Plasma Current and Pressure Profile Effects on Tearing Mode Onset in Steady-state Hybrid Scenarios on DIII-D Tokamak

Tearing mode (TM) instability is a kind of resistive magnetohydrodynamic instability that limits the performance of the tokamak plasma. A correct understanding of this phenomenon is essential for high performance steady-state operation, especially the onset of TMs. Based on the steady-state hybrid experiments performed on the DIII-D device, the occurrence of TM is identified and analyzed, and the effect of the plasma current and the pressure profiles on the tearing stability is investigated in terms of the tearing stability index Δ^. The characteristics of the mode is mainly investigated using the system of magnetic pick-up Mirnov probes. The FFT analysis and the phase-fitting method are applied to identify the mode onset, the mode amplitude, and the mode number in the experiments. The mode onset was defined for this thesis that the phasefolding disappears in the phase-fitting results of poloidal probe array. Since the tearing stability is sensitive to the equilibrium current and pressure profiles, the more accurate and tightly constrained equilibrium is reconstructed using the well-measured plasma profiles using various diagnostics for the discharges in the database. The characteristics of plasma current and pressure profiles at tearing mode onset in the database of DIII-D steady-state hybrid discharges seems to be more sensitive to the global feature of plasma profile through li and fp, and the effect of plasma resistivity at the mode surface through '( than the local feature of plasma profile through )* and )&. From the result of the best fit equation in the dimensionless form using +, and '-, the global feature of profiles and the current profile can affect more than the local feature of profiles and the pressure profile, respectively. The tearing stability index Δ is calculated with the experimental equilibria in two ways, by MHD codes (PEST-III and resistive DCON) and by MRE. They are verified and validated in reasonable agreement. It is noteworthy that the determined Δ′ can be positive regardless of the mode onset, so the conventional wisdom of Δ^> 0 for tearing destabilization may not be the sufficient condition, rather a positive value greater than a certain threshold could replace this under the toroidal geometry. The analytical formula of the tearing stability threshold Δ1 is reviewed for the semi-collisional regime and the collisionless banana regime. By comparing the analytical Δ1 with the Δ calculated from PEST-III code near the TM onset, it is found that the condition of Δ^> Δ1 is required for the mode onset in the experiment. A preliminary study on the Δ1 estimation from the normalized mode growth rate is performed by NIMROD code. The Δ2 can be fitted for negative or marginal growth rate using the relation between the normalized mode growth rate 3'- from NIMROD and the Δ from PEST-III. Finally, a stability diagram of 4 = 1 tearing mode onset is suggested with local and global features of plasma profiles. Onset condition of 4 = 1 TM is analyzed by the difference between Δ and Δ1 , and its stability diagram is derived in terms of the local (78∥ and 7:) and global (;<) variations for steady-state hybrid scenarios. To calculate Δ − Δ1 for the stability diagram, a novel modeling package has been developed by integrating IPS/FASTRAN for equilibrium reconstruction, PEST-III/DCON for linear stability Δ calculation, and the Δ1 solver for analytical Δ1 calculation. The stability boundary at the mode onset, Δ⁼ Δ1 , is mapped on )&-)* diagram. Characteristics of this stability boundary show that the TM unstable area expands, then the stability boundary moves as ;< increases. This stability diagram can be used to design and control experiments to avoid 4 = 1 TM