Electron beam characteristics in radially varying periodic magnetic fields

Periodic magnetic fields are being widely used for the light-weight focusing of beams in high-power traveling-wave tubes. In many tube designs, there exists a considerable amount of radial variation in the magnetic focusing field. The effect of this radial field variation is investigated analytically as an extension of the previous work in this field. The usual design curves of α vs β are plotted with three variable parameters: ripple, cathode shielding parameter , and radial field variation parameter x0. It is noted that it is important to keep the magnetic-field strength constant at the beam edge over a considerable variation of the magnetic-field parameter x0.