Let . The solution of Equation (3.64) in the vicinity of the rational surface is
for , and for . Here, Moreover, the real parameters and are fully determined by Equation (3.64) and the boundary conditions (3.65)–(3.67). Note that, in general, is continuous across the rational surface (in accordance with Maxwell's equations), whereas is discontinuous. The discontinuity in implies the presence of a radially-thin, helical current sheet at the rational surface. This current sheet is resolved in a thin resistive layer that, in principle, can only be described by employing the full set of neoclassical fluid equations, (2.370)–(2.374), rather than the reduced set of marginally-stable ideal-MHD equations, (2.375)–(2.380).The value of at the rational surface,
is known as the reconnected magnetic flux [4]. Note that is, in general, a complex quantity. The complex quantity parameterizes the amplitude and phase of the current sheet flowing (parallel to the equilibrium magnetic field) at the rational surface. Asymptotically matching the solutions in the so-called inner region (i.e., the region of the plasma in the immediate vicinity of the rational surface) and the so-called outer region (i.e., everywhere in the plasma other than the inner region) with the help of Equations (3.63), (3.68), (3.69), and (3.73), we obtain where(3.75) |