UW-CPTC 08-10 Exponential Growth of Nonlinear Ballooning Instability

Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially at the same linear growth rate globally in the intermediate nonlinear phase. This theoretical prediction is confirmed in direct MHD simulations of nonlinear ballooning instability growth in a tokamak. The Lagrangian compression, which serves as a measure of nonlinearity of the ballooning perturbation, is monitored in the simulation. When the Lagrangian compression becomes of order of unity, the instability enters the intermediate nonlinear phase. During this phase, the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate corresponding to the linear phase, despite the nonlinear amplitude of the perturbation.