The asymptotic matching relations (11.90) and (11.91) can
be reexpressed in the forms (see Section 8.10),
Equations (11.123), (11.136), and (11.141) yield

(11.142) 
Employing the easily proved identity
,
we obtain
where use has been made of Equations (11.138), (11.139), as well as the fact that
as
.
However, according to Equation (11.137),
where use has been made of Equations (11.138) and (11.139).
The previous equation yields

(11.145) 
where use has been made of Equations (8.23), (8.25), (8.27), and (8.46), and (8.103).
Here, is the hydromagnetic time [see Equation (5.43)], and
is the toroidal momentum confinement time [see Equation (5.50)].
Equation (11.145) can also be obtained by integrating Equation (3.165) across the rational surface, making use of Equation (3.140), as well as the
identification

(11.146) 
If we compare Equation (11.145) with Equation (8.102) then we can see that the discontinuity in the MHD fluid
velocity gradient that develops at the rational
surface is a factor
smaller in our neoclassical driftMHD model than the corresponding discontinuity in our nonneoclassical driftMHD model.
The reason for this reduction is that the strong poloidal flowdamping present in the former model prevents the poloidal plasma rotation profile from
being modified by the localized electromagnetic torque produced at the rational surface. Instead, only the toroidal plasma rotation profile is modified by the
electromagnetic torque [4,18].
It follows from Equations (11.113), (11.127), (11.130), (11.136), and (11.140) that
Here,

(11.148) 
and use has been made of the fact that
is continuous across the separatrix.
The previous equation can be combined with Equations (8.10), (8.23)–(8.27), (8.103), and (11.77), (11.79), and (11.144) to
give [2,3,7,14,15,20,21,23]
where


(11.150) 


(11.151) 


(11.152) 


(11.153) 


(11.154) 