified how x-ray emission and neutron yield depend on target parameters.

Provided theoretical framework for optimizing Z-pinch performance.

Abstract

Implosions of magnetically-driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically-driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the $(A, M)$ parametric plane, where $A$ is the in-flight aspect ratio and $M$ is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of $A\gg1$, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters.