  The separation between the last closed flux surface of a plasma and the
external coils that magnetically confine it is a limiting factor in the
construction of fusion-capable plasma devices. This plasma-coil separation must
be large enough so that components such as a breeding blanket and neutron
shielding can fit between the plasma and the coils. Plasma-coil separation
affects reactor size, engineering complexity, and particle loss due to field
ripple. For some plasmas it can be difficult to produce the desired flux
surface shaping with distant coils, and for other plasmas it is infeasible
altogether. Here, we seek to understand the underlying physics that limits
plasma-coil separation and explain why some configurations require close
external coils. In this paper, we explore the hypothesis that the limiting
plasma-coil separation is set by the shortest scale length of the magnetic
field as expressed by the $\nabla$B tensor. We tested this hypothesis on a
database of > 40 stellarator and tokamak configurations. Within this database,
the coil-to-plasma distance compared to the minor radius varies by over an
order of magnitude. The magnetic scale length is well correlated to the
coil-to-plasma distance of actual coil designs generated using the REGCOIL
method [Landreman, Nucl. Fusion 57, 046003 (2017)]. Additionally, this
correlation reveals a general trend that larger plasma-coil separation is
possible with a small number of field periods.

Plasma Physics