Evolution of Electron Thermal Transport Through a Magnetic Relaxation Event in MST

Magnetic relaxation events known as sawteeth are a consistent feature of the 400kA standard discharges in MST. At the sawtooth crash, global particle and energy confinement change substantially. Within 0.5 ms the global energy confinement time decreases by a factor of two or more (from 2 ms to less than 1 ms), and the pressure and current profiles flatten. The electron thermal diffusivity ($\chi_e$) profile evolves on the time scale of the sawtooth cycle (6 to 8 ms) peaking just before the crash, then flattening and reaching a minimum after the crash. The relatively low $\chi_e$ in the core after the crash allows the flattened pressure and current profiles to slowly peak once again. A quantitative analysis of these transport quantities is directly dependent on the input power ($P=\int \mathbf{E}\cdot \mathbf{J} \mathrm{dV}$). By applying Faraday's law, to get the internal loop voltage, and then Poynting’'s theorem, $\mathbf{E}\cdot \mathbf{J}$, and thus the input power, can be determined. The internal loop voltage can be found by either a finite difference of a time series of equilibrium reconstructions or by reconstructing the time derivative of the Grad-Shafranov equation directly. We compare both methods to the simple Ohm’'s law approximation, $\mathbf{E}=\eta \mathbf{J}$, using an assumed resistivity profile.