Traveling-wave tube analysis of the Adler tube

The cyclotron waves on an electron beam in the pump field of the Adler tube are studied with respect to their circular polarization. It is found that positive and negative circularly polarized beam waves are coupled through the pump electric field. As a consequence of the coupling, the small signal traveling-wave analysis leads to the conclusion that the positive circularly polarized beam wave is comprised of the fast signal wave and all idlers of frequencies
n(\omega \pm \omega_{p})
where n is an even integer, while the negative circularly polarized wave is comprised of all idlers with odd integral values of n. This information appears to be new, and can perhaps be used to design input and output couplers which discriminate against unwanted idler waves.