A method of manufacturing electromagnet coils for use in a magnetic resonance imaging system having a main field magnet, the electromagnet coils disposable in a non-homogeneous external magnetic field generated by the main field magnet, the method comprising: forming a coil representation of a coil surface for the electromagnet coils by generating a representation of the current density for the electromagnet coils over the surface where the electromagnet coils are disposable; setting a plurality of requirements for a plurality of performance metrics for the electromagnet coils, the plurality of performance metrics comprising an efficiency metric, an energy metric, an eddy field metric, a magnetic field-shape metric, and at least one of a net external torque metric and a net external force metric, wherein the efficiency metric is defined as the gradient strength per unit current drivable through the electromagnetic coil, wherein the energy metric is defined as 0.5 times the product of inductance of the electromagnetic coil and a square of the current, wherein the magnetic field-shape metric is based on the sum of the squared difference between the magnetic field produced by the plurality of electromagnet coils and a target magnetic field over a set of positions in a volume of interest, wherein the net external torque metric and the net external force metric are respectively based, at least in part, on a torque and a force exerted on the electromagnet coil by the non-homogeneous external magnetic field; forming a performance functional for generating a current density pattern over the coil surface, wherein the performance functional is based on the plurality of performance metrics, the coil representation, and a range of positions of the coil representation with respect to the non-homogeneous external magnetic field; optimizing the performance functional based on the plurality of requirements, thereby providing an optimized performance functional; generating a current density pattern over the coil surface based on the optimized performance functional; and obtaining a plurality of coil windings for the electromagnet coils from the current density pattern, thereby providing a plurality of obtained windings. forming a coil representation of a coil surface for the electromagnet coils by generating a representation of the current density for the electromagnet coils over the surface where the electromagnet coils are disposable; setting a plurality of requirements for a plurality of performance metrics for the electromagnet coils, the plurality of performance metrics comprising an efficiency metric, an energy metric, an eddy field metric, a magnetic field-shape metric, and at least one of a net external torque metric and a net external force metric, wherein the efficiency metric is defined as the gradient strength per unit current drivable through the electromagnetic coil, wherein the energy metric is defined as 0.5 times the product of inductance of the electromagnetic coil and a square of the current, wherein the magnetic field-shape metric is based on the sum of the squared difference between the magnetic field produced by the plurality of electromagnet coils and a target magnetic field over a set of positions in a volume of interest, wherein the net external torque metric and the net external force metric are respectively based, at least in part, on a torque and a force exerted on the electromagnet coil by the non-homogeneous external magnetic field; forming a performance functional for generating a current density pattern over the coil surface, wherein the performance functional is based on the plurality of performance metrics, the coil representation, and a range of positions of the coil representation with respect to the non-homogeneous external magnetic field; optimizing the performance functional based on the plurality of requirements, thereby providing an optimized performance functional; generating a current density pattern over the coil surface based on the optimized performance functional; and obtaining a plurality of coil windings for the electromagnet coils from the current density pattern, thereby providing a plurality of obtained windings.