A field coil is a superconducting coil that shapes a strong magnetic field: superconductors wound on a frame with more exotics and cooled with coolant, put together in an Assembler. Every drive core has one at its centre, and the flagship and the mass driver are built with one. Ring segments, the fusion reactor and the shield generator take two each.
Most of a field coil's material cost is in its superconductors.