Proper orthogonal decomposition and Galerkin projection for a three-dimensional plasma dynamical system

A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of sheer flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.