Field-reversed configurations (FRC) exhibit several remarkable symmetrical properties. In the idealized FRC, Bz at the geometric axis and separatrix are of the same value but have opposite signature. The total poloidal flux at the inner field-lines (geometric axis to the O-point) is equal to that of the outer field-lines (O-point to the separatrix), which perfectly cancels out so that there remains zero flux at the separatrix. With these properties, a semi-analytical model of the radial profile is constructed. The symmetric (SYM) model begins with an analytical description of the current density profile j θ(r) having symmetric features. The model then takes into account of finite current at the separatrix that brings in asymmetric features. It is the combination of these two attributes, which determine the radial profile for the SYM model. This gives a generalized description that is applicable to a wide range of FRC settings for peaked and hollow current density profiles. Comparisons are made with the well-known rigid rotor (RR), two-point equilibrium (2PE), and Cobb et al model for two cases: (1) FRC behaves more symmetrically for conditions when Bz at the geometric axis (Bs) is almost equal to Be, and (2) asymmetric when Bs is lower than Be. A possible equilibrium profile for high performance FRCs at Be = 0.5 T is also presented.
The effect of rigid electron rotation on the Grad–Shafranov equilibria of a class of FRC devices