Dynamics of resistive double tearing modes with broad linear spectra

Abstract

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 semi-empirical 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 (MHD) activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks.

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

“…The early evolution begins with a linear phase followed by one where low-m modes are nonlinearly driven by the faster high-m modes. These stages were discussed in detail in [33,34] and are found to be similar here. Thus, in the following, we focus on the subsequent fully nonlinear regime.…”

“…The results for q s = 2 DTMs are directly applicable to other values of q s [13]. This includes cases with nearby q s = 1 resonant surfaces for which the dynamics of resistive DTMs were recently described in [34]. The relaxation of the q profile is generally of practical interest for issues of current profile control, plasma stability and confinement.…”

“…This is in contrast to the situation typically found for large inter-resonance distances where the lowestm modes dominate linearly and produce large coherent island structures in the early stages of the nonlinear regime (e.g., [9,38]). With a broad spectrum of unstable modes, the detailed evolution depends on the initial conditions [34]. Independently of the initial conditions, the advanced stages of the annular collapse tend to be dominated by island and E×B flow structures with m ∼ m peak .…”

Linear analysis of plasma pressure-driven mode in reversed shear cylindrical tokamak plasmas

“…It is found that the smaller the ∆r, the more easily the transition to PDM can be triggered. In previous researches, [16,17] it is found that in small ∆r the high-m modes may dominate over low-m modes and the DTM has broad linear spectra. However, in these contributions, the effects of the plasma beta are not included due to the limitation of the reduced MHD model.…”

“…[13][14][15] For sufficiently closed rational surfaces, high-m modes may dominate over low-m modes and the DTM has broad linear spectra. [16,17] Other effects on DTM, such as toroidal or poloidal shear flows, [18] Hall effect, [19] guiding field, [20] viscosity, [21] anomalous electron viscosity effect, [22] and self-induced Alfven resonance, [23] have also been investigated.…”