Dynamics of resistive double tearing modes with broad linear spectra

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied in a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable. In this paper, it is first demonstrated that linear DTM theory predicts the dominance of high-m DTMs. A semi-empirical formula for estimating the poloidal mode number of the fastest growing mode, m_peak, is obtained from the existing linear theory. Second, using nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, whereby small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant for the understanding of the magnetohydrodynamic (MHD) activity near the minimum of q and may thus be of interest to studies concerned with stability and confinement in advanced tokamaks.