Coupling of tilting gaussian beam with hybrid mode in the corrugated waveguide

The mode-conversion loss in the matching between the gaussian beam emanated from the gyrotron and the hybrid mode in the circular corrugated waveguide with the diameter of 2a is discussed. By numerical calculation, it is found that the loss considerably increases and optimum waist size w₀ changes when TEM₀₀ mode with the wavelength λ is injected with offset or tilt. By fitting numerical data to the polynomial function, it becomes evident that the scaling formulas of the losses for the off-axis shift r_d and for the tilt angle θ are derived to be 2.3(r_d/a)² - 2.2(r_d/a)⁴ and 3.9(aθ/λ)² - 5.6(aθ/λ)⁴ for fixed w₀/a=0.643, respectively. To keep the mode-conversion loss ≤1% for the frequency of 168 GHz and 2a=88.9 mm, tilting angle and offset should be less than 0.1 degrees and 2.9 mm, respectively.