At TRIUMF, a large experimental particle and nuclear physics research facility on the campus of the University of British Columbia, one major programme involves the production of intense beams of unstable isotopes of alkali atoms (potassium K, rubidium Rb, francium Fr). These have the advantage that since their valence shell contains only one electron, their closed shell structure when they are ionised simplifies calculations.
Many isotopes are produced when bombarding a calcium oxide target with 0.5 GeV protons from the TRIUMF accelerator. Until recently, the desired isotope was selected by means of the TRIUMF Isotope Separator On-Line (TISOL)—now decommissioned and replaced by a combined separator/accelerator called ISAC—and sent as a low-speed beam to experimental areas.
You are asked to design a (much) simplified version of TISOL. More specifically, you want to select 38K ions whose energy is 20 keV. 38K has a mass of 6.3×10−26 kg. Separation should proceed in two steps, as illustrated below.
[Figure: Diagram showing ion path through (1) Velocity Selector and (2) Mass Separator with radius R, showing the desired path of a 20 keV 38K ion]
The figure shows the desired path of a 20 keV 38K ion through the system. This path is to be achieved by means of suitable uniform time-independent electromagnetic fields. Interactions between ions can be neglected here.
(a) In the first step, out of all ions (38K or not) entering the velocity selector from the left, only those that have a speed corresponding to a 20 keV 38K ion should be undeflected. Suggest a field configuration that can do this, draw a sketch showing the direction of the field(s), and derive as much information as you can about the magnitude of the field(s).
(b) In the second step, only 38K ions should be deflected so that the radius R of their trajectory is 2.1 m. Again, suggest a suitable field configuration for this, draw a sketch showing the direction of the field(s), and derive as much information as you can about the magnitude of the field(s).