In terms of the coupled equations of the radiation field and motion of the electron in a traveling wave tube amplifier, the threshold current at which the limit cycle or chaotic oscillation of the radiation field starts occurring is obtained. The result of numerical calculation shows that the nonlinear unsteady states may appear in a certain range of the parameters for the radiation field. The eff ect of the detuning on the threshold is relatively strong when the interaction r egion is longer. The relations of the output power with the three parameters (de tuning, current and interaction length) become chaotic when the device operates in the highly nonlinear regime, and the higher output power can be obtained if t he parameters are controlled suitably.