-5EXPERIMENTAL The best practical instrument to use in a study of ion source characteristics is the parallel-field analyzer originally developed by Thomson.° In this device, the beam of ions is passed through parallel electric and magnetic fields, these fields being transverse to the original direction of the beam, as indicated in Fig. 2. After leaving the region of the fields, the beam travels a certain distance and impinges on a plate perpendicular to the original beam direction. A system of rectangular coordinates may be set up on such plate with the origin at the point of impact of the undeflected beam, the x axis in the direction in which the beam is displaced by the electric field, and the y axis in the direction in which the beam is displaced by the magnetic field. The equations of motion of an ion in the arrangement of fields shown in Fig. 2 can be solved exactly, but are quite complicated. However, inthe case where the radius a of the circular magnetic field is much less than the radius of curvature R of the ion trajectory in the magnetic field, a relatively simple approximate solution can be obtained. These equations can then be used to give initial conditions of motion of the ion in the field-free space between the deflecting system and the collector plate. They in turn permit evaluation of the deflections x (by the electric field) and y (by the magnetic field) of the point of impact of the ion beam, as functions of the velocity y, mass m, and charge q of the ions, the electric and magnetic field strengths E and H, and the dimensions of the apparatus (a and £ in Fig. 2); ~2alH 1q ye xFale- 4.4 -agn. 4 Vv 1/2 mv 9001834 0) " (2) |