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This paper discusses simulation and modeling of the slow wave structure of a folded-waveguide terahertz traveling wave tube (TWT) using the Improved Concurrent Electromagnetic Particle In Cell (ICEPIC) software. This is the first time ICEPIC has been used for simulation of a TWT amplifier. Cold test simulations compare favorably with analytical models; at 368 GHz, the on-axis interaction impedance is 7.8 Ω. Hot test (beam included) ICEPIC simulations were used to determine the effects of space charge on the gain calculations. At 368 GHz, the normalized beam plasma frequency from ICEPIC simulations is Ωp = 0.56. Analysis of our ICEPIC simulations at 368 GHz indicates a normalized beam plasma frequency 75% larger than an analytical model we improvised from a sheath helix model taken from the literature. The hot test ICEPIC simulations at 368 GHz for a 64 periods long slow wave structure and a 10 mA, 25 kV electron beam produce small signal gain of 27 dB. The small-signal fractional 3-dB bandwidth of the TWT is 2.9%. The saturated fractional 3-dB bandwidth is 3.2%. Large signal simulations indicate that the saturated power at 368 GHz is 39.4 dBm and the saturated gain is 21.8 dB. A snapshot of a cross section of the electron beam shows bunching in space and a corresponding modulation in the velocity of the electron beam.