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

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 components such as a breeding blanket and neutron shielding can fit between the plasma and the coils. Plasma-coil separation affects reactor scales, coil 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. Understanding the underlying physics limiting plasma-coil separation can explain why some configurations require close external coils. We explore the hypothesis that the smallest plasma-coil separation is comparable to the shortest scale length of the magnetic field as expressed by the ∇B tensor. We tested this hypothesis on a database of ~ 40 stellarator and tokamak configurations. For this database, the plasma-coil separation compared to the minor radius varies by over a factor of 10. The magnetic scale length is well correlated to the plasma-coil separation of coil designs using the code REGCOIL. There is also a general inverse trend between the number of field periods and plasma-coil separation.