In Chapters 4 and 8, we derived a reduced model that describes the nonlinear response of a tokamak
plasma to a tearing perturbation in the inner region, which is situated in
the immediate vicinity of the so-called rational magnetic flux-surface at which the perturbation
resonates with the equilibrium magnetic field. (See Chapter 3.) Our derivation employs
the simplifying approximation of ignoring the specifically neoclassical terms (e.g., the terms associated with ion poloidal flow damping [22] and the bootstrap current [1]) in the neoclassical fluid equations, (2.370)–(2.374).
Our justification for this approximation is that the terms in question have their origin in friction between trapped and passing particles. However, trapped ions make radial excursions from magnetic flux-surfaces that are of order the ion banana
width. (See Section 2.7.) This width is a few centimeters in a tokamak fusion
reactor. (See Table 2.4.) Hence, if the radial width of the inner region is much less than the ion banana width then we would not
expect ion neoclassical effects to contribute to the plasma response in the inner region (because the trapped
ions would average over the spatial structure of the inner region). The
electron banana width is of order a few tenths of a centimeter in a tokamak fusion reactor. (See Table 2.4.) Thus, we would not expect electron neoclassical
effects to contribute to the plasma response in the radially thin
resistive layers characteristic of the linear response regime. (See Chapter 6.) On the other hand, in the nonlinear response regime, a tearing mode generates a magnetic island chain
at the rational surface whose radial width (which constitutes the effective width of the inner region) can easily exceed the ion banana width. (See Section 5.16.) Under these circumstances, there
is no justification for neglecting the specifically neoclassical terms in the neoclassical fluid equations. The aim of this chapter is to repeat the analysis of Chapters 4 and 8,
including the neoclassical terms in Equations (2.370)–(2.374), in order to produce a reduced model that is suitable for analyzing the dynamics of
wide magnetic island chains.
