The switching of magnetic field gradient coils in magnetic resonance imaging (MRI) inevitably induces transient eddy currents in conducting system components, such as the cryostat vessel. These secondary currents degrade the spatial and temporal performance of the gradient coils, and compensation methods are commonly employed to correct for these distortions. This theoretical study shows that by incorporating the eddy currents into the coil optimization process, it is possible to modify a gradient coil design so that the fields created by the coil and the eddy currents combine together to generate a spatially homogeneous gradient that follows the input pulse. During the pulsing of magnetic field gradients in MRI, multiexponentially decaying eddy currents are always induced within the conducting materials of the MR imager. Eddy currents in cold, highly conductive radiation shields of the superconducting magnet produce particularly longacting effects relative to the image acquisition period (1-2). These secondary magnetic fields are known to cause spatial and temporal degradation of the gradient uniformity within the imaging volume, which often results in undesired misregistration and intensity-phase variations in both images and spectra.With the recent push of MRI towards high signal-tonoise ratios (SNRs) and improved image resolution, tremendous efforts have been made to prevent and minimize the eddy-current fields. For instance, active screening is often engaged to minimize leakage fields and hence spatially and temporally complex residual eddy currents induced in the cryostat vessel (3-8). Unfortunately, the use of active shielding layer(s) occupies vital space inside the bore of the magnet, increases system cost, and reduces gradient efficiency. Furthermore, residual eddy currents are never completely removed through active shielding, and experimental compensation methods are also required for optimal results (9,10).During the design of conventional gradient coils (cylindrical, planar, etc.), the current distributions in one or more gradient layers are commonly optimized to obtain a target gradient uniformity in the imaging volume while satisfying other design constraints such as minimum inductance, resistance, leakage fields, force, torque, and maximum gradient efficiency (1). Traditionally, these design approaches do not take eddy currents into direct consideration when optimizing the gradient coil. Consequently, during the pulsing of the gradient current, eddy currents are induced in the cryostat vessel and other conducting materials that lead to degradation of the target field uniformity and the field stability.In 1986, Turner and Bowley (13) were among the first to introduce an analytical technique for passive magnetic screening. Their study considered spatial eddy-current variations in a thick, highly conductive, infinitely long aluminum shield as the secondary source contributing to target gradient fields. By varying the single-layer gradient coil positions to accommodate for the spatial presence of ed...