A three-dimensional multifrequency interaction model for helix traveling wave tubes is described. Spatial variation of the amplitude of the wave is found by field theory. With the help of paticle-in-cell （PIC） method and space harmonic current and charge expansion, the three-dimensional space charge field is found. using the code, 8—18GHz wide band TWT is simulated for different frequencies. Also, the nonlinear AM-AM and AM-PM distortion,third-order intermodulation products and fifth-order intermodulation are computed. The hot data of experiment is close to the code computation in saturation output power and output gains in the range of 8—18GHz.