  This work presents scaling relations for the peak thermal pressure and
stagnation time (over which peak pressure is sustained) for an imploding
spherical plasma liner formed by an array of merging plasma jets. Results were
derived from three-dimensional (3D) ideal hydrodynamic simulation results
obtained using the smoothed particle hydrodynamics code SPHC. The 3D results
were compared to equivalent one-dimensional (1D) simulation results. It is
found that peak thermal pressure scales linearly with the number of jets and
initial jet density and Mach number, quadratically with initial jet radius and
velocity, and inversely with the initial jet length and the square of the
chamber wall radius. The stagnation time scales approximately as the initial
jet length divided by the initial jet velocity. Differences between the 3D and
1D results are attributed to the inclusion of thermal transport, ionization,
and perfect symmetry in the 1D simulations. A subset of the results reported
here formed the initial design basis for the Plasma Liner Experiment [S. C. Hsu
et al., Phys. Plasmas 19, 123514 (2012)].
