An unstable tearing mode in a tokamak plasma reconnects magnetic flux at the so-called rational magnetic flux-surface, where the mode resonates with the equilibrium magnetic field (see Section 3.7), to produce a rotating (in the laboratory frame) magnetic island chain (see Sections 5.16 and 9.5).

Mode locking is a process by which the rotation of a slowly growing magnetic island chain in a tokamak plasma is braked due to electromagnetic interaction with a rigid electrically conducting wall surrounding the plasma (see Sections 3.9 and 3.10), causing the chain to eventually lock (i.e., become stationary in the laboratory frame) to a static error-field (see Section 7.1) [2,3,4,6,9,10,11,12,13,14]. Locked magnetic island chains are strongly correlated with disruptions (i.e., sudden, catastrophic losses of thermal and magnetic energy) in tokamak plasmas [5]. In most tokamaks, the role of the conducting wall is played by the metallic vacuum vessel that surrounds the plasma.

As we saw in the previous chapter, the growth of a magnetic island chain in a tokamak fusion reactor is only governed by linear theory for a comparatively short period of time after its onset, its subsequent time evolution being governed by nonlinear theory. Hence, it is reasonable to suppose that the slowing down and locking of a magnetic island chain in such a reactor is governed by nonlinear theory. The aim of this chapter is to employ the nonlinear resonant response model derived in Chapter 8 to investigate rotation braking in tokamak fusion reactors. It is assumed that, once the rotation frequency of the island chain has been reduced to a small value by rotation braking, even the smallest residual error-field would be sufficient to completely arrest the chain's rotation.