Theory of gyrotron amplifier in a waveguide with inner dielectric material

Properties of the gyrotron interaction in a waveguide with inner dielectric rod are investigated for a hollow electron beam, including influence of azimuthally asymmetric perturbations. Stability analysis is carried out for an electron distribution function in which all electrons have the same value in the energy and canonical angular momentum but a lorentzian distribution in the axial momentum, A closed algebraic dispersion relation for a gyrotron amplifier with a centre rod of dielectric is obtained assuming that the hollow electron beam is thin. From numerical analysis of this dispersion rulation, it is shown that, stability behaviour of thes fust wave mode is remarkably independent of the dielectric constant. With a small axial momentum spread (Δ≲0.005), a super bandwidth is shown to be attainable by a mixed mode operation.