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.
This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting wMls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low- frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency ωc to a wider usage range, which is restricted to be much larger than the plasma frequency ωp in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold λb, which is greatly dependent on the parameter ωc/ωp. The larger ωc/ωp is, the smaller λb will be needed. Moreover, the system parameters, including the wave number kx of the perturbations and the relativistic mass factor γb, will also influence the growth rate of diocotron instability obviously.
