Generalized radial profile of field-reversed configurations based on symmetrical properties

Abstract

Field-reversed configurations (FRC) exhibit several remarkable symmetrical properties. In the idealized FRC, B z 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 B z at the geometric axis (B s ) is almost equal to B e , and (2) asymmetric when B s is lower than B e . A possible equilibrium profile for high performance FRCs at B e = 0.5 T is also presented.

Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

“…The NUCTE-III device geometry parameters are used, with a length of 1.5 m and a maximum radius of 0.17 m as described in details in reference [25]. The 2D equilibrium of the MRR-1 model shown in figure 8 is obtained using 16)- (18). A detailed description of the code and 2D FRC equilibrium fitting (FRC-EFIT) using the MRR-1 and -2 models will be presented in future publications.…”

“…As shown above, the pressure profile determines the FRC equilibrium. Various analytical pressure profile models such as the (extended) Hill's vortex [12,13], rigid-rotor (RR) [1,14], extended Solov'ev [15], 2PE (two-point equilibrium) [16,17], and symmetric (SYM) [18] models have been proposed as functions of r for theoretical and experimental purposes. In numerical simulations, dozens of pressure expressions for the numerical solution of G-S equation have been proposed [3,4,19,20].…”

A new tool GSEQ-FRC for two-dimensional field-reversed configuration equilibrium

“…However, non-perturbative internal magnetic field measurement is still difficult. Therefore, theoretical/model equilibrium calculations are particularly important in the study of FRCs, where many equilibrium models such as rigid-rotor (RR) [1], two-point equilibrium [11], three-point equilibrium [12], symmetric [13] and modified rigid-rotor (MRR) [6] are proposed.…”

A new tool for two-dimensional field-reversed configuration equilibrium study

“…However, non-perturbative internal magnetic field measurement is still difficult. Therefore, theoretical/model equilibrium calculations are particularly important in the study of FRCs, and many equilibrium models such as Rigid-Rotor (RR) [1], two-point equilibrium (2PE) [11], three-point equilibrium (3PE) [12], symmetric (SYM) [13] and Modified Rigid-Rotor (MRR ) [6] are proposed.…”