Solution in Presence of External Magnetic Field-Coil

The most general solution to the cylindrical tearing mode equation, (3.60), in the outer region can now be written

where the real functions and are specified in Sections 3.8 and 3.9, respectively. Moreover, the real function is a solution of that satisfies(3.114) | ||

(3.115) | ||

(3.116) |

In general, is continuous across the field-coil (in accordance with Maxwell's equations), whereas is discontinuous. The discontinuity in is caused by the helical current flowing in the field-coil. The complex quantity

determines the amplitude and phase of the perturbed magnetic flux at the field-coil. The complex quantity parameterizes the amplitude and phase of the helical current sheet flowing in the field-coil. It follows from Equations (3.37), (3.38), (3.110), and (3.111) thatSimultaneously matching the outer solution, (3.112), across the rational surface, the resistive wall, and the field-coil, we obtain

Here, where use has been made of Equations (3.81), (3.118), and (3.119).