Computing the Non-Uniform Current Effects on the Magnetic Field in Sector Coil Dipoles

In this study, we extend the previous 'Segmentation method', which was originally suggested to calculate harmonic coefficients of solenoid magnets, to apply to high temperature superconductor (HTS) accelerator dipole magnets. The key idea of the segmentation method is to divide the current flowing domain into several segments to find its equivalent loop currents, by whose magnetic fields or corresponding field quality can be analytically calculated. This paper formulates an equation to calculate the multipole coefficients by segmented loop currents which represents the current densities of a sector-coil dipole magnet. The extended segmentation method is validated by comparison with analytic and inverse method through the multipole coefficient calculation. Second, the segmentation method is applied on an example model of a dipole magnet whose non-uniform current densities which are calculated by using the H-formulation based finite element method. The multipole coefficient calculation results and magnetic field are compared between the uniform and non-uniform current density using the segmentation method. Finally, a case study of extending the obtained 2D current density profile to 3D space is conducted with several assumptions.