Magnetic Field Homogeneity

The necessary degree of spatial uniformity of the field can be achieved only by carefully placing the coils at specific spatial locations. It is well known that a single loop of wire will produce, on its axis, a field that is directed along the coil axis and that can be expressed as a sum of spherical harmonic fields. The first term in this sum is constant in space and represents the desired field that is completely independent of position. The higher-order terms represent contaminating field inhomogeneities that spoil the field uniformity. More than a century ago, a two-coil magnet system — known as the Helmholtz pair — was developed which produced a much more homogeneous field at its center than is produced by a single current loop. This design is based on the mathematical finding that when two coaxial coils of the same radius are separated by a distance equal to their radius, the first nonzero contaminating term in the harmonic expansion is of the fourth order. This results in an increased region of the field homogeneity, which, although it is useful in many applications, is far too small to be useful in MRI scanners. However, the principle of eliminating low-order harmonic fields can be extended by using additional coils. This is the method now used to increase the volume of field homogeneity to values that are useful for MRI. For example, in the commonly used six-coil system, it is possible to eliminate all the error fields through the twelfth order.

In practice, manufacturing tolerances and field perturbations caused b extraneous magnetic field sources — such as steel girders in the building surrounding the magnet — produce additional inhomogeneity in the imaging region. These field imperfections are reduced by the use of shimming fields. One approach — active shimming — uses additional coils (either resistive coils, superconducting coils, or some of each) which are designed to produce a magnetic field corresponding to a particular term in the spherical harmonic expansion. When the magnet is installed, the magnetic field is carefully mapped, and the currents in the shim coils are adjusted to cancel out the terms in the harmonic expansion to some prescribed high order. The alternative approach — passive shimming — utilizes small permanent magnets that are placed at the proper locations along the inner walls of the magnet bore to cancel out contaminating fields. If a large object containing magnetic materials — such as a power supply — is moved in the vicinity of superconducting magnets, it may be necessary to reset the shimming currents or magnet locations to account for the changed pattern of field inhomogeneity.