Stability of a cylindrical electron beam in nonsinusoidal periodic magnetic-focusing fields

The Theory of Mendel, Quate, and Yocum is extended to include experimental and analytical examination of magnetic fields whose axial variation is periodic, but not sinusoidal. Magnetic fields of this type are encountered in many typical periodic focusing structures. Minimum-ripple flow is achieved by setting the rms value of the magnetic field equal to the Brillouin value of the field. The fraction of a beam current traversing a long hollow drift tube has been measured as a function of the amount of departure of the magnetic field variation from a sinusoidal one.