Third harmonic Brillouin scattering of laser in weakly and strongly coupled plasmas

•Temporal growth rate of third harmonic Brillouin instability is obtained in both weakly and strongly coupling regimes.•Relativistic and thermal effects are taken into account in our model.•Collision and Landau damping effects are also examined in this research.•For the strongly coupled regime, the growth rate is higher than that in the weakly coupled regime.•In the weakly coupled regime, the growth rate strongly depends on the plasma temperature.•The growth rate has a reduction on enhancing the laser frequency. In this theoretical research, the mechanism of third harmonic stimulated Brillouin scattering (SBS) of laser in the interaction with a homogeneous unmagnetized plasma is investigated. Using the fluid model, we set up two coupled equations describing the third harmonic SBS and solve them to find the maximum temporal growth rate of the instability in both weakly and strongly coupling regimes. Electron-ion collision and Landau damping effects are also examined in this research. Results show that the growth rate in the strongly coupled regime is higher than that in the weakly coupled regime. It has also a reduction on enhancing the laser frequency. Moreover, in the weakly coupled regime, the growth rate strongly depends on the electron thermal velocity.