Optimization of fill factor equation in Halbach design

Selection (spatial in homogenous) and excitation (spatially homogenous) fields are designed with Halbach magnets for magnetic particle imaging (MPI) and magnetic resonance imaging (MRI). Permanent magnet parameters (length and remanent flux density) and geometrical parameters (fill factor (FF), number of magnets, and system radius) are key factors for Halbach applications. The effect of fill factor ratio at magnetic flux density was investigated with 4 and 8 cylindrical magnets. A new mathematical expression was developed for accurate placement of the magnets even at 100% filling ratio $(FF = 1)$. Numerical simulations were conducted for the proposed model and magnetic flux density of 4 magnets system was 17% more accurate as compared to the model in the literature.