Re-appraisal and extension of the Gratton-Vargas two-dimensional analytical snowplow model of plasma focus evolution in the context of contemporary research

Abstract

Recent resurgence of interest in applications of dense plasma focus and doubts about the conventional view of dense plasma focus as a purely irrotational compressive flow have reopened questions concerning device optimization. In this context, this paper re-appraises and extends the analytical snowplow model of plasma focus sheath evolution developed by F. Gratton and J.M. Vargas (GV) (Energy Storage, Compression and Switching, Ed. V. Nardi, H. Sahlin, and W. H. Bostick, Eds., vol. 2. New York: Plenum, 1983, p. 353) and shows its relevance to contemporary research. The GV model enables construction of a special orthogonal coordinate system in which the plasma flow problem can be simplified and a model of sheath structure can be formulated. The Lawrenceville Plasma Physics (LPP) plasma focus facility, which reports neutron yield better than global scaling law, is shown to be operating closer to an optimum operating point of the GV model as compared with PF-1000.

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

“…This paper continues the earlier discussion of the (revised) Gratton-Vargas model [1,2] of the Dense Plasma Focus (DPF). In the first part of this series [1], the emphasis was on explaining the rationale for this model, its foundations and providing a glimpse into its reach. The discussion of Part I was limited to a time just before the current derivative singularity (CDS) and radial position of the model current sheath just short of the "pinch radius".…”

“…The traditional fascination with such kaleidoscopic view of DPF has blinded researchers to the possibility of a much simpler core of physics underlying this complex phenomenology. Against this backdrop, the fitting of current variation of four large facilities [3] using the formalism of the revised Resistive Gratton -Vargas (RGV) model [1,2] demonstrates, for the first time, the existence of such simple core of physics. 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.…”

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

“…Judging by the experience of the two DPF devices (NX2 at Singapore [11] and FF1 at Lawrenceville [12], USA) which have reported significantly higher neutron yield than devices of comparable energy by operating at higher than 10 mbar deuterium pressure, and numerical simulations with the Lee model at 60 torr [13] which also show increased neutron yield, one could expect orders of magnitude improvement in the yield of fusion neutrons (or other binary reactions) if efficient DPF operation could be achieved at deuterium pressures of 0.1-1 bar. This paper explores the design parameter space for such HPO-DPF operating with deuterium using the revised Resistive Gratton-Vargas (RGV) model [10,14,15] with a view to identify a practicable set of system parameters and their scaling.…”

Analytic model for the dynamic Z-pinch

“…25,26 These modifications consist essentially in the introduction of fitting parameters with little or no physical meaning, which cannot be assured to have a universal character and to apply to different experiments. 44 Regardless of the limitations of the SP and SL models, the availability of simple models like these is very useful because such models allow us to have a first approach to complex phenomena and can serve as a guide for the design and subsequent analysis of experiments or sophisticated numerical simulations.…”