Theory of Magnetron Amplifier in a Helix-Loaded Waveguide With the Inner Dielectric Material

The theory of the propagation of the magnetized hollow relativistic electron beam with a dielectric rod at its axis through the sheath helix that inserted into the magnetron-type conductor is presented. The dispersion relation is obtained with the aid of the proper boundary conditions. The effects of an electron beam, inner dielectric, helix, and magnetron-type conductor parameters on the growth rate are studied numerically. The numerical results show that the presence of the cavity considerably increases the growth rate. In the fast wave mode, we have the maximum value of the growth rate when the dielectric rod and the electron beam are close to each other. The maximum growth rates for the fast and slow wave modes occur to the special value of the helix radius. The results show that the growth rate increases with the decreasing of the axial momentum spread. Comparison of the two modes shows that the growth rate of the slow wave mode is higher than that of the fast wave mode, but the bandwidth of the fast wave mode is wider than that of the slow wave mode.