Fluctuation-induced electromotive forces in current-driven tokamak sawtooth relaxation

We show via nonlinear MHD modeling a causal relationship between the fluctuation-induced 'dynamo' EMF and the cyclic equilibrium profile relaxation in current-driven tokamak sawtooth activity. Sawteeth have been of keen interest in tokamak research (see Jardin et al. 2020, Heidbrink & Victor 2020, e.g.), and we highlight the role of dynamo EMF in impulsive sawtooth magnetic relaxation. Using the NIMROD code, we perform nonlinear zero-beta 3D visco-resistive MHD simulations initialized with q profiles reaching just below 1 on axis. This leads to current-driven sawtooth cycles, originally described by Kadomtsev. A dynamo EMF, the spatial average of the nonlinear product of velocity and magnetic fluctuations in Ohm's law, arises naturally in the relaxation process. In 3D simulations, with fluctuations of multiple toroidal mode numbers included, the dynamo EMF is localized to the core near the q=1 surface and is correlated in time with quasiperiodic bursts in fluctuation amplitudes, driving the core q profile above 1, a change of several percent, during the corresponding crash events. Comparing these cases to the quiescent equilibria in 2D simulations highlights the causal character of the dynamo EMF in the sawtooth dynamics. Details of the fluctuation dynamics are observed to vary with the location of the q=1 surface. For example, for larger q=1 radius, a subsequent oscillation in n=1 energy occurs after the main n=1 crash, possibly reflecting partial rather than complete reconnection in the main crash.