As before (see Section 4.4), all quantities in the inner region are assumed to be functions of , , and only. Here, and are the poloidal and toroidal angles, respectively, whereas and are the poloidal and toroidal mode numbers, respectively, of the tearing mode. (See Sections 3.2 and 3.3.) We can write
Evaluating the normalized neoclassical drift-MHD fluid equations, (11.16)–(11.18), up to second order, we obtainwhere is defined in Equation (4.49), , and
To first order, Equations (11.35) and (11.36) again give the equilibrium force balance constraint(See Section 4.4.) The scalar product of Equation (11.35) with yields The scalar product of Equation (11.36) with gives The scalar product of the curl of Equation (11.35) with yields Finally, the scalar product of the curl of Equation (11.36) with gives
Our final reduced neoclassical drift-MHD model takes the form [7,8,10]where Here, we have suppressed the ordering superscripts. If we compare Equations (11.46)–(11.51), to our previous reduced non-neoclassical drift-MHD equations, (4.67)–(4.74), then we can see that the former set of equations contain many additional terms. The additional term involving the parameter in Equation (11.46) is due to the bootstrap current. The additional terms involving the parameters and in Equation (11.47) are due to neoclassical parallel momentum and heat fluxes. Finally, the additional terms involving the parameter in Equations (11.48) and (11.49) are due to neoclassical poloidal flow damping.