## 3 The International Stellarator Confinement Database and the ISS04 Scaling Law  
To allow for this study to be as general as possible, the largest publicly available database of the energy confinement in Stellarators has been analysed [19]. The International Stellarator Confinement DB comprises entries from the eight most relevant machines operated in the world at the time of its constitution: ATF, CHS, Heliotron E, Heliotron J, LHD, TJ-II, W7-A, and W7-AS. For the sake of comparison with the literature and with specific experiments [20; 21], the same variables and selection criteria reported in [22] for the derivation of the ISS04 scaling have been adopted (ISHCDB 26). An overview of the analysed database is provided in Table 1.  
As a cautionary note, some limitations of the DB have to be mentioned. With regard to the physics, the discharges included present quite different plasma wall interactions: the database indeed contains devices with different plasma facing components, diverted plasmas and limited plasmas, and a variety of wall conditioning techniques. The heating schemes, neutral beam, and electron cyclotron resonance are also different. The underlying hypothesis is therefore that these dissimilarities do not influence dramatically the main confinement properties of the plasmas. The statistical limitations of the database will be discussed later in the paper. Notwithstanding the aforementioned deficiencies, the International Stellarator confinement DB was used to derive the most widely accepted scaling law for the energy confinement time in Stellarators: the so-called ISS04 [22]. The ISS04 scaling law is reported \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantity** & \(\left(\mathbf{min}^{(\circ)},\,\mathbf{max}^{(\circ)}\right)\) & \(\left(\mathbf{\mu},\boldsymbol{\sigma}\right)\) \\ \hline \(a\)\([m]\) & \(([0.088,\,0.634])\) & \(([0.23,0.12])\) \\ \(R\)\([m]\) & \(([0.938,\,3.821])\) & \(([1.94,0.68])\) \\ \(P\)\([\)MW\(]\) & \(([0.04,\,6.52))\) & \(([1.09,1.35])\) \\ \(n_{e}\)\([10^{19}m^{-3}]\) & \(([0.22,\,34.31])\) & \(([54.2,\,7.40])\) \\ \(B\)\([T]\) & \((0.44,\,2.56])\) & \(([1.37,\,0.63]\) \\ \(t_{2/3}\) & \(([0.092,\,1.607]\) ) & \(([0.73,\,0.44]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main quantities in the International Stellarator Confinement database and their range of values. The meaning of the symbols is the usual: \(a\) is the minor radius, \(R\) the major radius, \(P\) the input power, \(n_{e}\) the average electron density, \(B\) the on-axis magnetic field, and \(t_{2/3}\) the rotational transform at two thirds of the minor radius. as Equation (1) for the reader's convenience and was obtained with log regression, assuming therefore a priori that its most appropriate mathematical form is a power law monomial. \[\tau_{E}^{ISS04}=0.134\ a^{2.28}R^{0.64}p^{-0.61}n_{e}^{0.54}B^{0.84}t_{\frac{3}{ 3}}^{0.41} \tag{1}\]  
In Equation (1), \(a\) indicates the minor radius, \(R\) the major radius, \(B\) the magnetic field on axis, \(n_{e}\) the average plasma density, and \(t_{2/3}\) the rotational transform at two thirds of the minor radius. It is worth mentioning that, since in the literature the uncertainties affecting \(f_{ren}\) are not reported, it is impossible to calculate the confidence intervals of Equation (1). To fit the data of the various machines, the ISS04 scaling law requires introducing a renormalization factor, called \(f_{ren}\), specific to each device or even to different ranges of the operational parameters in the same machine [22]. This renormalization coefficient is commonly believed to account for different levels of optimization, determined by the fine tuning of quantities not leaving a signature in the 0D entries included in the DB. The use of a renormalisation factor to determine the ISS04 poses several issues. First, the statistical coherence and soundness of the approach are doubtful. Secondly, such a fudge factor tends to obscure more than clarify the underlying physics.