The advantages of using symmetrical and asymmetric eigenmodes of a slow-wave system (SWS) in a relativistic traveling-wave tube (TWT) with multi-pass amplification are discussed. The nonlinear theory of such a TWT amplifier is developed. The parameters of the SWS of the Ka-band TWT amplifier based on a combination of the lower symmetric E01 mode and the asymmetric hybrid HE11 mode are calculated. The calculated efficiency of the amplifier reaches 28% with a gain of about 40 dB. The results of the calculations are confirmed by 3D particle-in-cell (PIC) simulation, in which an output power of 200 MW and a total gain of about 40 dB are obtained when the amplifier is driven by a 500 keV/2 kA hollow electron beam with a total pulse duration of 25 ns. Amplification of short millimeter-wave pulses is also demonstrated in PIC simulations, in which an output peak power of about 180 MW with a pulse duration of the order of 1 ns is obtained.

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