Toroidal coupling of disparate helical tearing modes

Abstract

An analytical model has been developed for toroidal coupling of tearing modes with different helicities in the low-β and large aspects ratio tokamaks. A standard characteristic value problem has been naturally composed according to the structure of magnetohydrodynamic (MHD) solutions. The explicit general dispersion relation has been obtained by the asymptotic matching. The growth rates (characteristic values) and corresponding flux perturbations (characteristic functions) of the toroidal tearing mode have been derived. The toroidal coupling plays a role mainly through the correction for the ideal MHD solutions. Without loss of generality, variation tendency of growth rates has been analyzed for a toroidal tearing mode with cylindrical components m/n and (m+1)/n, the results indicate that (1) The toroidal coupling has a destabilizing effect on the tearing modes; (2) the ‘‘beating’’ of the growth rates of two components leads to strong coupling, even if the coupling parameter C is quite small, and the coupling effect does not explicitly rely on magnitude of Δ′(0)m of cylindrical component, so that Δ′(0)m ∼ ε is neither a necessary nor sufficient condition for strong coupling.