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.
Modelling toroidal rotation damping in ITER due to external 3D fields