研究目的

To present an analytic theory for Smith–Purcell device in which a cylindrical metal–dielectric grating was derived by an annular electron beam propagating along the grating axis and to compare the first-order and second-order growth rates of the modes which are in phase with the beam.

研究成果

In this paper, we have presented a theory of Smith–Purcell radiation from a metallic–dielectric cylindrical grating. In this configuration, the effect of grating parameters on the dispersion curves, growth rate and start current is considered. Loading dielectric and making slots with smaller lengths and higher depths lead to flatter dispersion curves and reduce the operating frequency of beam–wave interaction. Consideration of the first-order and second-order growth rates at resonance points reveals that increasing the depth and decreasing the length of the slots, decreasing ??r and also expanding the beam thickness give rise to higher values of normalized growth rate. Also, increasing the relative velocity of the beam enhances the growth first, and then, it starts to fall depending on the frequency at the operating point. Comparison between two growth curves reveals that the second-order growth rate is more accurate especially when larger values for the slot length and beam thickness, as well as smaller ones for the slot depth, are taken. In addition, the start current required for BWO operation of SP-FEL is derived by using the boundary conditions and the dispersion relation. It is shown that increasing the relative dielectric permittivity increases the start current at first. However, the start current falls when ??r is larger than about 9. Moreover, increasing the grating length, as well as decreasing the slot length and depth, reduces the threshold current. These results can be employed to optimize the FELs based on Smith–Purcell radiation.