A detailed study of the bootstrap current dependence upon some plasma profile parameters is performed and the relations between this intrinsic current with plasma equilibrium quantities such as internal plasma inductance, normalized and poloidal beta values, loop voltage and central safety factor are analysed within an equilibrium calculation valid for arbitrary aspect ratio tokamaks. In the equilibrium model, the total plasma current is given by the sum of the diamagnetic, Pfirsch–Schlüter and the neoclassical ohmic and bootstrap currents. We considered here only cases where the bootstrap current is generated by thermal particles and its profile is calculated by using the fitted formulae proposed by Sauter et al. Strong anisotropies and deep gradients (related to the presence of internal transport barriers) in the plasma pressure profiles are not taken into account. We have also accounted in our analysis for variations of Zeff, plasma elongation, triangularity, magnetic field and plasma current. This study is performed for the spherical tokamak Experimento Tokamak Esférico (ETE), and estimates obtained for the bootstrap current fraction (Ibs/Ip) are compared with a general empirical scaling law proposed by Hoang et al. Due to some deviations observed between Hoang's scaling and our results, a new expression for Ibs/Ip, given in terms of the normalized beta, cylindrical q, internal inductance parameter (li) and peakedness of pressure profile (cp), is proposed. Moreover, a second expression given as a combination of these parameters described in terms of βpol and cp is also presented. Both formulations were obtained from a least-square fitting upon about 350 ETE equilibria, in which some stability criteria were taken into account. Errors mostly up to the order of 10% are obtained when both expressions are compared with the equilibrium estimates for the bootstrap current in ETE.
Bootstrap currents in radiofrequency driven tokamak equilibria
Experimental evidence for the bootstrap current in a tokamak