Small-signal field analysis of GYRO-TWT amplifier

Abstract

A kinetic–theory based method of analyzing the small–signal amplification of TE and TM mode interaction of a circular cylindrical waveguide linearly interacting with an annular beam of gyrating electrons in a gyro-TWT configuration is presented in the thesis. Making use of the linearized Vlasov equation satisfied by the perturbed electron phase space density, the perturbed propagation phase constant is shown to satisfy a biquadratic algebraic equation when the cyclotron resonance condition is assumed to hold at the operating frequency. The biquadratic equation has always a pair of real roots and a second pair of complex conjugate roots. The complex root with positive imaginary part gives rise to a wave solution growing exponentially with propagation distance. With the cyclotron-resonance condition enforced over the entire frequency range by allowing the gyro-radius and the relativistic factor to be frequency-dependent, the variation of initial growth rate exhibit a sharp but large maximum in the case of TE mode interaction. However, in case of TM mode interaction, the initial growth rate of the interacting TM wave is seen to exhibit two maxima on either side of the minimum, a sharp but large maximum to the left and a broad but a smaller maximum to the right. However, it is impractical to allow any such variation of the gyro-TWT parameters with respect to the operating frequency in an amplifier. Thus, it is mandatory to keep the values of the relativistic factor and the normalized gyro-radius invariant with respect to frequency. On fixing the amplifier parameters, the growth-rate curve in case of TE mode interaction no longer exhibits a peak around the design frequency but rather a montonic variation with respect to frequency leading to severe frequency distortion of any signal with a frequency band centered around the design frequency. However, a gyro-TWT amplifier optimally designed for interaction with a TM mode of a circular cylindrical waveguide is shown to be capable of decent small-signal gain over a broad band of frequencies around the design frequency