Speaker
Description
The transition from a hot, clean core to a dissipative, engineering-compatible edge renders separatrix density $n_{\text{sep}}$ and impurity concentration $c_{\text{sep}}$ central to confinement, pedestal stability and detachment control. Predicting them reliably—and quantifying their link to the true experimental actuators of fueling and seeding puffing rates—remains a key objective for reactor-relevant operation and tritium fuel cycle design.
However, papers that first proposed historical scalings with divertor neutral pressure $p_{0}$ reported qualitative violations of the classical power-law dependence
\begin{equation}
n_{\text{sep}} \sim p_0^{\alpha}
\end{equation} in impurity-seeded plasmas [Kallenbach_2018, Schweinzer_1999]. Although the physical cause of these violations is known [Lore_2022], no mathematical model has yet captured the observed range of exponents—spanning from negative to positive $\alpha$ values. Similarly, proxies for impurity concentration, such as
\begin{equation}
c_{\text{sep}} \sim n_{\text{sep}}^{\beta}
\end{equation} produced conflicting results. Reported $\beta$ values range from the theoretical −2 [Lengyel_1981] to about −5 [Järvinen_2023], at times even featuring non-log-linearities in $c_{\text{sep}}(n_{\text{sep}})$ [Body_2025].
In this work, we apply an empirical macro-to-micro approach. We build on our previous macroscopic multi-machine study [Moscheni_2025], combining experimental and numerical data from 32 magnetic-confinement devices. That analysis identified a non-linear function linking $n_{\text{sep}}$ with fueling $\Gamma_{\text{D}}$ and seeding $\Gamma_{\text{Z}}$ at detachment onset, reproducing high-level trends across machines with factor-2 accuracy.
Here, we apply a mathematically equivalent formulation to a new purpose-built database of 50+ SOLPS-ITER edge-plasma simulations [Bonnin_2016], covering devices from SPARC to EU-DEMO and spanning one order of magnitude in $n_{\text{sep}}$ and two in $c_{\text{sep}}$.
Once disentangled from $p_0$, trends for $n_{\text{sep}}$ and $c_{\text{sep}}$ become consistent with the unified functional form
\begin{equation}
\begin{bmatrix}n_{\text{sep}} \ c_{\text{sep}}\end{bmatrix} = \begin{bmatrix}N_0 \ C_0\end{bmatrix} \times (\Gamma_{\text{D}} + \Gamma_{\text{Z}})^{\begin{bmatrix}N_1 \ C_1\end{bmatrix}} \times (\Gamma_{\text{Z}})^{\begin{bmatrix}N_2 \ C_2\end{bmatrix}}
\end{equation}which links separatrix quantities to the puffing rates. This formulation reproduces all qualitative behaviours reported in the literature while explaining apparent contradictions in $\alpha$ and $\beta$ as different manifestations of the same underlying relationship. By comparing the fitted $N_i$ and $C_i$ across machines, we assess their invariance and their dependence on the trajectory followed in the two-dimensional space of puffing rates.
Future work will extend the database to additional divertor configurations, explore the underlying physics [Lomanowski_2025], and pursue experimental validation alongside ongoing studies—predominantly involving un-seeded scenarios [Silvagni_2025].
Meanwhile, the derived scalings offer practical guidance for edge-plasma modelling, experiment planning, and real-time operation in current experiments and next-generation power plants.