Analytical study of the magnetic field generated by multipolar magnetic configuration

Abstract

The magneto-statics eld from a parallelepiped magnet which can turn around an axis, is the rst step to nd the whole magnetic field in a multipolar con guration. This con guration is present in the ion sources, which are heated by electron cyclotron resonance. We present the analytic formulas to calculate this magnetic eld 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 con nement region, several graphics are shown with directions and magnitude's gradients of the magnetic field to help understand better the con nement system. Our results are confronted with experimental ones. These formulas are very useful in research of plasma magnetic con nement in ion sources through computational simulations.