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We investigate the effects of runaway electron current on the dispersionrelation of resistive magnetohydrodynamic modes in tokamaks. We present a newtheoretical model to derive the dispersion relation, which is based on theasymptotic analysis of the resistive layer structure of the modes. It is foundthat in addition to the conventional resistive layer, a new runaway currentlayer can emerge whose properties depend on the ratio of the Alfv\'en velocityto the runaway electron convection speed. Due to the contribution from thislayer, both the tearing mode and kink mode will have a real frequency inaddition to a growth rate. The derived dispersion relation has been comparedwith numerical results using both a simplified eigenvalue calculation and aM3D-C1 linear simulation, and good agreement is found in both cases.

Structure and overstability of resistive modes with runaway electrons