On the representation of dense plasma focus as a circuit element

Abstract

Space propulsion is unique among many proposed applications of the Dense Plasma Focus in being critically dependent on the availability of a scaling theory that is well-grounded in physics, in conformity with existing experimental knowledge and applicable to experimentally untested configurations. This paper derives such a first-principles-based scaling theory and illustrates its application to a novel space propulsion concept, where the plasma focus sheath is employed as a power density amplifying mechanism to transport electric energy from a capacitive storage to a current-driven fusion load. For this purpose, a Generalized Plasma Focus problem is introduced and formulated. It concerns a finite, axisymmetric plasma, driven through a neutral gas at supersonic speed over distances much larger than its typical gradient scale length by its azimuthal magnetic field while remaining connected with its pulse power source through suitable boundaries. The Gratton-Vargas equation is rederived from the scaling properties of the equations governing plasma dynamics and solved for algebraically defined initial (insulator) and boundary (anode) surfaces. Scaling relations for a new space propulsion concept are derived. This consists of a modified plasma focus with a tapered anode that transports current from a pulsed power source to a consumable portion of the anode in the form of a hypodermic needle tube continuously extruded along the axis of the device. When the tube is filled with deuterium, the device may serve as a small-scale version of magnetized liner inertial fusion (MAGLIF) that could avoid failure of neutron yield scaling in a conventional plasma focus.

Update on the Scientific Status of the Plasma Focus

“…Certain observations (discussed in Sections 4.2.3 and 5.1.1 (d)) are difficult to reconcile with this interpretation. The representation of a plasma focus as a circuit element has been examined from first principles [364] using Poynting's theorem. It is seen that representation of the plasma focus as a circuit element is not exactly congruent with the more accurate description in terms of fields (see Section 8.2.4).…”

“…This conjecture is put in doubt by the observed delay of more than 200 ns between the destruction of plasma column and the current derivative minimum. Recently, this issue has been discussed in a first-principles framework [364] but the question remains open. This aspect is discussed further in Section 8.2.4.…”

“…If the current derivative singularity is really because of the rise in inductance as the plasma radius decreases, then this delay cannot be explained. This question has been examined from a first-principles point of view [364]. Its gist is given below.…”

“…Comparing terms on the right hand side with expressions for electric power through standard electric circuit elements, it can be shown [364] that while terms labeled I and III are proper analogs of rate of change of energy in a suitably defined inductance and capacitance, there is no exact analog of the power associated with the motional impedance represented by the rate of change of that inductance. There is also no exact circuit theory analog of the last term that would be non-zero in case there are 3D magnetic and velocity fields, e.g., in the post pinch plasma.…”

Magnetic field induction and magnetic force distribution profiles in plasma focus discharge device

“…A short-duration, high-density, and condensed plasma is produced at the electrodes' centerline when a high-pulsed potential is applied to a low-pressure gas between coaxially-cylindrical electrodes. It can thus produce an intense beam of charged and neutral particles, as well as radiation emission [1,2].…”