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This paper reviews some of the assumptions made and some of the general problems involved in analyzing the behavior of electron streams coupled to circuits. It explains why a wave approach is used. The propagation constant of the wave is obtained in terms of the properties of the electron stream and the impedance of the circuit. Some general properties of waves are discussed. The importance of fitting boundary conditions in the solution of an actual problem is discussed, and examples, including that of “backward-gaining” waves, are discussed.
Jacob R. Pierce (1951) studied this question.