Minimum energy MRI gradient coils of general geometry

The author presents a new method for the design of gradient coil systems for magnetic resonance imaging (MRI) with minimum energy. The new method eliminates previous restrictions on coil geometry and provides a unified approach for systems of any shape, including traditional cylindrical and planar systems. Realistic constraints can easily be enforced, such as the length of the cylinder in a cylindrical system, the size of the plane in a planar system, or the presence of current-free slots or holes. The method can deal with the eddy currents induced in conducting objects, and with shielded or double-shielded coil systems. The magnetic energy is minimized after all effects have been included, resulting in a truly optimized real-world system. The method also employs a new optimization scheme. A design example is presented and shown to have a substantially lower energy, smaller inductance and better gradient quality than previous similar designs.