Fig. 1. Cross section of quasi-optical waveguides in elliptic coordinate system: (a) Normal confocal waveguide; (b) double confocal waveguide.

Fig. 2. Transverse geometry with the annular electron beam and electric field distributions of TE_{0, 11} mode in two types of quasi-optical waveguides: (a) Normal confocal waveguide; (b) double confocal waveguide.

Fig. 3. Mode spectrum in double confocal waveguide.

Fig. 4. Double confocal cavity: (a) Structural diagram; (b) axial field profile of TE_0,11,1 mode.

Fig. 5. Beam-wave coupling factors as functions of electron beam radius R_b for different modes in double confocal waveguides.

Fig. 6. Beam-wave coupling factors for TE_0,11 mode in single and double confocal waveguide: (a) Radial distribution of coupling factor ; (b) azimuthal distribution of coupling factor L_s for an annular electron beam with R_b = 1.65 mm.

Fig. 7. Calculated results of starting current I_st (V₀ = 40 kV, α = 1.5, R_b = 1.65 mm): (a) For different modes in double confocal cavity; (b) for mode in double and single confocal cavity.

Fig. 8. Simulation results of output field E_x and E_y for double confocal cavity: (a) Time variation; (b) spectrum.

Fig. 9. Simulation results of the distribution of electronic field E_x in double confocal cavity: (a) At output port; (b) at the xz plane (y = 0); (c) at the yz plane (x = 0).

Fig. 10. Simulation results of the distribution of electronic field E_y in double confocal cavity: (a) At output port; (b) at the xz plane (y = 0); (c) at the yz plane (x = 0).

Fig. 11. Simulation results for single confocal cavity: (a) Time variation of the output field E_x and E_y; (b) spectrum of the output field E_x.

Fig. 12. Simulation results of output power for double confocal cavity and single confocal cavity.

Fig. 13. Expanded results of the output field E_x and E_y for double confocal cavity around 100 ns.