Book Description

The sawtooth crash is a hazardous, disruptive phenomenon that is observed in tokamaks whenever the safety factor at the magnetic axis is below unity. Recently, Tokamak Test Fusion Reactor (TFTR) experimental data has revealed interesting features of the dynamical pressure evolution during the crash phase. Motivated by the experimental results, this dissertation focuses on theoretical modeling of the finite pressure effects on the nonlinear stage of the sawtooth crash. The crash phase has been studied numerically employed a toroidal magnetohydrodynamic (MHD) initial value code deduced from the FAR code. For the first time, by starting from a concentric equilibrium, it has been shown that the evolution through an m/n = 1/1 magnetic island induces secondary high-n ballooning instabilities. The magnetic island evolution gives rise to convection of the pressure inside the inversion radius and builds up a steep pressure gradient across the island separatrix, or current sheet, and thereby triggers ballooning instabilities below the threshold for the axisymmetric equilibrium. Due to the onset of secondary ballooning modes, concomitant fine scale vortices and magnetic stochasticity are generated. These effects produce strong flows across the current sheet, and thereby significant modify the m = 1 driven magnetic reconnection process. The resultant interaction of the high-n ballooning modes with the magnetic reconnection process is discussed.