Fast-wave Propagation in Plasma-filled Waveguides†

Abstract

In the analysis of the waves which propagate in a waveguide completely or partially filled with a stationary plasma column or an electron beam drifting with a uniform velocity and collimated with a magnetic field of finite magnitude, it is necessary to include the effects of the rotation of the electric field in order to treat the waves which have phase velocities comparable to or greater than the velocity of light. Certain interesting features of perturbed waveguide modes and cyclotron modes become apparent only when the dynamic nature of the electric field is recognized in the analysis. These features are the influence of cyclotron frequency and the polarization of waves on the propagation characteristics. The cyclotron modes are found to be purely transverse electric at cut-off, gradually changing in character along their propagation curves through hybrid to purely transverse magnetic modes at cyclotron resonance. A classification of modes of propagation is proposed, and formulae for cut-off frequencies as functions of the cyclotron frequency as well as some representative Brillouin diagrams are given. Equations for neutralized electron beams are obtained when the Lorentz transformation is applied to the equations for stationary plasmas. The solutions for stationary plasmas can be transformed directly into the solutions for neutralized electron beams.