Nonlinear theory of harmonic peniotron and gyrotron interactions in a rising-sun slotted waveguide

A fully three-dimensional nonlinear theory is presented for the generation of harmonic peniotron and gyrotron radiation from a gyrating electron beam propagating through a multistage rising-sun type slotted waveguide. For an axisymmetric beam, a strong peniotron interaction is present if the dominant azimuthal mode index, l, of the waveguide modes is equal to s=l-1 where s is the cyclotron harmonic number and the gyrotron interaction is strong when l=s. Numerical results are shown for a two-stage, six-vane rising-sun circuit to illustrate the stable and efficient operation of the second harmonic peniotron in the π-mode (TE₃₁-like). The modes competing with the gyropeniotron amplification mechanism are suppressed in the two-stage rising-sun configuration. Simulations show that second harmonic gyropeniotron amplifier in the π-mode can operate at an efficiency of 45% with a 70-kV, 3-A beam having a velocity ratio 1.4, an axial velocity spread of 4%, and a guiding center spread of 4% in the presence of a guide magnetic field 2% below grazing. The instantaneous bandwidth of the amplifier is 4.6%. Since the spent beam is nearly monoenergetic, extremely high efficiency in excess of 70% could be achieved by using a single stage depressed collector to recover energy from the beam