Multilayer transverse gradient coil design

Abstract

ABSTRACT:In small, cylindrical gradient coils consisting of a single layer of wires, the limiting factor in achieving large magnetic field gradients is the rapid increase in coil resistance with efficiency. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, mathematical expressions have been developed that allow the design of multilayer coils. These expressions have previously been applied to the design of a four-layer z-gradient coil. As a further development, the equations have now been modified to allow the design of multilayer transverse gradient coils. The variation in coil performance with the number of layers employed has been investigated for coils of a size suitable for use in NMR microscopy, and the effect of constructing the coil using wires or cuts in a continuous conducting surface has also been assessed. We find that at fixed resistance a small wire-wound two-layer coil offers an increase in efficiency of a factor of about 1.5 compared with a single-layer coil. In addition, a two-layer coil of 10-mm inner diameter has been designed and built. This coil had an efficiency of 0.41 Tm Ϫ1 A Ϫ1 , a resistance of 0.96 Ϯ 0.01 ⍀, and an inductance of 22.3 Ϯ 0.2 H. The coil produces a gradient that deviates from linearity by less than 5% over a central cylindrical region of interest of height and length 6.2 mm.

A stream function method for gradient coil design

“…Mathematically, the expression for the current basis function f n (r) is then [9] where N n is the number of triangles in a particular current element and ⌬ ni denotes an i th triangle belonging to node n. To simplify notations, we rewrite Eq. [9] as: [10] where v ni ϭ e ni /(͉e ni ͉͉d ni ͉). Clearly, the divergence of f n (r) is zero and the flux through the edges containing the selected node is unity.…”

“…Leggett et al (10) investigated the multilayer transverse cylindrical gradient coils. They also relied on a Fourier series expansion of the current.…”

Reverse‐engineering of gradient coil designs based on experimentally measured magnetic fields and approximate knowledge of coil geometry‐application in exposure evaluations

“…Carlson's approach is applied to generate coils of finite length (17). The azimuthal component of the current density for instance can be expressed as a sum of orthonormal functions multiplied by the stream function coefficients a nq (18):…”

Theory of gradient coil design methods for magnetic resonance imaging

“…A good level of screening can be achieved in multilayer coils (81,110), and small versions of such coils can yield higher efficiencies at fixed resistance than conventional two-layer (primary and screen) coils, and that performance improves as the number of layers increases. Simulations showed by Legget et al (81) showed that by optimizing multilayer coils for cooling it is possible to achieve significantly higher gradient strengths at a fixed maximum operating temperature.…”