3D modelling and design of current conical magnets

This paper presents a new method for the design of conical magnets with minimum power dissipation. The new method provides a general inverse approach for designing magnet systems with a revolution axis (conical magnets), including traditional cylindrical systems. The conical magnets are modelled through an analytical function of their current density. Using the spherical harmonics expansion of the magnetic field generated by currents flowing on the conical surface, the relationship between currents and field has been inverted. Hence, to evaluate the conical current density required to generate a specified field (B_x, B_y or B_z) everywhere in 3D space, a software program has been developed