Mode stability analysis in the beam-wave interaction process for a three-gap Hughes-type coupled cavity chain

Based on space-charge wave theory, the formulae of the beam-wave coupling coefficient and the beam-loaded conductance are given for the beam-wave interaction in an N-gap Hughes-type coupled cavity chain. The ratio of the nonbeam-loaded quality factor of the coupled cavity chain to the beam quality factor is used to determine the stability of the beam-wave interaction. As an example, the stabilities of the beam-wave interaction in a three-gap Hughes-type coupled cavity chain are discussed with the formulae and the CST code for the operations of the 2π, π, and π/2 modes, respectively. The results show that stable operation of the 2π, π, and π/2 modes may all be realized in an extended-interaction klystron with the three-gap Hughes-type coupled cavity chain.