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Tearing modes with real frequencies in the plasma frame (i.e. in addition tothe Doppler shift due to $E\times B$ rotation) are of potential importancebecause of their effect on the locking process. In particular, it has recentlybeen shown [J. M. Finn, A. J. Cole, and D. P. Brennan, Phys. Plasmas (Letters),22:120701, 2015] that the Maxwell torque on the plasma in the presence of anapplied error field is modified significantly for tearing modes having realfrequencies near marginal stability. In addition, it is known [J. M. Finn andR. A. Gerwin, Phys. Plasmas, 3:2344, 1996] that resistive wall tearing modescan be destabilized below their no-wall limits by rotation, if the tearingmodes have real frequencies near marginal stability. In this paper we firstderive the tearing mode dispersion relation with pressure gradient, field linecurvature and parallel dynamics in the resistive-inertial (RI) regime,neglecting the divergence of the $E\times B$ drift and perpendicularresistivity. The results show that the usual Glasser effect, a toroidal effectwhich involves real frequencies, occurs in this simplified model, which ignoresperpendicular resistivity and the divergence of the $E\times B$ drift. We alsofind, using a similar simple model, the surprising result that in theviscoresistive regime with pressure gradient, favorable curvature due totoroidal effects, and parallel dynamics, a similar Glasser-like effect isfound. We show that in both regimes the existence of tearing modes with complexfrequencies is related to nearby electrostatic resistive interchange modes withcomplex frequencies. We discuss the effect on locking to an error field and thesignificant lowering of the threshold for destabilization of resistive walltearing modes, which can be much more pronounced than the weak effect observedfor RI tearing modes without pressure-curvature drive in Finn and Gerwin, 1996.

Real frequency tearing layers with parallel dynamics and the effect on locking and resistive wall modes