Small Signal Power Theorem for Electron Beams

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Abstract
An analysis is presented of a filament beam in arbitrary dc electric and magnetic fields. The trajectory of the filament beam in the absence of ac fields may thus follow an arbitrary curve. It is shown that the electromagnetic power delivered by the filament beam is, within the assumptions of small signal theory, balanced by a decrease in the beam of a quantity, the ``generalized ac power'' in the beam. This ac power involves products of the small signal beam-excitation amplitudes. The ac power theorem for a filament beam can be extended to a thick beam. This is done to find the small signal ac power theorem for a two-dimensional rectilinear beam of finite thickness. The power theorem presented here is applicable to M-type and E-type traveling-wave devices. Applications to the noise theory and signal analysis of electron beams are indicated.

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