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

Abstract

Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally-unidirectional shock propagation in this coordinate system enables construction of a system of 7 onedimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.

Design Parameter Space for a High Pressure Optimized Dense Plasma Focus Operating with Deuterium

“…In this picture, there is no need for an instability-triggered plasma diode action to accelerate ions, in conformity with the fact that in many cases, there is no instability whatsoever and still the neutron yield is unaffected [28]. This is also in accordance with the neutron diagnostics [22] that reveals a toroidal motion of center of mass of reacting deuterons.…”

“…This paper attempts to provide a scaling theory, enabling future construction of machines operating in high pressure optimized mode. The scheme of constructing dimensionless conservation law equations [22] for the DPF predicts that the plasma density in the pinch phase should increase when the plasma focus operates efficiently at high fill density of deuterium. It also predicts occurrence of toroidally streaming energetic deuterium ions [22] without the mediation of instabilities or anomalous resistivity.…”

“…The scheme of constructing dimensionless conservation law equations [22] for the DPF predicts that the plasma density in the pinch phase should increase when the plasma focus operates efficiently at high fill density of deuterium. It also predicts occurrence of toroidally streaming energetic deuterium ions [22] without the mediation of instabilities or anomalous resistivity. If these two predictions are experimentally borne out in the case of HPO-DPF, the nuclear reaction rate may increase by orders of magnitude over that predicted by traditional models [18].…”

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 insights provided by the RGV model have been instrumental in providing unambiguous demonstration [10] of existence of lower and upper bounds on the velocity of DPF plasma current sheath (PCS) related to material properties of the fill gas arising out of fundamental principles of physics such as laws of conservation of mass, momentum and energy and ionization stability. A large body of previously unexplained data from many prestigious laboratories concerning existence of axial magnetic field and toroidally moving fast ions has been similarly shown, with crucial inputs from the RGV model [1,2], to be a natural consequence of conservation laws [11].…”

“…The scheme of constructing dimensionless variables mentioned above can be extended [11] to the equations governing plasma dynamics, in which the plasma density is normalized to the gas fill density and the plasma pressure is normalized to the magnetic pressure due to the instantaneous current at the anode radius. This scheme maps the 10 parameters describing a DPF facility -voltage V 0 , capacitance C 0 , static inductance L 0 , static resistance R 0 , gas pressure p 0 (or mass density 0 ρ ), anode radius a, insulator radius I R , cathode radius C R , anode length A L and insulator length I L on to 7 independent dimensionless parameters of the RGV model.…”