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 with 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 and may peak around m = m peak ∼ 10 . In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of m peak on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high- m modes leads to a rapid turbulent collapse in an annular region, where 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 to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks.