Fringing Flux Corrections for Magnetic Focusing Devices

Abstract

When a charged particle approaches a region of uniform magnetic field its trajectory is affected by the fringing field. Compensation for the effect of the fringing field may in some cases be achieved by the use of virtual field boundaries which are outwardly displaced from the actual boundaries. A definition of the virtual boundary in terms of the effect of the fringing field upon the trajectories is formulated. A procedure for calculating the displacement d of the virtual from the actual field boundary is given using the methods previously developed for calculating ion trajectories in non-uniform magnetic fields. Using this procedure several values of the displacement for various magnet dimensions and conditions have been calculated. A method of altering the geometry of sector-type mass spectrometers to correct for the effects of the fringing fields is proposed. It is shown that the angular and spatial separations of the individual ion trajectories in an ion beam of small angular spread as it approaches a uniform field region through a fringing field are approximately the same as for the ideal case wherein the magnet field changes discontinuously at the boundary.