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8 - Electron Flow in Crossed Fields

Published online by Cambridge University Press:  27 April 2018

Richard G. Carter
Richard G. Carter
Affiliation:
Lancaster University
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Summary

The electron velocity in a linear, cylindrical (pencil), electron beam is determined by the potential difference between the cathode and the beam tunnel, taking space-charge potential depression into account. The effect of space-charge forces is to cause the beam radius to expand and static electric and magnetic fields can act as electron lenses. Beam spreading can be opposed by a uniform axial magnetic (solenoid) field if the beam is rotating. The conditions for stable flow are established using Busch’s theorem. The beam radius varies periodically (scalloping) if the initial conditions are incorrect. Increasing the current density increases the equilibrium beam radius to an extent controlled by the fraction of the magnetic flux linking the cathode (the beam stiffness). A pencil beam can also be collimated by a periodic array of converging magnetic lenses in periodic permanent magnet (PPM) focusing. Its properties are similar to those of a solenoid-focused beam with the addition of a periodic ripple in the radius. The design of practical focusing systems is described and the effects of imperfections including thermal velocities and trapped ions are discussed. Brief consideration is given to periodic electrostatic focusing and to the control of annular and sheet electron beams.
Type
Chapter
Information
Microwave and RF Vacuum Electronic Power Sources , pp. 287 - 316
Publisher: Cambridge University Press
Print publication year: 2018

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