A Theory of the Solenoid Beta-Ray Spectrometer

Abstract

A theory of the magnetic lens beta‐ray spectrometer utilizing the uniform field of a long solenoid is developed. First the case of a point source is considered, and it is found that the resolving power, for a given solid angle, is maximum when the emission angle α (average angle between the rays leaving the source and the axis) is 45° 37′. Then the theory is extended to the case of a disk source, and it is found that for a given intensity (product of the source area by the solid angle) there is an optimum source diameter and an optimum emission angle, ranging in practical cases between 36° and 40°. The problem of optimum conditions when the quantity of copper in the solenoid and the electric power available are limited by economical considerations is also studied, and it is found that the optimum α‐value is in this case about 21°.