A theoretical investigation is made in order to find approximate repre¬sentations for the small-signal analysis of magnetron beams. The present investigation is of particular interest for the understanding of the initiation of the degenerating effects occurring in magnetron beams as well as of the small-signal aspects of the beam-circuit coupling problem. Three new analytical thick beam models are suggested and investigated. The first is a self-consistent model in which the effect of a d-c velocity distribution is included. The second approximate beam model includes only the two slipping r-f surface charge layers on each side of the beam. This model gives a physical picture of the coupling between the six characteristic waves associated with the two equivalent surface charge layers. In the final model the effects of the r-f space charge density inside the beam are introduced in an approximate way. This model is only valid for moderately thick beams and a solution for the Brillouin beam case indicates that the r-f space charge density has the effect of decoupling the waves associated with the surface charge layers. The present analytical models include the effects of three beam characteristics: the space charge density, a linear slip and a velocity distribution. For moderately thick beams all of these characteristics are of importance for the description of characteristic waves which are in near synchronism with the average d-c electron velocity across the beam.
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