Analytical study of the magnetic field generated by multipolar magnetic configuration

The magneto-statics field from a parallelepiped magnet which can turn around an axis, is the first step to find the whole magnetic field in a multipolar configuration. This configuration is present in the ion sources, which are heated by electron cyclotron resonance. We present the analytic formulas to calculate this magnetic field outside the volume of the magnet. To model the magnet, we considered a constant magnetization vector inside of magnet volume. Therefore, the magnetic scalar potential method can be used. We present the results by a hexapolar system. Their magnetic field components are calculated on confinement region, several graphics are shown with directions and magnitude's gradients of the magnetic field to help understand better the confinement system. Our results are confronted with experimental ones. These formulas are very useful in research of plasma magnetic confinement in ion sources through computational simulations.