Simulation Progress
New 1-D simulations performed by Dr. John Guillory and Mr. Lerner have indicated that the thermal–resistive instability alone will not generate filamentation in the early stages of the plasma focus discharge.
The thermal-resistive instability occurs when more current flows through one part of the plasma than another, causing the plasma electrons to heat up faster, which reduces the resistance of the plasma, causing still more current to flow. In the new simulation, a “hot” cell with more current was placed next to a “cold” cell with less current. The simulation modeled heat generation, current flow and heat flow between the two cells. In one case, an initial 1% difference in current flow was amplified by the instability to a 33% difference. However, as electron temperature increased, so did heat flow between the two cells, so the temperature difference then started to decrease. The fact that large differences in current flow did not occur and that the instability took as long as 60 ns to peak indicates that this instability may not do much to “seed” the development of the main pinch instability, caused by the magnetic forces on the plasma particles.
This indicates that it will be a good idea to seed the formation of the filaments by using a ring of small pins around the inner edge of the cathode plate, where the current first begins to flow. Since current will start from the sharp tips of the pins, there will be regions of higher and lower current density, giving the pinch instability a head start. We are now integrating these pins, which have also been used in other DPF design, into our drawings.
The next simulation, still 1D, will simulate all the physical processes, including the pinch forces, acting on a contracting filament, once formed. It will assume cylindrical symmetry, which greatly simplifies the electromagnetic calculations.

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