Hollow-beam focusing with electrostatic and periodic magnetic fields

A new method of focusing a hollow cylindrical electron beam is presented. The focusing system consists of a cylindrical center conductor inside the beam, a cylindrical outer conductor enclosing the beam, and a series of periodic magnets outside the tube. A radial electrostatic field between the conductors provides an outward force on the electrons. The periodic magnetic field produces an inward force on the electrons. The inward and outward forces can be adjusted to provide a balance of all the forces acting on the electrons at both boundaries of the beam by choosing the electric and magnetic fields properly. An approximate analysis has been made and is presented which gives necessary design information. A number of curves are presented which are useful in designing focusing systems of this type. Experimental results on a beam tester show that current transmission of over 90 per cent for perveance up to 11 micropervs can be obtained readily. The adjustments are not critical and the performance is very stable.