In the diffusiveresistive response regime (see Section 5.9),
where , and(7.12) 
In the viscousinertial response regime (see Section 5.11),
(7.13) 
(7.14) 

Interpolating between the diffusiveresistive and the viscousinertial response regimes, we can write
(7.15) 
Figure 7.1 shows the real and imaginary components of , as functions of the normalized EcrossB frequency at the rational surface, , calculated from Equations (7.16)–(7.18) for a lowfield tokamak fusion reactor. The calculation parameters are , , , , and . (See Table 5.1.) If we compare Figure 7.1 with the exact numerical result shown in Figure 5.5 then we can see that the analytic approximation (7.16)–(7.18) captures most of the salient features of the layer response. In particular, if we had tried to model the layer response just using either the diffusiveresistive or the viscousinertial response regimes alone then the agreement with the numerical results would have been very poor. The diffusiveresistive response regime predicts that is purely imaginary, and that is a monotonically increasing function of . On the other hand, the viscousinertial response regime does not predict a resonance (i.e., a point where ) at (i.e., when the electron fluid at the rational surface is stationary). Neither of these prediction are consistent with the data shown in Figure 5.5. Thus, it is clear that, in order to be reasonably accurate, an analytical approximation to the layer response must interpolate between a constant response regime (in this case, the diffusiveresistive) and a nonconstant response regime (in this case, the viscousinertial).
We saw in Section 5.13 that the relevant linear resonant response regimes in a highfield tokamak fusion reactor are the viscousresistive and the viscousinertial.
In the viscousresistive response regime (see Section 5.9),
(7.19) 
(7.20) 
Interpolating between the viscousresistive and the viscousinertial response regimes, we can write
(7.21) 

Figure 7.2 shows the real and imaginary components of , as functions of the normalized EcrossB frequency at the rational surface, , calculated from Equations (7.22)–(7.24) for a highfield tokamak fusion reactor. The calculation parameters are , and . (See Table 5.1.) As before, if we compare Figure 7.2 with the exact numerical result shown in Figure 5.6 then we can see that the analytic approximation (7.22)–(7.24) captures most of the salient features of the layer response.