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The separation between the last closed flux surface of a plasma and theexternal coils that magnetically confine it is a limiting factor in theconstruction of fusion-capable plasma devices. This plasma-coil separation mustbe large enough so that components such as a breeding blanket and neutronshielding can fit between the plasma and the coils. Plasma-coil separationaffects reactor size, engineering complexity, and particle loss due to fieldripple. For some plasmas it can be difficult to produce the desired fluxsurface shaping with distant coils, and for other plasmas it is infeasiblealtogether. Here, we seek to understand the underlying physics that limitsplasma-coil separation and explain why some configurations require closeexternal coils. In this paper, we explore the hypothesis that the limitingplasma-coil separation is set by the shortest scale length of the magneticfield as expressed by the $\nabla$B tensor. We tested this hypothesis on adatabase of > 40 stellarator and tokamak configurations. Within this database,the coil-to-plasma distance compared to the minor radius varies by over anorder of magnitude. The magnetic scale length is well correlated to thecoil-to-plasma distance of actual coil designs generated using the REGCOILmethod [Landreman, Nucl. Fusion 57, 046003 (2017)]. Additionally, thiscorrelation reveals a general trend that larger plasma-coil separation ispossible with a small number of field periods.

The Magnetic Gradient Scale Length Explains Why Certain Plasmas Require Close External Magnetic Coils