Some basic considerations of sector magnets

Since sector field magnets are widely used in ion implanters and isotope separators, it is appropriate that designers and operators appreciate their limitations through an ability to trace the path of charged particles in magnetic fields. This paper considers a sector magnet with variable angle pole tips. Initially, the direction and displacement of output rays, relative to magnet reference points, are deduced. This leads to an expression for the image distance in terms of the source distance, the sector included angle, and the angles of incidence and exit of input and output beams. The magnetic field of sector magnets extends beyond the physical boundary of the magnet itself and this fringe field can influence the path of incident particles before they enter the hard field boundary. Assuming an analytical expression for the fringe field variation, its influence on particle path radius and effective increase in magnetic volume can be estimated. Finally, the isotopic resolving power of a given sector field magnet may be calculated.