Fig. 1. Beam-wave interaction circuit configurations of the 220 GHz Gyro-TWT (a) The 3-D structure diagram, (b) the interaction circuit schematic

Fig. 2. Dispersion diagram of 220 GHz PDL Gyro-TWT，（U0=70kV，beam velocity pitch factor α=1.2，magnetic detuning ratio b=0.98. Point A，B，C are backward wave oscillation points. The red circular area is convective instability area）

Fig. 3. The coupling coefficient of 220 GHz PDL Gyro-TWT versus normalized guide center radius

Fig. 4. The start current of absolute instability oscillation U0=70kV, (a) losses circuit with different b, (b) lossy circuit with different conductance

Fig. 5. The start length of backward wave oscillations with voltage U0=70kV and current I=3A, (a) longitudinal field profiles in losses circuit, (b) start length changing versus different conductance

Fig. 6. The linear gain versus frequency with losses and different conductance lossy circuit（U0=70kV，I=3A，α=1.2，b=0.98）

Fig. 7. The normalized field profiles of three backward wave oscillations in losses circuit（U0=70kV，I=3A，α=1.2，b=0.98）

Fig. 8. At 220 GHz，U0=70kV, I0=3A, B=8.16T, alpha=1.2,Pin=0.3W,σ=58S/m (a) the effect of the number of periods on the output power and gain, when Ld/Lp=0.83, (b) the effect of the dielectric slot ratio on the output power and gain when the number of periods is 21

Fig. 9. At 220 GHz，comparison of gain versus interaction circuit length（U0=70kV，I0=3A，B=8.16T，alpha=1.2，Pin=0.55W, and σ=58S/m）

Fig. 10. Pbeam，Pout and Ploss versus interaction circuit length（U0=70kV，I0=3A，B=8.16T，alpha=1.2，Pin=0.3W and σ=58S/m，at 220 GHz）

Fig. 11. The TE11 backward wave oscillation phenomenon (with TE01 as input signal at 220 GHz, U0=70kV, I0=3APin=0.55WL0=4.5mm, L1=36mm, L2=9.5mm, εr=11-4.4J,ro-rw=0.3mm) (a) evolution of the quadratic root value of Ppeak in the output part versus time (b) frequency spectrum of the output signals

Fig. 12. Attenuation of dielectric versus the dielectric thickness with εr=11-4.4J

Fig. 13. The TE21 backward wave oscillation phenomenon (with TE01 as input signal at 220 GHz, U0=70kV, I0=3APin=0.55WL0=4.5mm, L1=36mm, L2=10.2mmεr=11-4.4Jro-rw=0.43mm) (a) evolution of the quadratic root value of Ppeak in the output part versus time, (b) frequency spectrum of the output signals

Fig. 14. Output port signal of the four mainly competitional modes versus the simulation time at zero drive

Fig. 15. The 3D-PIC simulation results of optimized model (Pin=0.55W, at 220 GHz) (a) evolution of the quadratic root value of Ppeak in the output port versus time, (b) frequency spectrum of the output signals

Fig. 16. Comparison of output power versus frequency with Pin=0.55W at 220 GHz

Fig. 17. Comparison of output power gain versus Pin at 220 GHz