A two-temperature thermal non-equilibrium model is used to simulate and compare the arc characteristics within the converging-diverging and traditional cylindrical plasma torches. The modeling results show that the presence of the constrictor within the converging-diverging torch makes the evolution characteristics of the arc significantly different from that of cylindrical torch. Compared with a cylindrical geometrical torch, a much higher plasma flow velocity and relatively longer high temperature region can be generated and maintained inside the converging-diverging torch. In the constrictor of converging-diverging torch, the normalized radius of arc column increases and the degree of thermodynamic equilibrium of the plasma is significantly improved with the increase of axial distance. The radial momentum balance analysis shows that for the cylindrical torch, the pressure gradient that drives the arc expansion and the Lorentz force that drives the arc contraction dominate the radial evolution of the arc. While at the converging and constrictor region of a converging-diverging plasma torch, the radial gas dynamic forces in arc fringes pointing toward the arc center enhance the mixing of the cold gas of boundary layer with the high temperature gas of the arc center, increasing the average gas temperature and decreasing the thickness of cold boundary layer, thereby facilitating the formation of diffusion type arc anode attachment at the diverging section of torch.