1963 | OriginalPaper | Buchkapitel
Axially-symmetric space-charge flow in a decelerating space
verfasst von : D. A. Dunn, R. P. Borghi, R. C. Morwood
Erschienen in: Microwaves
Verlag: Macmillan Education UK
Enthalten in: Professional Book Archive
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To the extent that an electron beam of finite cross-section in a decelerating space can be considered as a one-diraensional problem, the theory presented by Pay, Samuel and Shockley [l] and by others [5], [6], [7] provides an adequate description of the beam at currents less than that of limiting perveance. If the current exceeds that corresponding to limiting perveance, it has been shown that the device does not select one of the static modes, but chooses a time-varying solution to the problem [2], [3]. Below limiting perveance the static theory is correct. The results of this static theory may be summarized as follows. Electrons are injected into the space between two. parallel planes at a velocity corresponding to the potential of the first plane with a current density J. The spacing between planes is d and the second plane is at potential V2 The solution of Poisson’ s equation in one dimension yields the form of the potential V(z)between the values V1 and V2 at z = 0 and z = das a function of the injected current density J.