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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.
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 a example, the stabilities of the beam-wave interaction in a three-gap Hughes-type coupled cavity chain are discussed with the formula and the CST code for the operations of the 2π, π, and π / 2 modes, respectively. These 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.