Calculation of Boozer magnetic coordinates for multiple plasma regions (with either closed or open flux surfaces) connected by magnetic separatrices

摘要

Magnetic coordinates (psi(T)=radial label of flux surfaces, theta=poloidal, and phi=toroidal angle) are introduced in toroidal magnetoplasma equilibria in order to straighten the field lines [described by: theta-iota(psi(T))phi=constant on any flux surface, iota(psi(T)) being the rotational transform]. The simplest method for analyzing the ideal magnetohydrodynamic (MHD) stability expands the perturbed plasma displacement (xi) over right arrow in magnetic coordinates and solves the normal mode equation through one-dimensional (1D) radial finite elements. This paper extends the calculation of (Boozer) magnetic coordinates to simply connected equilibria that embed a magnetic separatrix, with regular X-points ((B) over right arrow not equal 0), and reach the symmetry axis, with singular magnetic X-points ((B) over right arrow =0). These configurations include multiple plasma regions, whose outermost one (surrounding plasma) is not composed by toroidal surfaces closed around a single magnetic axis. Two examples are chosen: (i) flux-core-spheromak (FCS) configurations, where the surrounding plasma is a screw pinch, with open flux surfaces; (ii) Chandrasekhar-Kendall-Furth (CKF) configurations, where it is a toroidal shell, carved by multiple toroidal plasma regions. This paper shows that a proper ordering of the radial coordinate psi(T), the requirement of continuity for theta and phi and an (iota) over bar matching condition (between neighboring mesh points on opposite sides of the connecting separatrix) resolve the ambiguities in the definition of magnetic coordinates in both CKF and FCS cases. However, a few metric coefficients diverge at the separatrices; therefore, often numerical MHD stability codes do not use magnetic coordinates there, but adopt local two-dimensional (2D) finite elements. This paper instead investigates all the divergences, in order to allow for the asymptotic analysis of (xi) over right arrow near the separatrices, with the purpose of maintaining the magnetic coordinate method and the 1D radial finite elements in the ideal MHD stability analysis. (C) 2005 American Institute of Physics.