LPP simulation team to participate in Dense Z-Pinch Conference in August

Lawrenceville Plasma Physics� simulation team (John Guillory, David Voss and Eric Lerner) has been developing an advanced computer simulation of the focus fusion process.  They will present a paper on the subject at the International Dense Z-Pinch Conference in Alexandria, Virginia.  The paper abstract is below.

This conference occurs every few years, attracting dense plasma focus researchers from around the world. It will be a good opportunity for the researchers to catch up on each others� work and discuss common problems.

The paper will discuss the formation of the filaments in the early stages of the focus fusion process. As a current builds up within the dense plasma focus, the plasma sheath carrying the current breaks up into filaments.  This starts the first of a series of instabilities that compress the plasma to high density. Guillory and colleagues have calculated that the �thermal-resistive instability� can pinch the electron currents together faster than the �pinch effect� itself. The thermal-resistive instability occurs when electrons start to bunch up slightly from random fluctuation. The resistance of the plasma causes it to heat up more in these slightly bunched regions.  The additional heating reduces the resistance of the plasma.  As resistance falls in these regions the current increases, driving a feedback loop of more heating, lower resistance, more current and so on until the electrons are tightly bunched into filaments.

The pinch effect, which is caused by the interaction of currents with magnetic fields, pulls the heavier ions into the filaments.  Ions drifting parallel to the electron filaments are pushed towards them as the ions cross the circular magnetic field lines around the filaments. (Magnetic force pushes at right angles both to the magnetic field lines and to the direction of motion.)  As the ions move inwards, interaction with helical magnetic field lines starts them revolving around the filament axis, producing the tiny vortices that give the filaments stability.

The team has also overcome a snag that was holding up the development of the simulation.  In the simulation, a model of the external circuit (including the capacitors and switches) is connected to the currently-2-D simulation of the plasma inside the plasma focus electrodes. When the simulation was run, however, the current in the device rose far faster than actually occurred in experiments. In May this problem was solved and preparation is under way to use the 2-D simulation to feed a limited 3-D simulation to model filament formation.

Abstract for Dense Z-Pinch Conference

Theory of Electron Current Filamentation Instability and Ion Density Filamentation in the Early Development of DPF Discharge*

John Guillory - George Mason University School of Computational Sciences, retired

David V. Rose - Voss Scientific, Albuquerque NM 87108

Eric J. Lerner - Lawrenceville Plasma Physics, West Orange NJ 07052

Our 2D kinetic simulation of the initial stages of plasma formation in a dense plasma focus and other�s simulations [1] show the formation, in a few tens of nanoseconds, of a dense layer of plasma (ne ~ 10 18 cm -3, Te ~ 3 eV) in a thin layer surrounding the insulator-covered central anode of the focus device, and carrying axially-directed current at rather high current density.

Earlier work on the filamentation of dense cathode plasma in high-power diodes [2] seems to indicate that the anode plasma current layer in a DPF device could be subject to the same instability, creating a growth of axially-directed filaments in the current density.  The growth rate for resistive-thermal-driven filamentation, e.g. at 30 torr and ~3 eV electron temperature, exceeds that due to non-thermal current (JxB) driving, and is determined by electron dynamics [ibid], so its evolution is quicker than the response-time of the ions.

Nonetheless, with such a growing current-density perturbation as a seed and its increasing rippling of the azimuthal magnetic field as a driver, the ions will eventually take part in the azimuthal bunching, forming filaments in the ion density as well.  The resistive-thermal-driven filamentation fields thus serve to �hurry up� the development of ion density filamentation, as shown approximately in the work presented here.  This theory predicts, for light ions, a relatively early (~250ns) development of visible filaments along the anode, perhaps even before the main run-down phase of the focus plasma motion, and these filaments may persist during the �liftoff� of the current layer to form the rundown phase of the plasma front.

*Work supported by Lawrenceville Plasma Physics, Inc.

Author contact:  jguillor at gmu dot edu

�Development of the Ionization Wave in the Breakdown of the Plasma Focus Device�, V. Yordanov, I. Ivanova-Stanik & A. Blagoev, J. Phys. D: Appl. Phys. 40, 2522 (2007)

�Thermal-Resistive Current Filamentation in the Cathode Plasma of a Pinch-Reflex Diode� V.K.Tripathi, P.F. Ottinger & J. Guillory, J. Appl. Phys. 54, 3043 (1983)