A Detailed Analysis of Beam Formation with Electron Guns of the Pierce Type

During the past few years there have been several additions to the family of microwave tubes requiring long electron beams of small diameter and high current density. Due to the limited electron current which can be drawn from unit area of a cathode surface with some assurance of long cathode operating life, high density electron beams have been produced largely through the use of convergent electron guns which increase markedly the current density in the beam over that at the cathode surface. An elegant approach to the design of convergent electron guns was provided by .J. R. Pierce 1 in 1940. Electron guns designed by this method are known as Pierce guns and have found extensive use in the production of long, high density beams for microwave tubes. More recent studies, reviewed in Section 2, have led to a better understanding of the influence on the electron beam of (a) the finite velocities with which electrons are emitted from the cathode surface, and (b) the :lefocusing electric fields associated with the transition from the accelerating region of the gun to the drift region beyond. Although these two effects have heretofore been treated separately, it is in many cases