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A study of electron beams and their formation in electrostatic electron guns

University of British Columbia

A theoretical study is made of the formation of electron beams in electrostatic fields. The electron motion is assumed to be normal, congruent and regular, so that the equations governing the motion can be set up in terms of the action function. By assuming convenient functional forms of the action function, of the potential and of the metrical coefficients, some new solutions are then found by the method of separation of variables. These solutions are studied in detail, and are shown to have some desirable properties. In order to employ a given space-charge flow solution in electron gun design, a method is developed to take into account the distortion of the field due to the anode aperture. In this method, the gun is considered to be made up of two regions, separated outside the beam by an auxiliary anode. The desired space-charge flow is assumed to exist in the cathode region, while in the anode region the effect of space-charge on the electrostatic field is assumed to be negligible. An estimate is made of the accuracy of these assumptions. The fields about four idealized anode geometries are obtained by using Schwarz-Christoffel transformations, and a study is made of the relevant properties of these fields. One of these fields, which has been called the "wrap-around field", is shown to have properties that are very desirable for convergent electron guns. The above design method is illustrated by two examples; namely, a gun producing a beam that is initially parallel and rectilinear, and a gun producing a beam that is initially radial and convergent; the latter incorporates the wrap-around field in the anode region. Physical considerations involved in the determination of the electrodes to maintain a given beam are briefly discussed, and it is shown that the sensitivity of the field conditions at the beam boundary to errors in the field at other locations decreases at an exponential rate with distance. A method is suggested for determining beam-forming electrodes that avoids the need for an auxiliary anode to maintain the beam.

Text

2011-10-28

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http://hdl.handle.net/2429/38407

Electrical and Computer Engineering

University of British Columbia

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