Comparison of bootstrap current and plasma conductivity models applied in a self-consistent equilibrium calculation for tokamak plasmas

Abstract

Different bootstrap current formulations are implemented in a self-consistent equilibrium calculation obtained from a direct variational technique in fixed boundary tokamak plasmas. The total plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch–Schlüter, and the neoclassical Ohmic and bootstrap currents. The Ohmic component is calculated in terms of the neoclassical conductivity, compared here among different expressions, and the loop voltage determined consistently in order to give the prescribed value of the total plasma current. A comparison among several bootstrap current models for different viscosity coefficient calculations and distinct forms for the Coulomb collision operator is performed for a variety of plasma parameters of the small aspect ratio tokamak ETE (Experimento Tokamak Esférico) at the Associated Plasma Laboratory of INPE, in Brazil. We have performed this comparison for the ETE tokamak so that the differences among all the models reported here, mainly regarding plasma collisionality, can be better illustrated. The dependence of the bootstrap current ratio upon some plasma parameters in the frame of the self-consistent calculation is also analysed. We emphasize in this paper what we call the Hirshman–Sigmar/Shaing model, valid for all collisionality regimes and aspect ratios, and a fitted formulation proposed by Sauter, which has the same range of validity but is faster to compute than the previous one. The advantages or possible limitations of all these different formulations for the bootstrap current estimate are analysed throughout this work.