Suppose that and . It follows that , , and
(6.11) 
(6.12) 
Suppose that and . It follows that , , and
(6.14) 
(6.15) 
Suppose that and . It follows that , , and
(6.17) 
(6.18) 
Suppose, finally, that and . It follows that , , and
(6.20) 
(6.21) 
Table 5.1 gives estimates for all of the normalized quantities that appear in the layer equation, (6.5), for a lowfield and a highfield fusion reactor. (See Chapter 1.) Likewise, Table 6.1 gives estimates for all of the unnormalized quantities that appear in the growthrate formulae (6.13), (6.16), (6.19), and (6.22) [except for , which is ] for a lowfield and a highfield fusion reactor. (See Chapter 1.)
According to Equations (6.1), (6.3), (6.13), (6.16), (6.19), and (6.22), a linear tearing mode is unstable (except in the resistiveinertial growthrate regime, in which it is marginally stable) when the tearing stability index, , is positive, and is stable otherwise [4]. Moreover, the perturbed magnetic field associated with the mode corotates with the electron fluid at the resonant surface [1]. Finally, the mode grows on a hybrid timescale that is much greater than the hydrodmagnetic time, , but much less than the resistive evolution time, . Note that, in all cases, the growthrate goes to zero as . This is not surprising because, as is clear from Equation (5.39), the perturbed helical magnetic flux at the resonant surface, , is constrained to take the value zero in the limit that . In other words, magnetic reconnection at the resonant surface (which corresponds to a finite at ) is impossible in the absence of plasma resistivity [4].

There are three main factors, other than plasma inertia and resistivity, that affect the growthrate of a tearing mode in a conventional tokamak plasma. First, the strength of diamagnetic flows in the plasma, which is parameterized by the diamagnetic frequency, (and by the normalized diamagnetic frequency, ). Second, the anomalous perpendicular diffusion of momentum and particles, which is parameterized by the momentum and particle confinement timescales, and (and by the magnetic Prandtl numbers, and ). Third, finite ion sound radius effects, which are parameterized by the ion sound radius, (and by the normalized ion sound radius ).
There are four tearingmode growthrate regimes—the resistiveinertial, the viscousresistive, the semicollisional, and the diffusiveresistive—and their extents in  space are illustrated in Figure 6.1 [3]. Note that Figure 6.1 differs somewhat from Figures 5.1 and 5.2 because in the latter two figures it is assumed that whereas in the former figure it is assumed that . This refined ordering eliminates the nonconstant response regimes, and significantly modifies the extent of the resistiveinertial growthrate regime. It is clear from Figure 6.1 that a lowfield tokamak fusion reactor lies in the diffusiveresistive growthrate regime, whereas a highfield tokamak fusion reactor lies in the viscousresistive growthrate regime. (See Section 5.13.)
The absence of nonconstant response regimes in Figure 6.1 should come as no surprise. As we saw in Section 5.12, nonconstant resonant layers are characterized by , where is the radial layer thickness. Hence, according to Equation (6.2), asymptotic matching of such a layer to the outer solution is only possible if (given that resonant layers in tokamak plasmas are invariably very thin compared to the minor radius of the plasma). However, low tearing modes in conventional tokamak plasmas are characterized by rather than [6]. (As before, we are neglecting modes, which are characterized by , because they are not really tearing modes.)