Bounds imposed on the sheath velocity of a dense plasma focus by conservation laws and ionization stability condition

TL;DR

This paper derives bounds on the sheath velocity in dense plasma focus devices based on conservation laws and ionization stability, explaining its independence from device parameters and linking it to material constants.

Contribution

It establishes theoretical bounds on sheath velocity using conservation laws and ionization stability, clarifying its independence from device geometry and energy.

Findings

Sheath velocity bounds depend on material constants of the gas.

Conservation laws underpin the sheath velocity limits.

Velocity is independent of device geometry and capacitor impedance.

Abstract

Experimental data compiled over five decades of dense plasma focus research is consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and wind pressure resisting its motion. The resulting sheath velocity, or the numerically proportional drive parameter, is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of sheath velocity on device parameters, have their roots in local conservation laws for mass, momentum and energy coupled with the ionization stability condition. Both upper and lower bounds on sheath velocity are shown to be related to material constants of the working gas and independent of the device geometry and capacitor bank impedance.