Identification of new MHD mechanisms responsible for plasma performance-setting in tokamaks and the use of analytic theory for informing and improving numerical models

Tokamak plasma performance is significantly limited by long-wavelength MHD instabilities. Despite these modes being a necessary condition for good plasma operation, they are subtle, leading to mistakes being made in both analytical and numerical approaches to their modelling. For pressure driven instabilities, the stabilising role of ordinarily dominant effects such as magnetic field line bending and compression are typically very small, and as such, many apparently weak effects are critical. It is for this reason that realistic geometry, as defined by the boundary conditions of the laboratory plasma, finite beta effects, equilibrium flows, and kinetic corrections typically determines plasma stability. This presentation documents the role that analytic theory plays in understanding linear and nonlinear MHD instabilities, and in informing codes of their errors, and advising improved models. Alternative calculations of nonlinearly saturated instabilities are presented, and their virtues and applications are compared. Showcased are the effects of parallel magnetic field fluctuations, centrifugal corrections associated with strong toroidal flows, and the continuum damping of internal kink modes and Kelvin Helmholtz-like modes due to respectively zonal and geodesic acoustic modes. Finally, after the review of the aforementioned topics, a model will be presented which is consistent with tokamak hybrid scenarios where the plasma ceases to diffuse over resistive confinement timescales. An ideal nonlinear MHD model is offered as an alternative to the flux pump hypothesis which has recently excited some in the magnetic fusion community for enabling high-performance sawtooth-avoiding plasma operation.