Kinetic effects on the stability properties of field-reversed configurations. II. Nonlinear evolution

Results of three-dimensional hybrid simulations of the field-reversed configuration (FRC) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs. A wide range of s̄ values is considered, where the s̄ is the FRC kinetic parameter, which measures the number of ion gyroradii in the configuration. The linear and nonlinear stability of MHD modes with toroidal mode numbers n⩾1 is investigated, including the effects of ion rotation, finite electron pressure, and weak toroidal field. Low-s̄ simulations show nonlinear saturation of the n=1 tilt mode. The n⩾2 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to ion spin-up in the toroidal direction. Large-s̄ simulations show no saturation of the tilt mode, and there is a slow nonlinear evolution of the instability after the initial fast linear growth. Overall, the hybrid simulations demonstrate the importance of nonlinear effects, which are responsible for the saturation of instabilities in low-s̄ configurations, and also for the increase in FRC lifetime compared to MHD models in high-s̄ configurations.