The space-charge limiting current of a sheet relativistic electron beam in a rippled rectangular waveguide

The expression of the space-charge limiting current of a sheet relativistic electron beam propagating in a rippled rectangular waveguide is derived. Using numerical computation, interesting results of the space-charge limiting current are provided. For the same sheet relativistic electron beam, the space-charge limiting current in a rippled rectangular waveguide with an average height of b(e) and a ripple amplitude of h(0) is less than that in a smooth-walled rectangular waveguide with a height of b(e)-2h(0), and larger than that in a smooth-walled rectangular waveguide of a height of b(e)+2h(0), and increases as the ripple period decreases. In addition, the larger the ripple amplitude of the rectangular waveguide is, the more rapidly the space-charge limiting current increases with the decrease in the ripple period. These results should be of interest to the area of propagation of intense sheet relativistic electron beam in a rippled rectangular waveguide for application of generating high-power microwaves. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3216457]