[en] The magnetic fluctuations resulting from the nonlinear evolutions of high-β/sub p/ long parallel wavelength resistive MHD modes are studied for tokamak plasmas with a free boundary. Large amplitude fluctuations cause increased magnetic field stochasticity with increasing epsilonβ/sub p/. These fluctuations, when coupled to an anomalous energy loss mechanism, may lead to β/sub p/-saturation in total input power. Modeling of the H-mode with a line tied plasma to the divertor plate shows substantial stabilization of edge instabilities. Calculations for recent high β noncircular discharges in DIII compare well with experimental observations