Comparison of the effects of realistic flux surface models on calculations of plasma asymmetries in DIII-D

Abstract

Several methods are presented for improving upon the traditional analytic “circular” method for constructing a flux-surface aligned curvilinear coordinate system representation of equilibrium plasma geometry and magnetic fields, and the most accurate Asymmetric Miller method is applied to calculations of poloidal asymmetries in plasma density, velocity, and electric potential. Techniques for developing an orthogonalized coordinate system from a general curvilinear representation of plasma flux surfaces and for representing the poloidal component of the magnetic field in the orthogonalized curvilinear system are developed generally, in order to be applied to four plasma flux-surface models. The formalism for approximating flux surfaces originally presented by Miller is extended to include poloidal asymmetries between the upper and lower plasma hemispheres, and is subsequently shown to be more accurate at fitting the shapes of flux surfaces calculated using EFIT than both the traditional “circular” model and two alternative curvilinear models of comparable complexity based on Fourier expansions of major radius, vertical position, and minor radius. Applying the coordinate system orthogonalization technique to these four models allows for calculations of the poloidal magnetic field which, upon comparison to a calculation of the poloidal field performed in a Cartesian system using the experimentally based EFIT prediction for the Grad-Shafranov equilibrium, demonstrates that the asymmetric “Miller” model is also superior to other methods at representing the poloidal magnetic field. A system of equations developed by representing the poloidal variations of velocity, density, and electric potential using O(1) Fourier expansions in the flux-surface averaged neoclassical plasma continuity and momentum balances is solved using several variations of both the “Miller” and “circular” curvilinear models to set geometric scale factors, illustrating the effects that these improvements in geometric modeling have on tokamak fluid theory calculations.