Self-consistent equilibrium calculation through a direct variationaltechnique in tokamak plasmas

Abstract

A self-consistent equilibrium calculation, valid for arbitrary aspect ratiotokamaks, is obtained through a direct variational technique that reducesthe equilibrium solution, in general obtained from the 2D Grad-Shafranovequation, to a 1D problem in the radial flux coordinate ρ. The plasmacurrent profile is supposed to have contributions of the diamagnetic,Pfirsch-Schlüter and the neoclassical ohmic and bootstrap currents. Aniterative procedure is introduced into our code until the flux surfaceaveraged toroidal current density ⟨JT⟩, converges towithin a specified tolerance for a given pressure profile and prescribedboundary conditions. The convergence criterion is applied between the⟨JT⟩ profile used to calculate the equilibriumthrough the variational procedure and the one that results from theequilibrium and given by the sum of all current components. The ohmiccontribution is calculated from the neoclassical conductivity and from theself-consistently determined loop voltage in order to give the prescribedvalue of the total plasma current. The bootstrap current is estimatedthrough the full matrix Hirshman-Sigmar model with the viscositycoefficients as proposed by Shaing, which are valid in all plasmacollisionality regimes and arbitrary aspect ratios. The results of theself-consistent calculation are presented for the low aspect ratio tokamakExperimento Tokamak Esférico. A comparison among different modelsfor the bootstrap current estimate is also performed and their possiblelimitations to the self-consistent calculation is analysed.