Convex optimisation of gradient and shim coil winding patterns.

Gradient and shim coils were designed using boundary element methods with convex optimisation. The convex optimisation framework permits the prototyping of many different cost functions and constraints, for example ℓ(p)-norms of the current density. Several examples of gradients and shims were designed and simulated to demonstrate this, as well as to investigate the behaviour of new cost functions. A mixture of ℓ(1)- and ℓ(∞)-norms of the current density, when used as a regularisation term in the field synthesis problem, was found to produce coils with bunches of equally spaced windings that do not take up all of the available surface. This is thought to be beneficial in the design of coils that will be manufactured from wire with a fixed cross-section.