We theoretically present the waveform controls of terahertz (THz) radiations generated from homogeneous and rippled plasma within inhomogeneous external electrostatic field. The Particle-in-cell (PIC) simulations is implemented to demonstrate generation and controllability of three types of THz pulses: single frequency THz pulse in homogeneous plasma, broadband THz pulse and dual frequency THz pulse in rippled plasma. The single frequency THz pulse can be tuned via shifting the knob of electron density of homogeneous plasma. Waveform of broadband THz pulse can be regulated into an envelope-like shape by varying amplitude of electron density of rippled plasma. The two center frequencies' interval of dual frequency THz pulse can be controlled by wave numbers of density distribution of rippled plasma. This work provides a potential means to generate the dual frequency THz pulses with two harmonic frequencies (ω+Ωω, Ω=2) or incommensurate frequencies (ω+Ωω, Ω=1.7,1.8, 2.2…).
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