Speaker
Description
To manage erosion and protect against heat fluxes, tokamak power plants will need to be operated with detached divertors. To design future tokamaks around core-edge-integrated operating scenarios, we need fast, accurate detachment models. We developed a model to calculate the impurity concentration needed to detach the first $\lambda_q$ of the outer divertor. This model is based on the 0D analytical ‘Lengyel’ model, which forms the basis of other models such those by Goldston [1] and Reinke [2]. We extended the Lengyel model to include corrections for the cross-field transport in the divertor, power and momentum loss due to recycled neutrals, and turbulent broadening of $\lambda_q$ [3]. Our extended Lengyel model reproduces the empirical ‘Kallenbach’ scaling [4], which has been validated against detachment studies from several tokamaks including JET and ASDEX Upgrade [5]. In addition, a dedicated validation against a detached ASDEX Upgrade shot shows that our model can simultaneously predict the impurity concentration, divertor neutral pressure and separatrix temperature at detachment onset with reasonable accuracy [3]. The extended Lengyel model finds a transition from $c_z \propto n_{sep}^{-2}$ at low densities to about $c_z \propto n_{sep}^{-3}$ at high densities, encompassing the range of experimental scalings determined on ASDEX Upgrade and JET [6]. Applied predictively, the model finds that the ARC V3A tokamak ($P_{sep}$~120MW, $n_{sep}$~$10^{20}/m^3$) should access detachment with ~1% argon in the divertor. This is only slightly higher than on existing tokamaks due to the long divertor leg length and high absolute density — and significantly less than the ~6% predicted by the standard Lengyel model.
[1] R. J. Goldston et al 2017 Plasma Phys. Control. Fusion 59 055015
[2] M. L. Reinke 2017 Nucl. Fusion 57 034004
[3] T. Body, A. Kallenbach, T. Eich 2025 Nucl. Fusion 65 086002
[4] A Kallenbach et al 2016 Plasma Phys. Control. Fusion 58 045013
[5] S.S. Henderson et al 2024 Nucl. Fusion 64 066006
[6] S.S. Henderson et al 2021 Nucl. Mat. & Energy 28 101000