Synthesis of the Magnetic Field Using Transversal 3D Coil System

Abstract

Magnetic field is usually generated using magnets realized as a set of simple coils. In general, those magnets generate magnetic field with nonzero components in all directions. Usually during the design process only one component of the magnetic field is taken into account, and in the optimisation procedure the currents and positions of simple coils are found to minimize the error between the axial component of the magnetic field and the required magnetic field in the ROI. In this work, it is shown that if the high quality homogeneous magnetic field is generated then indeed one may neglect non-axial components. On the other hand, if the obtained magnetic field is not homogeneous either due to design requirements of too restrictive constrains, then all other components may severely deteriorate the quality of the magnetic field. In the second part of the paper, we show how to design a 3D transversal coil system to solve problems which are intractable in the 1D case.

Generalization of Helmholtz coil problem

“…Ideally, in a threedimensional region of interest, the magnetic field vector should have a constant axial and zero radial component. We can express the magnetic field components as the required field (0) B and error terms in the form [10] (0) (0)…”

“…As before, certain data had to be recalculated and we did so for the column labeled with 4** in Table 2. The last row in this table (denoted as Level) contains values of normalized magnetic field obtained via (10). In other words, this constant multiplied by 0 C B is the on-axes magnetic field in the given scope of | / | z a with the defined homogeneity δ .…”