Is the radial component negligible in the design of magnetic resonance imaging devices?

In the design of coils for magnetic resonance imaging devices the radial field component is usually neglected, and in the optimization procedure the currents and positions of simple coils are found to minimize the error between the axial component and the required magnetic field in the region of interest. In this work, we consider two cases of the required magnetic field both of which are needed in magnetic resonance imaging devices, namely the homogeneous magnetic field, and the gradient magnetic field. We show that if the high quality homogeneous magnetic field is generated then indeed one may neglect the radial component. On the other hand if the magnetic field is not homogeneous either due to design requirements or too restrictive constrains, then the radial component may severely deteriorate the quality of the magnetic field. We also propose an optimization method to reduce the radial component and study its performance for the gradient coil design problem. Our findings are illustrated by several examples.