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

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.

Accepted for publication in Physics of Plasmas on 20th August 2014

Cited by in corpus (5)

• Axial magnetic field and toroidally streaming fast ions in the dense plasma focus are natural consequences of conservation laws in the curved axisymmetric geometry of the current sheath
• Re-appraisal and extension of the Gratton-Vargas two-dimensional analytical snowplow model of plasma focus - Part II: Looking at the singularity
• Re-appraisal and extension of the Gratton-Vargas two-dimensional analytical snowplow model of plasma focus - III: Scaling theory for high pressure operation and its implications
• The Generalized Plasma Focus Problem and its Application to Space Propulsion
• On the failure of neutron yield scaling in the Dense Plasma Focus