Significance of the proximity constraint in the analysis of the higher-order-null divertors.

There is a family of poloidal divertors where, unlike in the standard x-point divertor, the poloidal field nulls are of the second or the third order. Remarkably, these structures can be created and manipulated by the remote PF coils situated at significant distance from the would-be nulls. Topological instability leads to a split of the second- and third-order nulls into two or three first-order nulls. The performance of these divertors depends substantially on the configuration of and distance between the nulls. Such processes as plasma convection, plasma divertor turbulence, plasma diffusion, prompt particle loss, and others significantly depend on the aforementioned factors. The report describes a unified approach for assessing the effect of the nulls orientation and separation on these and other processes; it is encapsulated into the process-dependent proximity constraints. Results of some of the existing experiments with the higher-order-null divertors are assessed in a unified way.