Numerical study of the formation, ion spin-up and nonlinear stability properties of field-reversed configurations

Results of three-dimensional (3D) numerical simulations of field-reversed configurations (FRCs) are presented. The emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n ≤ 1 tilt mode, where n is the toroidal mode number. The n ≤ 2 and n ≤ 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good qualitative agreement with the results from the SSX-FRC experiment. The simulations show the formation of an FRC in about 20-30 Alfvén times for typical experimental parameters. The growth rate of the n ≤ 1 tilt mode is shown to be significantly reduced compared with the MHD growth rate due to the large plasma viscosity and field-line-tying effects.