On the Analysis of Electronic Velocities by Electrostatic Means

In magnetic analysis of electronic velocities the plane containing the receiving slit is placed at the angle ${\Phi }_m=180\mathrm{}°$ to the plane containing the entrance slit. The "resolution," at ${\Phi }_m$, between two electrons of velocities $V$ and $v$ both entering normally to the plane of the entrance slit, is $d_m=2\mathrm{}\beta r_0$, where $\beta =\frac{\mathrm{}(V-v)\mathrm{}}{V}$. The "departure from perfect re-focussing," at ${\Phi }_m$ of two electrons of velocity $V$, one entering normally to the plane of the entrance list and the other at an angle $\alpha$ to the normal, is $s_m={\alpha }^2{r}_0$. Since in some experiments the use of a magnetic field is a disadvantage, it is of interest to investigate the analyzing possibilities of electrostatic fields. In the present paper the radial, inverse first power, electrostatic field is considered in this connection. It is found that by a proper construction of the apparatus it should be possible to analyze velocities almost as well as by magnetic means. The plane of the receiving slit should be placed at the angle ${\Phi }_e=127\mathrm{}°{17}^{\prime }$ to the plane of the entrance slit. The resolution at this angle is given by $d_e=(2\mathrm{}\beta -4\mathrm{}{\beta }^2)r_0$, and the "departure from perfect re-focussing" by $s_e=\frac{4{\alpha }^2{r}_0}{3}$. It is also found that the 180° and 90° positions of the plane of the receiving slit are highly unsatisfactory. These results are obtained from approximate solutions of the equation of the electronic orbits, and are checked by numerical integration.