Use of 3-D FDTD Method for Magnetic Field Diffusion Calculations in Complex Pinch Geometries

Summary form only given. MHD simulations for Z- and theta-pinches require the solution of the nonlinear magnetic field diffusion equation at every hydrodynamic time step. This can become a problem with "standard" solvers for such equations, given that the electrical conductivity, and hence the magnetic field diffusion coefficient, can vary by orders of magnitude through a plasma. The situation becomes worse in Eulerian MHD codes, where a computational cell can be totally emptied of plasma - the resulting vacuum region has essentially an infinite diffusion coefficient, requiring a near-zero time step. This last problem can be handled by using "flux-limited" transport, but the problem of small time steps remains. There is thus a need to develop solvers that can handle such variations in complex 3-D geometries. We have used the 3-D finite difference time domain (FDTD) method to handle such problems. This method directly updates Maxwell's curl equations in time, using an explicit technique, to yield the 3-D variation of electric and magnetic fields. It allows setting up of complex, multimaterial configurations. The problem of small time steps, governed by the Courant criterion and the speed of light, is handled by artificially increasing the free-space permittivity by a suitable factor. in this paper, we report on results obtained with this technique for the case of magnetic field diffusion in accelerating metallic liners in Z-pinch geometries relevant to magnetized target fusion. We examine two cases - one with cylindrical and another with quasi-spherical acceleration. The 3-D electromagnetic field yields the current density distribution through the liner as well as the support assembly, allowing accurate calculation of the electromagnetic forces and Joule heating. To our knowledge, this is the first time this powerful technique has been applied to Z-pinch simulation