Conditions and benefits of X-point radiation for the island divertor

We present a method to geometrically quantify the three magnetic island chains with the poloidal mode numbers m = 4, 5, and 6 (referred to in this paper as high-iota, standard, and low-iota islands, respectively), on which the W7-X divertor relies. The focus is on a comparative study of their detachment performance using a series of models of different physical and geometrical complexity, ranging from one- to three-dimensional (1D to 3D). In particular, it aims to identify the key physical elements behind the correlation between impurity radiation and island geometry and the associated detachment stability. Assuming intrinsic carbon as a radiator, we scan the three island chains with the EMC3-Eirene code based on otherwise identical code inputs. We find that the three islands behave differently in the radiation distribution, in the development of the radiation zones during detachment, and in the 'radiation costs', defined as the product of impurity and electron density near the last closed flux surface. While the radiation costs for the iota = 5/4 and 5/5 island chains linearly increase with the total radiation, the low-iota island with iota = 5/6 shows a bifurcation behavior in the sense that the radiation costs initially increase and then decrease when the total radiation exceeds a critical level. Consistent with the numerical trends, stable detachment, which is experimentally easy and robust to achieve with the standard iota = 5/5 island chain, remains an experimental challenge with the low-iota configuration. Dedicated numerical experiments show that the recycling neutrals and the ratio of parallel to perpendicular heat transport, which depends closely on the field line pitch, play a significant role in the formation and evolution of the radiation layer. A deeper understanding of the underlying physics relies on simpler models that explain why and how flux expansion can reduce the radiation costs. From these insights, we derive the conditions in which detached plasmas can benefit from the expansion of flux surfaces around the X-point. We show and explain why the current divertor design limits the actual capability of the high-iota configuration and propose solutions. The work is presented within a theoretical/numerical framework but cites relevant experimental evidence to emphasize its practical significance.