A Field-Gradient Coil Using Concentric Return Paths

Hemispherical gradient coils for magnetic resonance imaging

“…Differentiating Eq. [4] with respect to z and dividing by the current strength yields the coil efficiency, . Carrying out this process and then using Eqs.…”

“…Differentiating Eq. [4] with respect to x and also employing Eqs. [7] and [8] Both these measures are reduced by a factor of 4/3 relative to the axial coil.…”

“…[4] shows that setting all the coefficients, g l m and h l m except g 2 0 to zero, yields a perfect z-gradient inside the sphere (corresponding to a field varying as rP 1 (cos ) ϭ z). It can also be seen from Eq.…”

“…Since the expressions for the magnetic field, inductance and resistance (Eqs. [4], [7], and [8]), are all written in terms of full sphere harmonics, it is useful to express Eq. [12] using Eq.…”

“…Such low values are not optimal, particularly for transverse gradient coils, since they bring the return paths close to the center of the coil, thus reducing the coil efficiency. Several different approaches to overcoming this problem have been developed, including positioning the return paths on a concentric cylinder of larger radius (3,4); winding the gradient coil on a flared former (5), whose diameter is larger at the ends of the coil than at its center; inclusion of shoulder slots in the coil former (1). The most widely employed approach has been to make the transverse gradient coils asymmetric, so that the region of gradient uniformity is positioned closer to the inferior end of the gradient coil (6).…”