Description
In magnetic fusion devices, there exists an empirical upper limit for the achievable plasma density. Theoretical descriptions generally invoke energy transport and/or radiative losses as competing factors in setting that limit. In the case of tokamaks, the sequence of events is complicated by changes in the magnetic equilibrium and the onset of MHD instabilities. In that respect, stellarators offer a less convolved system to understand the basics of the density limit.
In this work, we introduce an energy balance model to investigate the mechanisms governing the density limit in stellarator devices. The model, based on the work presented in Itoh et al. (2001), assumes that both radiation and transport losses influence the density limit and includes them in the simplest, yet realistic form: impurity radiation is computed from cooling factors, augmented with estimates of impurity residence time, whereas transport is modelled with the empirical ISS04 scaling law. A quantitative density limit is then obtained from the marginal stationary power balance condition. We show that the density limit predictions are well represented by a scaling law of the form $n_\mathrm{lim}\propto\left(P_\mathrm{h}/V\right)^{\alpha}B^{\beta}c_\mathrm{imp}^{\gamma}$, where $P_\mathrm{h}$ is the heating power, $V$ is plasma volume, $B$ is the on-axis magnetic field, and $c_\mathrm{imp}$ is impurity concentration. Furthermore, we test the model with TJ-II and LHD experimental data. Data mining of the TJ-II discharge database yields a dataset of approximately 500 different plasma states at the density limit. While the modelled density limit does show an order-of-magnitude agreement and a correlation with the observations, significant deviations are observed, which are attributed to the unavailability of accurate impurity concentration measurements in the device. For LHD, 37 curated discharges from the 24th and 26th experimental campaigns were analysed, showing much better agreement between the experimental results and the model, that often outperforms the reference Sudo scaling. Curation and modelling of W7-X data is on-going. In light of our results, we will qualify the present understanding of density limit in stellarators and draw conclusions on the projections for the density limit in reactor scenarios.