Sideways force due to coupled kink modes in tokamaks

Abstract

The paper is devoted to calculation of the sideways force on the vacuum vessel wall in tokamaks at the early stage of disruptions before possible appearance of the halo currents. The theory developed so far predicts quite a large force due to a single-helicity kink mode. This concept is revisited here. It is demonstrated that the existing single-mode models are incompatible with the natural requirement that the sideways force on the plasma must be practically zero. The latter can be satisfied by incorporating a secondary coupled mode, which is the main new element here compared to the earlier analytical approaches. With this difference, the derivations are performed in the standard cylindrical model that is widely used in the resistive wall mode studies. The resistive wall effects are accounted for as determining the wall reaction on the plasma-driven perturbations. The derived expressions explicitly reveal the sideways force dependence on γτw with a maximum at γτw=O(1), where γ is the kink growth rate and τw is the resistive wall time. It is proved that the amplitude of the sideways force produced by the kink modes must be much smaller than expected from the existing scalings.