Tokamak plasmas are invariably subject to small amplitude, static, magnetic perturbations—known as error-fields—that are primarily generated by magnetic field-coil misalignments. A resonant error-field can drive magnetic reconnection in an intrinsically tearing-stable plasma, resulting in the formation of a locked (i.e., non-rotating in the laboratory frame) magnetic island chain at the resonant magnetic flux-surface. (See Section 5.16.) Tokamak plasmas containing locked magnetic island chains often terminate in disruptions [14,15]. Fortunately, error-field driven magnetic reconnection is strongly suppressed by the naturally occurring rotation of the electron fluid at the resonant surface. However, when the error-field amplitude rises above a certain critical value, the electron fluid rotation at the resonant surface is suddenly arrested, and error-field driven reconnection proceeds unhindered. This phenomenon is known as error-field penetration [4,6,7], and has been observed in many tokamak experiments [3,8,9,10,11,12,13,16,17].

In this chapter, we shall calculate the critical error-field amplitude required to trigger penetration on the assumption that, prior to penetration, the rotational suppression of error-field driven magnetic reconnection is sufficiently strong that the resonant plasma response is governed by linear layer physics [2,4,6,7].