Analytic spherical torus plasma equilibrium model

Abstract

An analytic spherical torus plasma equilibrium model is developed from a general solution to the Grad–Shafranov equation. The analytic model allows the calculation of axisymmetric plasma equilibria with arbitrary aspect ratio, elongation, triangularity, and diamagnetism. Using a numerical method, examples of optimized analytic equilibria are presented with plasma profiles similar to those of bootstrapped spherical tokamaks. Numerical results obtained from analytic equilibrium solutions for plasmas with aspect ratios A=1.4, elongations κ=3.0, and Troyon factors g=6.7 suggest that spherical tori can achieve toroidal beta values as large as βt≈35% at poloidal beta values βp≈1.53, with stable magnetic wells, W⩾0.

Analytical Solution of High <i>β</i>_pEquilibria with Natural Inboard Poloidal Null Configuration Obtained in the Spherical Tokamak QUEST

“…All these functions are obtained from the two basic surface functions U(ψ) and V(ψ) evaluated by numerical integration as described in ref. [2]. In ref.…”

“…The constants in the above equation can be expressed as functions of plasma geometrical parameters like, inverse aspect ratio ε, elongation k, triangularity δ [2].…”

“…However, a number of powerful yet simpler models to solve GSE analytically are described in refs. [1][2][3] and they have their inherent ability to choose geometrical parameters independently. We have here used the analytical solution discussed in ref.…”

“…To describe such high β p equilibria and to study its stability properties, analytical solution to GradShafranov equation (GSE) is often useful. Earlier work of Solov'ev [1] with a simple pressure and poloidal current profile is extended [2][3][4] by including more linear stream functions to describe high β p configuration. The issue of β p equilibrium limit has been addressed theoretically earlier [1][2][3][4].…”

“…Earlier work of Solov'ev [1] with a simple pressure and poloidal current profile is extended [2][3][4] by including more linear stream functions to describe high β p configuration. The issue of β p equilibrium limit has been addressed theoretically earlier [1][2][3][4]. Nevertheless, owing to the dearth of experimental demonstration of IPN configuration, comparison of such models with experimental data is far from adequate.…”