Bootstrap current fraction scaling for a tokamak reactor design study

• New bootstrap current fraction scalings for systems codes were derived by solving the Hirshman–Sigmar model.
• Nine self-consistent MHD equilibria were constructed in order to compare the bootstrap current fraction values.
• Wilson formula most successfully predicted the bootstrap current fraction, but it requires current density profile index.
• The new scaling formulas and IPDG accurately estimated the fBS values for the normal and weakly reversed shear tokamaks.

We have derived new bootstrap current fraction scalings for systems codes by solving the Hirshman–Sigmar model, which is valid for arbitrary aspect ratios and collision conditions. The bootstrap current density calculation module in the ACCOME code was used with the matrix inversion method without the large aspect ratio assumption. Nine self-consistent MHD equilibria, which cover conventional, advanced and spherical tokamaks with normal or reversed shear, were constructed using numerical calculations in order to compare the bootstrap current fraction values with those of the new model and all six existing models. The Wilson formula successfully predicted the bootstrap current fraction, but it requires current density profile index for the calculation. The new scaling formulas and IPDG accurately estimated the bootstrap current fraction for the normal and weakly reversed shear tokamaks, regardless of the aspect ratio. However, none of the existing models except the Wilson formula can accurately estimate the bootstrap current fraction for the reversed shear tokamaks, which is promising for the advanced tokamak operation mode.