Tearing mode stability in a low-beta plasma with sawteeth

Abstract

The magnetohydrodynamic (MHD) and two-fluid growth rates of a low-β m=2∕n=1 tearing mode in the presence of well-separated central sawtooth oscillations are examined using new reconstructions of experimental equilibria in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)]. The linear resistive stability index Δ′ alone is insufficient for determining the mode stability in toroidal geometry. Coupling to other rational surfaces is important even at low β. For the cases considered here, coupling to the 1∕1 is stabilizing while coupling to the 3∕1 is destabilizing. Matching the outer ideal MHD solution to the inner tearing layer solutions can change the marginal point depending on the inner layer model. The PEST3 code [A. Pletzer, A. Bondeson, and R. L. Dewar, J. Comput. Phys. 115, 530 (1994)] is used to determine matrix solutions for the ideal MHD n=1 mode that have singular jumps at each of the rational surfaces q=1, 2, and 3. This outer region solution is matched asymptotically to the desired resistive MHD inner layer solutions of Glasser, Greene, and Johnson, where the interchange parameter H is small in the low-β DIII-D plasma, while the inverse β parameter G is large. The most important effects in the dispersion relation are found to be the resistive interchange parameter DR and the coupling to the 1∕1 surface. Two-fluid diamagnetic effects were examined only in the uncoupled case, and modify the growth rate significantly. Both electron and ion diamagnetic effects are important at large diamagnetic frequencies ω*i⪢γMHD and Te≃Ti.