Fig. 1. （a），（b）Layout of the EIO circuit.（c）Dispersion diagram of the EIO and（d）the electric distribution of the operation 2π mode.

Fig. 2. The（a）M²R/Q and the（b）normalized beam-loading conductance variations with the beam voltage in the cases of 5-11gaps.

Fig. 3. （a）Output radiation power，operating frequencies，and oscillation-starting time versus cy.（b）Three-dimensional PIC simulation results：the 2D variation of output power relative to cy and the emission current.

Fig. 4. （a）Output radiation power，operating frequencies，and oscillation-starting time versus e.（b）The distributions of Ez field along the center line of the beam tunnel with the increase of e.

Fig. 5. The circuit output characteristics versus operation current when U is（a）17.5，（b）18.0 and（c）18.4 kV respectively. The oscillation-starting condition is characterized by comparing the output power P_out，starting time T_s and operation frequency f of the EIO circuit.

Fig. 6. （a）The fabricated copper EIO structure.（b）Measured values of reflection parameter S11 and simulated values at conductivities of 1.6e7 S/m and 5.8e7 S/m.

Fig. 7. Output radiation power，operating frequencies，and oscillation-starting time versus conductivity.