The field-reversed configuration (FRC) is a compact torus with little or no toroidal magnetic field. A theoretical understanding of the observed FRC equilibrium and stability properties presents significant challenges due to the high plasma beta, plasma flows, large ion gyroradius, and the stochasticity of the particle orbits. Advanced numerical simulations are generally required to describe and understand the detailed behavior of FRC plasmas. Results of such simulations are presented in this paper. It is shown that 3D nonlinear hybrid simulations using the HYM code [E. V. Belova et al, Phys. Plasmas7, 4996 (2000)] reproduce all major experimentally observed stability properties of elongated (theta-pinch-formed) FRCs. Namely, the scaling of the growth rate of the n=1 tilt mode with the S*E parameter (S* is the FRC kinetic parameter, E is elongation, and n is toroidal mode number), the nonlinear saturation of the tilt mode, ion toroidal spin-up, and the growth of the n=2 rotational mode have been demonstrated and studied in detail. The HYM code has also been used to study stability properties of FRCs formed by the counterhelicity spheromak merging method. A new stability regime has been found for FRCs with elongation E1, which requires a close-fitting conducting shell and energetic beam ion stabilization.

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