Constrained length minimum inductance gradient coil design

A gradient coil design algorithm capable of controlling the position of the homogeneous region of interest (ROI) with respect to the current-carrying wires is required for many advanced imaging and spectroscopy applications. A modified minimum inductance target field method that allows the placement of a set of constraints on the final current density is presented. This constrained current minimum inductance method is derived in the context of previous target field methods. Complete details are shown and all equations required for implementation of the algorithm are given. The method has been implemented on computer and applied to the design of both a 1:1 aspect ratio (length:diameter) central ROI and a 2:1 aspect ratio edge ROI gradient coil. The 1:1 design demonstrates that a general analytic method can be used to easily obtain very short gradient coil designs for use with specialized magnet systems. The edge gradient design demonstrates that designs that allow imaging of the neck region with a head sized gradient coil can be obtained, as well as other applications requiring edge-of-cylinder regions of uniformity.