In this dissertation new designs for gradient coils are presented. The principal work is on better shielding for fringe field reduction. Fringe fields from gradient coils produce eddy currents in surrounding metal structures. Such eddy currents can degrade image quality and lead to acoustic noise. The acoustic effects are magnified for high-field Magnetic Resonance Imaging (MRI) scanners because of increased Lorentz forces. Conventional actively shielded gradient assemblies consist of primary and secondary coils in the shape of cylindrical shells surrounding the imaging volume. One of the principal regions of field leakage is at the ends of the gradient structure, and these fields are responsible for substantial eddy current generation. Our new shielded gradient coil designs that feature the inclusion of an endcap have significantly reduced fringe field at the cryostat inner bore. We discuss the degree to which the suppression of peak fringe fields corresponds to a reduction in the acoustic noise generated near the end of the warm bore.; Energy efficient capped actively shielded elliptical gradient coils are also designed. In comparison with traditional uncapped elliptical designs the newly proposed design substantially reduces the fringe field at the inner cryostat bore. And compared to a cylindrical design (with a diameter matched to the elliptical semi-major axis), a good reduction in magnetic energy is observed.; In addition, a design for a very short, symmetrical, and winged X-gradient insertable head coil is presented. With a smaller radius, an insertable head gradient coil has the advantage of less stored magnetic energy. The corresponding smaller inductance leads to higher slew rates. Lower torque from Lorentz forces is another advantage for these coils. When designing an insertable head coil one must remember the geometry is impacted by the shoulders. In consequence, asymmetric unshielded and shielded designs have been developed. Gradient designs with a shoulder cut-out to achieve longer coil lengths and symmetric and asymmetric insertable head coils with outward flares have all been designed. Gradient characteristics achieved by our designs are compared with a symmetric shoulder cutout design and an asymmetric shielded coil design. Apart from the uniformity along the z-axis direction the new coil achieved characteristics similar to that of coils almost twice its length.
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