The excitation of THz radiation by the interaction of an ultra short laser pulse with the modes of a miniature corrugated plasma waveguide is considered. The axially corrugated waveguide supports the electromagnetic (EM) modes with appropriate polarization and subluminal phase velocities that can be phase matched to the ponderomotive potential associated with laser pulse, making significant THz generation possible. This process is studied via full format Particle-in-Cell (PIC) simulations that, for the first time, model the nonlinear dynamics of the plasma and the self-consistent evolution of the laser pulse in the case where the laser pulse energy is entirely depleted. It is found that the generated THz is characterized by lateral emission from the channel, with a spectrum that may be narrow or broad depending on the laser intensity. A range of realistic laser pulse and plasma parameters is considered with the goal of maximizing the conversion efficiency of optical energy to THz radiation. As an example, a fixed drive pulse (0.55 J) with a spot size of 15 µm and duration of 15 f s produces 37.8 mJ of THz radiation in a 1.5 cm corrugated plasma waveguide with an on axis average density of 1.4 × 10 18 cm −3 .