Higher order calculations have been performed for a recently proposed high dispersion β-ray spectrometer with a winding magnetic field. It is shown that the radial aberration terms of ϕr 2 and ϕz 2 simultaneously vanish by a suitable choice of the second field coefficient a 2 and the slope k. In the third, fourth and fifth order approximation a focusing independent of ϕr can be achieved. With a focusing angle of 909.72° and a focusing independent of ϕz 2 and up to the fifth order independent of ϕr, the intensity distributions of point sources at the image plane are calculated. It is shown that, using spark chambers with infinite resolution at the source and detector planes, the resolution depends on the position of the point source, but, for a wide range of source coordinates, is always Δp p < 2 × 10 −5 . In the usual case of β-ray spectroscopy with exit slit the resolution is found to be better than that for corresponding flat spectrometers.
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