TRansmit Array Spatial Encoding (TRASE) is a Magnetic Resonance Imaging (MRI) method which uses phase gradients of the $B_1$ field – rather than magnitude gradients of the $B_0$ field – to achieve spatial encoding. The potential benefits and limitations of this technique are still being explored in both conventional and low-field magnets. This work designs a highly homogeneous, low-field magnet (<10 mT) to further studies of TRASE in this regime. The design method is novel and allows for ostensibly perfect field homogeneity. Furthermore, given that TRASE does not require the application of switched $B_0$ gradients, we propose to build the magnet on an aluminum housing which acts both as a heat sink and an effective low-frequency RF shield.
This talk will present the design method, convergence tests of this method, and the final design. The method is founded upon consideration of two coaxial cylindrical surfaces of finite lengths with surface currents on their bodies and end caps. Boundary conditions are set such that the outer surface perfectly shields the field created. Using finite element methods, the Laplacian of the magnetic scalar potential $Φ$, and hence magnetic field $B$, is found in the region between the cylinders. One is free to specify any solution to the Laplace equation in the inner region, including $Φ=-Bz/μ_o$, which gives a uniform field. By moving the outer surface farther and farther away, we are able to converge to a solution for a single, finite-length cylinder in free space with the perfectly uniform internal field of an infinitely long solenoid. The discontinuity of the scalar potential across the cylinder boundary is, in fact, equivalent to the stream function, and, as a result, evenly spaced contours of $ΔΦ$ give the coil winding pattern. Because no current flows at the center of the end caps, access holes can be created in these regions.