 In the tokamak design the total field is a combination of the external toroidal field and the current-induced poloidal one, so the "beta poloidal" is sometimes used to compare the relative strengths of these fields.And as the external magnetic field is the driver of reactor cost, "beta external" is used to consider just this contribution.In a tokamak, for a stable plasma, formula_2 is always much smaller than 1 (otherwise it would collapse).