The systematics of magnetic fluctuations resulting from the nonlinear evolution of high‐&bgr;plong parallel wavelength resistive magnetohydrodynamic modes are studied for circular tokamak plasmas with a free boundary. Large‐amplitude fluctuations cause increased magnetic field stochasticity with increasing &egr;&bgr;p. These fluctuations, when coupled to an anomalous energy loss mechanism, may lead to &bgr;psaturation with respect to total input power.