The folded waveguide structure is a promising slow-wave structure for terahertz traveling wave tubes.The influence of the beam tunnel on the circuit cold characteristics was analyzed,including dispersion relation,interaction impedance and circuit attenuation.The simulation results show that a beam tunnel with a rectangular cross section exhibits slightly steeper dispersion relation and higher attenuation coefficient than the beam tunnel with a circular cross section.Compared with the beam tunnel with a circular cross section,interaction impedance of beam tunnel with a rectangular cross section is lower about 0.5 Ω at a 220 GHz central frequency.For cold beam,the linear theory predicts a gain growth rate of 4.85 dB/cm and 5.22 dB/cm,respectively.They have a similar 3dB bandwidth of 6.3 GHz and 7.2 GHz.The large signal simulations show that the nonlinear gain is 24.42 dB and 28.44 dB at 220 GHz for 54 mm(100 periods)folded waveguide slow-wave structure with rectangular cross section and circular cross section,respectively.