The collisionality dependence of tokamak beta-limits

An interpretation of the collisionality dependence of beta(N), which has been observed in many tokamaks, is presented in terms of neoclassical tearing mode theory. Magnetic islands are predicted to be driven to large saturated widths by the perturbed bootstrap current, provided their width exceeds a certain threshold value. This width is of the order of the ion banana width for low collisionality plasmas, but is substantially larger in collisional plasmas (though still within the banana regime); below this threshold value the stabilizing ion polarization current causes an island to decay. Assuming that 'background' MHD events such as ELMs or sawteeth can provide an initial 'seed' magnetic island of width w greater than or similar to 2 cm (through toroidal coupling, for example) one can develop a model equation which retains the essential properties of neoclassical tearing mode theory and is able to reproduce many of the experimental trends associated with the reduced beta-limit.