Linear theory of slow wave cyclotron interaction in double-ridged folded rectangular waveguide

A general dispersion relation for slow wave cyclotron traveling wave interaction in a folded waveguide is derived from a fluid dynamical treatment. The serpentine structure is formed by folding a double-ridged rectangular waveguide so that the orientation of the magnetic field changes (H-plane bend) instead of the conventional E-plane bend configuration. The H-plane bend structure has the potential for the production of high power, broad band radiation. For a cold beam, the linear theory predicts a gain of 2.0-2.5 dB/cm and a bandwidth of 20-25% in the millimeter wave frequencies. The bandwidth is sensitive to the axial velocity spread of the beam. The bandwidth decreases to 10% at δυ_z/υ_z=3%. Means to suppress the backward wave oscillations have to be applied for using the full bandwidth