First-Principles Density Limit Scaling in Tokamaks Based on Edge Turbulent Transport and Implications for ITER

A first-principles scaling law, based on turbulent transport considerations, and a multimachine database of density limit discharges from the ASDEX Upgrade, JET, and TCV tokamaks, show that the increase of the boundary turbulent transport with the plasma collisionality sets the maximum density achievable in tokamaks. This scaling law shows a strong dependence on the heating power, therefore predicting for ITER a significantly larger safety margin than the Greenwald empirical scaling [Greenwald et al., Nucl. Fusion, 28, 2199 (1988)] in case of unintentional high-to-low confinement transition.

Figure 1

Time trace of the gas flux, electron density from Thomson scattering, radiation intensity, and magnetic perturbations for the JET discharge No. 80823. The MARFE event is identified by the strong increase of the radiation measured above the $X$ point. The MARFE onset precedes the appearance of a locked mode, which eventually leads to the plasma disruption. The red dashed vertical line represents the time of the MARFE onset, $t_M\simeq 20.9\mathrm{s}$. The onset of the locked $N=1$ mode occurs at 21.95 s, while the disruption time is at 21.1 s.

Figure 2

Radial profile of the electron density (a), electron temperature (b), and electron pressure (c) as a function of the normalized radial coordinate at three different times of the JET discharge No. 80823. The time of the MARFE onset is denoted as $t_M$ (see Fig. 1). The radial profiles are obtained by fitting Thomson data with splines (Hermite form), imposing the profile and its first derivative to vanish at ${\rho }_{\mathrm{pol}}=1.1$ and enforcing the monotonicity of the profile in the edge region.

Figure 3

(a) Experimental edge density measured by means of Thomson scattering at the onset of the MARFE compared with the theoretical prediction $n_{\lim }$ provided by Eq. (12) with $\alpha =3.3\pm 0.3$. (b) Experimental measured maximum line-averaged density ($n_{\mathrm{avg}}$) compared with the prediction provided by the empirical scaling law in Eq. (1) (red dashed line). For comparison purpose, a proportionality factor is also considered in the empirical scaling when evaluating the $R^2$ parameter. Different marker shapes and colors are used to distinguish between the standard density limit (DL) and the density limit of discharges with an $H$-mode phase (HDL). As examples, the error bars are shown for the discharge with the lowest and highest density.