Abstract
The theory of tenuous hollow relativistic electron beam in the magnetron-type helix loaded waveguide was presented in the presence of sheath and axial magnetic field. The dispersion relation was obtained with the aid of the proper boundary conditions. The effects of electron beam, helix, and vane parameters on the gain and Doppler-shifted frequency were investigated numerically. The numerical results show that the presence of the vane considerably increases the gain. It has been shown that the maximum values of the gain occur at lower harmonics and the maximum values of the Doppler-shifted frequency occur at higher harmonics. The results show that the gain of the system increases when the helix move away from the vane.
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