Dynamic mode decomposition for plasma diagnostics and validation

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system with high fidelity. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the helicity injected torus with steady inductive (HIT-SI) magnetohydrodynamics. Importantly, the DMD produces interpretable, dominant mode structures, including a stationary mode consistent with our understanding of a HIT-SI spheromak accompanied by a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions across the domain of analyzed data.