## 5 Scaling Laws and Optimisation
### Extrapolation to the Demonstrative Reactor Region of the Parameter Space  
This section is meant to compare the various scalings, for the configuration with and without shear, and to investigate their extrapolation to the next generation of devices and to the reactor. The legitimacy of this extrapolation exercise derives from the fact that no renormalization factor has been introduced to extract from the data the scaling laws with SR via GP. The use of ISS04 to estimate the confinement time of the reactor studies is not immediate, since it provides no guidance about the renormalization factor to be adopted in the calculations. In the following, for comparison's sake, it is assumed that \(f_{ren}=1\).  
The main devices investigated are reported in Table 6 together with their main engineering parameters [29; 30; 31]. The Helias configuration was the basis of HSR4 and HSR5 designs, and the quasi-axial symmetric NCSX is the reference for ARIES-CS. HSR/14 and HSR5/22 [30; 31], being scaled versions of W7X, are expected to be run in shearless configurations. For completeness' sake, it should be mentioned that in NCSX and ARIES-CS, the bootstrap current is expected to play a more important role than in the other configurations because it is meant to be responsible for an important fraction of the rotational transform.  
The estimates of the confinement time for the devices of Table 6 are summarised in Table 7. Inspection of the table suggests a couple of considerations. First, the predictions of ISS04 are basically confirmed by the results obtained with SR via GP. In any case, given the quality of the database available and the large extrapolations in most engineering parameters, the level of agreement of the new scalings with the IS004 is quite remarkable. On the other hand, the set of data for the shearless configuration includes devices with very different characteristics, as already emphasised in [22], in which they were attributed very different renormalization factors. Extreme caution is therefore appropriate to interpret the results for this configuration. In particular, the shearless devices extrapolate quite differently depending on the assumed dependence on the rotational transform, an aspect which will require careful experimental assessments in the future. It should also be stated one more time that the level of extrapolation from present day devices to the demonstrative reactor designs is very large, and there is no guarantee even that the physics of the energy transport will remain the same. The main objective of the exercise in this subsection is therefore not so much to provide accurate estimates of the energy confinement time but to verify that the various scalings do not present absurd unphysical trends out of samples, a check which is always recommended.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **ARIES-CS** & **HSR4/18** & **HSR5/22** \\ \hline a[m] & 1.7 & 2 & 1.8 \\ R[m] & 7.75 & 18 & 22 \\ P [MW] & 462 & 486 & 594 \\ \(n[10^{19}m^{-3}]\) & 40 & 26 & 21 \\ B[T] & 5.7 & 5.0 & 4.75 \\ \(t_{\frac{1}{3}}^{2}\) & 0.7 & 0.917 & 0.947 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters of the reactor studies considered.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & \(\tau_{E}^{ITER}[s]\) \\ \hline ISS04 Equation (1) & 2.65 \\ SHEAR Equation (2) & 2.34\({}^{3,29}_{29}\) \\ SHEARLESS03 Equation (3) & 2.76\({}^{3,41}_{0.11}\) \\ SHEARLESS02 Equation (4) & 2.08\({}^{3,40}_{21}\) \\ L mode literature Equation (7) & 2.12\({}^{3,29}_{22.00}\) \\ L mode SR via GP. Equation (8) & 2.78\({}^{3,30}_{2,18}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Extrapolations to ITER. The extrapolation of ISS04 have been obtained for \(f_{ren}=1\).