FOCUSING OF CHARGED PARTICLES IN A CYLINDRICALLY SYMMETRIC MAGNETIC FIELD PROPORTIONAL TO r−1

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Abstract
The aberrations associated with skew trajectories lying near the midplane of a "flat"-type β spectrometer with a magnetic field falling off as r−1 have been surveyed over wide ranges of values of the field strength at the source and of the angle of emission; Lafoucrière (1950) showed that such a field possesses a perfect focus for midplanar orbits. A field strength has been found for which the aberrations corresponding to finite aperture are exceedingly small; with a point source it would be possible to get transmissions of 2.3% and 6.0% at resolutions of 0.01% and 0.1% respectively. The defocusing resulting from finite source-height has been studied for this particular value of the field strength and has been found to be large; the resulting permissible source-area is so small that the luminosity of the instrument is inferior to that of a π√2 spectrometer.Methods of producing fields varying as r−1 over a wide range of r have been investigated; both iron pole-pieces and iron-free coils have been considered.