Applying Kelvin's method to plasma equilibrium and stability in the presence of shear-driven waves: Modal vs. Nonmodal evolution*

After decades of allowing the “non-normal” effects, introduced by gradients and shear, to evade the lens of generic time-asymptotic normal-mode (and, consequently, exponential time-dependence) stability analysis; the plasma community is adopting a new “nonmodal stability theory” paradigm for describing transience and inhomogeneity in fluid-like flows, following the hydrodynamical communities. Applying this new paradigm to DIII-D observations is the focus of the poster. 

We survey the system of plasma equations derived in a frame co-moving with the mean plasma flow (Kelvin’s frame). If spatial-Fourier harmonic structure is assigned to a perturbation so described, then non-exponential transient growth is a consequence of the flow-shear-induced non-normality, as are otherwise-overlooked time-dependent properties of the eigenmode. In particular, nonmodal behavior of drift wave instabilities is presented and compared to the normal mode analysis, scenarios relevant to fusion plasmas and anomalous transport experiments. 

Any nonstationary phenomenon observed in tokamak plasma is potentially influenced by nonmodal behavior. We analytically describe examples and contrast the modal and nonmodal interpretations of the observations. We also identify nonmodal clues in the data and document the pertinent experimental parameters. We confirm past predictions and find that modal and nonmodal approaches convey vastly dissimilar dynamics, independent of the stability or instability of the plasma.