A new set of analytical formulae for the computation of the bootstrap current and the neoclassical conductivity in tokamaks

A new set of analytical formulae for calculating the bootstrap current and the neoclassical conductivity in tokamak experiments is presented. Previous works comparing the widely used Sauter model with results of recently developed numerical neoclassical solvers have shown the Sauter model to be inaccurate at higher collisionalities typical of tokamak edge pedestals and in the presence of impurities. Thus, its applicability, particularly for the analysis of the highly interesting and highly complex plasma edge, is limited. For a revised set of analytical formulae, the procedure to determine the analytical formulae described by Sauter is repeated with the more accurate and more reliable numerical code NEO [E. Belli, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. For the determination of the respective bootstrap current coefficient, the linearity of neoclassical transport is exploited. This new set of analytical formulae consists of the same analytical structure as the original set of analytical formulae published by Sauter [Phys. Plasmas 6, 2834 (1999); ibid. 9, 5140 (2002)] and also continues to use only three neoclassical key parameters: the fraction of trapped particles f trap, the collisionality ν σ *, and the effective charge number Z eff.