A theoretical model is developed for calculating the eigenmodes of the multi-gap resonant cavity. The structure of concern is a kind of ladder-type circuit, offering the advantages of easy fabrication, high characteristic impedance （R/Q）, and thermal capacity in the millimeter wave to THz regime. The eigenfunction expansion method is used to establish the field expressions for the gaps and the coupling region. Then, the match conditions at the interface are employed, which leads to a group of complicate boundary equations in the form of an infinite series. To facilitate the mathematical treatments and perform a highly efficient calculation, these boundary equations are transformed into the algebraic forms through the matrix representations. Finally, the concise dispersion equation is obtained. The roots of the dispersion equation include both the axial modes in the gaps, which include the fundamental and the high-order modes, and the cavity modes in the coupling region. Extensive numerical results are presented and the behaviors of the multi-gap resonant cavity are examined.
The focusing and the stable transport of an intense elliptic sheet electron beam in a uniform magnetic field are investigated thoroughly by using the macroscopic cold-fluid model and the single-particle orbit theory.The results indicate that the envelopes and the tilted angles of the sheet electron beam obtained by the two theories are consistent.The single-particle orbit theory is more accurate due to its treatment of the space-charge fields in a rectangular drift tube.The macroscopic cold-fluid model describes the collective transport process in order to provide detailed information about the beam dynamics,such as beam shape,density,and velocity profile.The tilt of the elliptic sheet beam in a uniform magnetic field is carefully studied and demonstrated.The results presented in this paper provide two complete theories for systemically discussing the transport of the sheet beam and are useful for understanding and guiding the practical engineering design of electron optics systems in high power vacuum electronic devices.
