Analysis of Ion Trajectory in Mass Spectrometer with Circular Magnetic Field

Abstract

Magnetic field used in usual mass spectrometers is of so-called sector or Nier type with straight boundaries. In this paper, a circular magnetic field, which was originated by Bainbridge and has hitherto been disregarded, is taken up to apply it to multi-dispertion system with ion mirrors, simplifying the construction and adjustment of the spectrometer. Analysis of ion trajectory in this magnetic field is given.
In a symmetrical circular magnetic field, spherical aberration by a right angle deflection of ion beam becomes 4Rα³ where 2α is the aperture angle of the ion beam at its source and R the radius of trajectory. Rα² being the spherical aberration in a symmetrical sector field, the advantage of the circular field over the sector field is obvious; a significant improvement upon resolving power and sensitivity of mass spectrometer is therefore expected. by the use of circular magnetic field. Introducing the concept of “index of performance”, the author estimates the increase of the index at approximately 100% under ordinary working conditions.
On the assumption that, in double-dispersion system-the simplest case of multi-dispersion system-with one magnetic field and one ion mirror, the ion beam to the mirror and that reflected from the mirrror are correctly on the same route, dispersion distance and the beam width at the collector are evaluated.
Generally, chromatic and spherical aberrations increase in proportion to dispersion; in double dispersion system, they become roughly twice of those in single dispersion system while the width of the image of ion souce slit remains the same as that of the slit. Therefore, the resolving power now defind as the ratio of dispersion distance to twice of beam width, which is different from customarily accepted interpretation, do increase.
Especially, the third-order spherical aberration, as well as the second-order aberration, vanishes in a circular field by a right angle deflection, and the resolving power becomes independent of the aperture angle of ion beam at its source. This means that the sensitivity of a mass spectrometer can be increased at will without lowering the resolving power.