Cyclotron autoresonance acceleration with seventh harmonic co-generation

The TE₇₂ mode in a cylindrical waveguide at frequency 7ω has its group velocity υ_gr nearly equal to that of the TE₁₁ mode at frequency ω. In consequence, the two modes have nearly equal resonant magnetic fields for strongly coupled interactions at electron cyclotron resonance. This allows coherent radiation in the TE₇₂ mode to be generated at 7ω as a gyrating electron beam is energized using the TE₁₁ mode at frequency ω in the same waveguide. It is shown analytically that the electron gyration radius can approach 0.5431 times the waveguide radius during cyclotron autoresonance acceleration, for an axis-encircling beam injected with zero transverse momentum. This fact allows electron acceleration to relativistic energies using the TE₁₁ mode to lead to large enough axis-encircling orbit radii for strong coupling with the TE₇₂ fields. Results of a particle simulation study are discussed for a 300-kV, 30-A finite-emittance pencil beam injected into a 3.27-cm-radius waveguide, and driven with 20 MW of radio frequency (RF) power at 2.856 GHz. The results show that careful choice of the magnetic field profile, and suppression of the TE₁₁ mode after its power is depleted, can allow seventh-harmonic output to reach 10 MW at 20 GHz. Furthermore, it is shown that injection at the input of harmonic power can also benefit co-generation, both increasing seventh-harmonic output up to 16 MW and improving spent beam quality. Higher spent beam quality is advantageous for efficient beam energy recovery