Focus Fusion Society- LPP Simulation program releases early 1-D results, prepares for 2-D
and 3-D runs
Research initiated as collaboration between Focus Fusion Society mathematician Dr. Warwick
Dumas and Lawrenceville Plasma Physics, Inc. physicists Dr. John Guillory and Eric Lerner has released
preliminary 1-D results, which will be of interest to plasma focus scientists world–wide. The simulation,
of the formation of plasma filaments at the start of operation of a plasma focus device, shows the
interaction between two closely spaced filaments and gives indication to physicists of how the filaments
can best form to produce optimum fusion.
The simulation effort was initiated in 2010 when FFS’s Dr. Dumas in the UK and Henning Burdack
in Germany started to collaborate with an ongoing LPP simulation effort. The idea was to simulate the
formation, development and motion of the filaments of current that carry the electric pulse through the
plasma in a PF device. The aim was to model the electrons and ions as fluids, as is done in the widely
used magneto-hydrodynamic (MHD) approach, but to include more accurate physics than is allowed in
the MHD approximation.
The first stage was a 1-D simulation, taking the filament to be symmetric around its axis and only
simulating the radial distance from the axis. However, at each point complex equations would govern the
current flowing along the filament the motion of the ions and the electrons, their density and temperature
and the magnetic field strength. As in much such simulation, difficulties were encountered in the
simulations when the filament formed a shock wave, a sharp peak in density that is generating when the
hot plasma of the filament start to expand into the cool surrounding gas. It took much work, especially by
Dr. Dumas, to eliminate glitches that would make the calculations oscillate wildly near the shock front.
In early 2012, this work started to pay off as useful simulations were generated, showing the early
evolution of the filament as they expanded, before the magnetic fields that the current generated grew
strong enough to pinch the filaments back together again. What was most interesting was that the
simulation revealed how fast the filaments expanded and thus how much time it would be before they
bumped into each other, potentially disrupting themselves before the magnetic field organized and
isolated them. In the first video shown here, the graphs show the development of temperature (orange)
and density (black) of a filament. A shock wave moves outwards a then bumps into and is reflected from
an identical shock wave produced by nearing filaments. The reflection disrupts the filament at about
100 ns. In the scene video, the filaments are spaced farther apart and the disruption comes much later at
300 ns. LPP calculations indicate that in that later case, the filaments would already be moving so fast
they would outrace the shock wave from a neighboring filament and so end up isolated and smoothly
A scientific description of the simulation is included as a PDF document. The team expects to submit
a paper to a peer-reviewed journal shortly.
The simulation team is now moving toward a 2-D and full 3-D simulation that will allow them to
study the filaments as they move through the plasma, pinching to a higher density. Given the greater
complexity of these simulations, LPP has now hired Dr. Dumas as a consultant to allow him to work
full-time on the project. FFS will continue to participate in the project as needed and hopes that other
scientists will join it in the future.