Linear Dispersion Relation
Let us write [see Equation (5.33)]

(6.1) 
where is the growthrate of the tearing mode, whereas is the real
frequency of the mode in the laboratory frame. We shall assume that
. This assumption can
easily be verified a posteriori. (See Table 6.2.) Asymptotic matching (see Section 3.8) between the tearing mode solution in the outer region and that in the
thin resistive layer, surrounding the rational surface (see Section 3.7), that constitutes the inner region, yields a linear tearing mode dispersion relation of the form

(6.2) 
where use has been made of Equations (3.74) and (5.70). Here, is the Lundquist number at the rational surface [see Equation (5.48)], is the real tearing stability index (see Section 3.8),
whereas the complex layer matching parameter,
, is defined in Equation (5.69).
In a conventional tokamak fusion reactor [assuming that
, where is the poloidal mode number of the tearing perturbation],
,^{6.1} and
. (See Table 1.5.) Hence, the previous dispersion relation can only be satisfied if takes a
value that renders
. It is clear from Equations (5.61)–(5.65), (5.93), (5.94), (5.96), and (5.98) that this goal
can be achieved in all of the constant linear response regimes if

(6.3) 
Here, and
are the EcrossB and electron diamagnetic frequencies, respectively, at the
rational surface.
[See Equations (5.21), (5.29), (5.44), and (5.45).]
The previous equation implies that the tearing mode corotates with the electron fluid at the rational surface [1]. (See Section 2.24.)