A new scaling for divertor detachment

Abstract

The ITER design, and future reactor designs, depend on divertor 'detachment,' whether partial, pronounced or complete, to limit heat flux to plasma-facing components and to limit surface erosion due to sputtering. It would be valuable to have a measure of the difficulty of achieving detachment as a function of machine parameters, such as input power, magnetic field, major radius, etc. Frequently the parallel heat flux, estimated typically as proportional to P sep /R or P sep B/R, is used as a proxy for this difficulty. Here we argue that impurity cooling is dependent on the upstream density, which itself must be limited by a Greenwald-like scaling. Taking this into account self-consistently, we find the impurity fraction required for detachment scales dominantly as power divided by poloidal magnetic field. The absence of any explicit scaling with machine size is concerning, as P sep surely must increase greatly for an economic fusion system, while increases in the poloidal field strength are limited by coil technology and plasma physics. This result should be challenged by comparison with 2D divertor codes and with measurements on existing experiments. Nonetheless, it suggests that higher magnetic field, stronger shaping, double-null operation, 'advanced' divertor configurations, as well as alternate means to handle heat flux such as metallic liquid and/or vapor targets merit greater attention.

Overview of the SPARC tokamak

“…For this reason, data from SPARC on the divertor heat flux width scaling will be an important physics result and may help resolve the differences between empirical scaling and modelling predictions. This conservative approach to design does not preclude the exploration of detached divertor regimes, and SPARC will be able to test predictions for the impurity fractions required to induce detachment (Goldston, Reinke & Schwartz 2017; Reinke 2017). Two-dimensional fluid modelling work has also been performed for SPARC to gauge the possibility of detachment.…”

Divertor heat flux challenge and mitigation in SPARC

“…As mentioned in the introduction, access to dissipative divertor regimes in SPARC is difficult to predict. One method is to make use of the simple 1-D models developed by Reinke (2017) and Goldston, Reinke & Schwartz (2017) to examine the scaling for the impurity fraction needed to achieve detached divertor conditions with tokamak operating parameters (e.g. magnetic field, size).…”

Turbulence driven widening of the near-SOL power width in ASDEX Upgrade H-Mode discharges

“…Stangeby model or magnetic reconstruction. The expression for the parallel heat constant is taken from[5] and writes as f κ,0 (Z eff ) = 0.672 + 0.076 Z 0.5 eff + 0.252 Z eff (A3)…”