The Double Focusing Beta-Ray Spectrometer

The double focusing spectrometer recently proposed by Siegbahn and Svartholm has been analyzed and compared with the conventional semicircular spectrometer. A shaped magnetic field is required which possesses cylindrical symmetry as well as symmetry with respect to the median plane of the instrument. The magnetic field in the median plane is assumed to have the form $H=H_0-\frac{\mathrm{}(r-a)\mathrm{}\alpha H_0}{a}+\frac{{\mathrm{}(r-a)\mathrm{}}^2\beta H_0}{a^2},$ where $\alpha$ and $\beta$ are experimentally disposable shaping constants. The analysis, which has been carried through the second order of approximation, shows that double focusing occurs when $\alpha =\frac{1}{2}$. In general there will exist, for all types of spectrometers, second order defocusing terms which tend to lower the resolving power. However, these may be almost completely eliminated in the double focusing spectrometer by choosing $\beta =\frac{1}{8}$. A figure is presented showing the form of the focused image for a semicircular spectrometer and for several cases of the double focusing spectrometer. It becomes evident that when $\alpha =\frac{1}{2}$ and $\beta =\frac{1}{8}$, the intensity of the image as well as the resolving power become many times greater than for the former type of instrument.