Integrated modeling of advanced tokamaks for tearing mode avoidance on DIII-D

Understanding the physics of the onset and evolution of tearing modes (TMs) in tokamak plasmas is crucial for high-performance steady-state operations. The onset condition of (m,n) = (2,1) tearing stability, Δ′>Δc′>0, has been studied in DIII-D steady-state hybrid discharges with accurate equilibrium reconstruction and well-measured plasma profiles. Here, m is the poloidal mode number and n is the toroidal mode number. The onset of n=1 TMs is carefully identified using the Mirnov array to determine in-phase signals for the onset time and using electron cyclotron emission measurements to trace back from the saturated island width in the experiments for both initial island width and its growth rate. The tearing stability index Δ′ at TM onset is calculated in multiple ways, using the modified Rutherford equation and using the PEST-III or resistive DCON magnetohydrodynamic codes, and the results are in reasonable agreement with each other. The calculated Δ′ is compared with an analytical formula of the tearing stability threshold Δc′ to determine the condition for the mode onset, Δ′>Δc′. Finally, the local gradient effect of the plasma current and the pressure profiles on the tearing stability is investigated in terms of the difference between Δ′ and Δc′ through a series of modeled equilibria with the parametric variations. A database of experimental mode instability onsets is compatible with the simulated regions of instability obtained from the parametric variations.