Response Regimes in Tokamak Fusion Reactors

Figure: 5.3 Linear resonant plasma response regimes in $Q$-$P$ space for a low-field tokamak fusion reactor. The various regimes are the diffusive-resisitive (DR), the diffusive-inertial (DI), the viscous-resistive (VR), the viscous-inertial (VI), and the inertial (I). The range of probable $Q$ and $P$ values in the reactor are indicated by the $\times$ markers.

Figure 5.3 shows the linear response regimes in a low-field tokamak fusion reactor. The boundaries between the regimes are calculated with $D=3.021$. (See Table 5.1.) If we assume that $P\simeq \sqrt{P_\varphi\,P_\perp}\simeq 500$ and $Q\lesssim Q_\ast$, which implies that $Q\lesssim 2$ (see Table 5.1), then it is clear from the figure that the relevant response regimes are the viscous-inertial and the diffusive-resistive. Note that the respective inequalities, $c_\beta\ll Q^{-3/4}\,P^{1/4}$ and $c_\beta\ll P^{1/4}\, D^{3/2}$, that must be satisfied in order to justify our neglect of the ion parallel dynamics in the layer equation are very easily satisfied in the viscous-resistive and resistive-diffusive regimes. (See Section 5.7 and Tables 5.1 and 5.2.)

Figure 5.4 shows the linear response regimes in a high-field tokamak fusion reactor. The boundaries between the regimes are calculated with $D=2.257$. (See Table 5.1.) If we assume that $P\simeq \sqrt{P_\varphi\,P_\perp}\simeq 500$ and $Q\lesssim Q_\ast$, which implies that $Q\lesssim 1.5$ (see Table 5.1), then it is clear from the figure that the relevant response regimes are the viscous-inertial and the viscous-resistive. Note that the respective inequalities, $c_\beta\ll Q^{-3/4}\,P^{1/4}$ and $c_\beta\ll P^{1/2}$, that must be satisfied in order to justify our neglect of the ion parallel dynamics in the layer equation are very easily satisfied in the viscous-inertial and viscous-resistive regimes.

Figure: 5.4 Linear resonant plasma response regimes in $Q$-$P$ space for a high-field tokamak fusion reactor. The various regimes are the diffusive-resisitive (DR), the diffusive-inertial (DI), the viscous-resistive (VR), the viscous-inertial (VI), and the inertial (I). The range of probable $Q$ and $P$ values in the reactor are indicated by the $\times$ markers.