During the interaction of a relativistic circularly polarized laser pulse with an overdense plasma target, the longitudinal motion of bunches of electrons under the action of light pressure and electrostatic restore force can emit intense terahertz (THz) pulses. This mechanism allows high pump laser intensity and large electron number participating in the emission. Two-dimensional particle-in-cell simulations are carried out to investigate the THz emission. The results suggest that such a source can produce remarkably intense THz pulses with energy of several mJ/sr and power of tens of gigawatts, which could find applications in nonlinear studies and relativistic laser-plasma interaction diagnostics.

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