On simple models for field theories of certain electron-beam devices

Abstract

Beginning with a survey of the appropriate literature, the author shows that extant linear theories of phenomena in microwave electron-beam devices are of two types : (a) theories based upon field-theoretic models, attended by formidable analytical difficulties : and (b) transmission-Line theories, with much simpler mathematical structure, but which (being one-dimensional) do not yield the field vectors. With the aid of a somewhat artificial but geometrically and physically simple new (but non-periodic) model for the slow wave guide (affording very simple boundary conditions), the author defines and develops some properties of field-theoretic models which preserve much of the mathematical simplicity of tranamission-line theories, This is shown, in particular, that theories based upon his model are in general agreement with existing theories. The author then applies his model to solve the case of non-vanishing a.c. transverse velocity components in the beam, an d the resulting theory predicts the existence of an unexpectedly large number of waves in the beam, and-field system. The paper concludes with brief mention of some properties of theories based upon this new model in the case of multi-valued d.c. velocities in the beam, and on its modification into an actual periodic structure. (The important mathematical tools used are the Laplace transform and the theory of solutions of Hill's equation.)

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HERBERT H. SNYDER

† Present address: Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.