Global theory of microtearing modes in the tokamak pedestal

During the inter-ELM period, tokamak pedestals commonly display bands of magnetic fluctuations with discrete mode numbers. These ion scale fluctuations correlate with the evolution of the electron temperature profile and rotate in the electron direction. Though the observed spectrum is consistent with the microtearing mode (MTM), the conventional MTM theory does not explain the discrete nature of the fluctuations. In fact, due to the many rational surfaces present in the steep gradient region, conventional theory predicts a broadband of magnetic fluctuations. Here we extend the conventional local theory of the MTM to include the global variation of the temperature and density profiles. The offset between the rational surface and the location of the pressure gradient maximum emerges as a crucial parameter for MTM stability. Our extended theory predicts that an interaction of pressure and magnetic shear profiles is what leads to the n (the toroidal mode) number discrimination. Our predictions match observations on the Joint European Torus. Armed with these new insights from linear theory, we extend our investigation by constructing a weak turbulence model for the coupling, nonlinear evolution, and saturation of this unstable set of pedestal microtearing modes.