Generation of long prolate volumes of uniform magnetic field in cylindrical saddle-shaped coils

Abstract

We investigate the uniformity of the magnetic flux density (referred to as the field uniformity) within a series of coils designed to provide a prolate volume of field uniformity. Computational modelling of two cylindrical coil systems which have a sinusoidal current density distributed on the surface of the cylinder, shows the extent of prolate field uniformity along the cylindrical axis, with height and width of the magnetic volume limited by the radius of the cylinder. The first coil system consists of a cos θ coil–-a series of saddle-shaped filament loops spaced uniformly with respect to cos θ on the curved cylindrical surface, where θ is the angle between the radius of the cylinder and the horizontal radial axis (assuming a horizontal cylinder). The second coil system, named the ‘ELFcage’ coil, consists of saddle-shaped filament loops spaced uniformly with respect to a fixed Δθ, on the cylindrical surface. The volume of field uniformity is also compared with volumes generated by circular Helmholtz and Barker coil designs. For coil diameters of 2 m, the Helmholtz and Barker coils generate a volume of field uniformity within 1% to 3% of the field at the centre that extends ∼0.8 m and ∼1.4 m respectively along the axis of symmetry. This compares to an extent of 3 m and 6 m for both the cos θ and ELFcage coils wound on a 2 m diameter cylinder (8 m length), for 1% and 3% field uniformity respectively. Importantly, the ELFcage coil shows significantly greater field uniformity along the radial axis compared to the cos θ coil. An array of triaxial magnetometers was used to measure the volume of field uniformity within the cos θ coil system, consisting of two sets of orthogonal cos θ windings to generate radial fields and a solenoid winding to generate an axial field. These measurements confirmed the results obtained from computational modelling. The cos θ coil system is currently in use for calibration of magnetometers and for measuring the magnetic signatures of bulky prolate objects.