Ideal hydrodynamic scaling relations for a stagnated imploding spherical plasma liner formed by an array of merging plasma jets

TL;DR

This paper derives ideal hydrodynamic scaling relations for peak thermal pressure and stagnation time in a spherical plasma liner formed by merging jets, based on 3D simulations, providing insights for plasma liner design.

Contribution

It introduces new scaling relations for plasma liner parameters derived from 3D hydrodynamic simulations and compares them to 1D results, enhancing understanding of plasma liner behavior.

Findings

Peak thermal pressure scales linearly with number of jets, initial density, Mach number.

Stagnation time scales with initial jet length divided by initial velocity.

Differences between 3D and 1D results are due to thermal transport, ionization, and symmetry assumptions.

Abstract

This work presents scaling relations for the peak thermal pressure and stagnation time (over which peak pressure is sustained) for an imploding spherical plasma liner formed by an array of merging plasma jets. Results were derived from three-dimensional (3D) ideal hydrodynamic simulation results obtained using the smoothed particle hydrodynamics code SPHC. The 3D results were compared to equivalent one-dimensional (1D) simulation results. It is found that peak thermal pressure scales linearly with the number of jets and initial jet density and Mach number, quadratically with initial jet radius and velocity, and inversely with the initial jet length and the square of the chamber wall radius. The stagnation time scales approximately as the initial jet length divided by the initial jet velocity. Differences between the 3D and 1D results are attributed to the inclusion of thermal transport, ionization, and perfect symmetry in the 1D simulations. A subset of the results reported here formed the initial design basis for the Plasma Liner Experiment [S. C. Hsu et al., Phys. Plasmas 19, 123514 (2012)].