H-mode theory (Shaing and Crume Jr 1989 Phys. Rev. Lett. 63 2369) is e
xtended to include realistic effects such as charge-exchange momentum
loss and the magnetic stresses. Local critical plasma parameters for t
he onset of the bifurcation are obtained and can be compared quantitat
ively with experimental measurements. It is concluded that local criti
cal parameters are more meaningful in quantifying H-mode transition th
an the global power threshold scaling law.