  A Dense Plasma Focus (DPF) is a pulsed-power machine that electromagnetically
accelerates and cylindrically compresses a shocked plasma in a Z-pinch. The
pinch results in a brief (about 100 nanosecond) pulse of X-rays, and, for some
working gases, also a pulse of neutrons. A great deal of experimental research
has been done into the physics of DPF reactions, and there exist mathematical
models describing its behavior during the different time phases of the
reaction. Two of the phases, known as the inverse pinch and the rundown, are
approximately governed by magnetohydrodynamics, and there are a number of
well-established codes for simulating these phases in two dimensions or in
three dimensions under the assumption of axial symmetry. There has been little
success, however, in developing fully three-dimensional simulations. In this
work we present three-dimensional simulations of DPF reactions and demonstrate
that 3D simulations predict qualitatively and quantitatively different behavior
than their 2D counterparts. One of the most important quantities to predict is
the time duration between the formation of the gas shock and Z-pinch, and the
3D simulations more faithfully represent experimental results for this time
duration and are essential for accurate prediction of future experiments.
