PROPERTIES OF SOME USEFUL 2-DIMENSIONAL MAGNETIC FIELDS

The potentials and field vectors for a two-dimensional magnetic field of multipolarity 2N are derived. The usual results for quadrupoles (N=2), sextupoles (N=3) and octupoles(N=4) are obtained by substituting the appropriate value of N into the general equations. The paraxial equations of motion for charged particles in these fields are derived. The magnetic field produced by 2N parallel current elements equally spaced on the surface of a right circular cylinder is calculated; it is shown that this produces an approximation to a pure multipole field, with the approximation improving as N increases. It is also shown that among the various possible multipole field configurations, the quadrupole provides the strongest focussing effect for given power losses in the source coils. © 1968.