Cylindrical induction coil to accurately imitate the ideal magnetic dipole

In this work, we optimize the geometry of a cylindrical induction coil in order to improve the imitation of the ideal dipole field. First, we analyze a single-layer coil and find that for an optimum length-to-diameter ratio (L/D) of 0.86:1 the imitation error, computed for a four radii distance from the coil's center, is reduced by a factor of ∼12 (from 9.4 down to 0.73%) relative to a single-turn coil. Second, we analyze two different types of multilayer coils: one having for all the layers the same 0.86:1 optimum L/D (a coil with a trapezoidal cross section of the winding); and another having for each layer a different L/D (a coil with a rectangular cross section of the winding). The imitation error in this case is reduced by a factor of ∼22 and ∼33, correspondingly. We finally show that optimizing the multilayer coil makes the imitation error practically negligible (<0.28%) even at as short as four radii distances from the coil's center. Employing such optimized coil allows one to use the simple dipole model with a high degree of accuracy. It also relieves the system of having to spend extra time for computing the exact values of the coil field.