Optimization of the magnetic gradient scale length and its influence on plasma-coil separation in stellarators

The distance 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 distance must be large enough so that components such as a breeding blanket and neutron shielding can fit between the plasma and the coils. reactor size, engineering complexity, and particle loss due to field ripple. We explore the hypothesis that the limiting plasma-coil distance is set by the shortest scale length of the magnetic field as expressed by the ∇B tensor. We tested this hypothesis on a database of 45 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. Additionally, this correlation reveals a general trend that larger plasma-coil distance is possible with a small number of field periods. We compare several methods of penalizing a large magnetic gradient during optimization. We finally show that targeting the magnetic gradient scale length in stage I optimization allows for a larger coil-to-plasma distance in stage II optimization.