Magnetic design calculation and FRC formation modeling for the field reversed experiment liner

Integrated magnetic modeling and design are important to meet the requirements for (1) formation, (2) translation, and (3) compression of a field reversed configuration (FRC) for magnetized target fusion. Off-the-shelf solutions do not exist for many generic design issues. A predictive capability for time-dependent magnetic diffusion in realistically complicated geometry is essential in designing the experiment. An eddy-current code was developed and used to compute the mutual inductances between driven magnetic coils and passive magnetic shields (flux excluder plates) to calculate the self-consistent axisymmetric magnetic fields during the first two stages. The plasma in the formation stage was modeled as an immobile solid cylinder with selectable constant resistivity and magnetic flux that was free to readjust itself. It was concluded that (1) use of experimentally obtained anomalously large plasma resistivity in magnetic diffusion simulations is sufficient to predict magnetic reconnection and FRC formation, (2) comparison of predicted and experimentally observed timescales for FRC Ohmic decay shows good agreement, and (3) for the typical range of resistivities, the magnetic null radius decay rate scales linearly with resistivity. The last result can be used to predict the rate of change in magnetic flux outside of the separatrix (equal to the back-emf loop voltage), and thus estimate a minimum θ-coil loop voltage required to form an FRC