In this paper, the role of the Weibel instability in process modulation and the possible impacts of the oscillation of the beam-electron velocity of the plasma aimed at reaching higher energy yields were investigated. For this reason, the effect of the laser time-dependent electric fields at the presence of Coulomb collision on the growth rate of the Weibel instability in the beam-plasma medium was calculated in dense and unmagnetized plasmas. The results showed that the velocity oscillation (due to the time-dependent electric field) leads to an increase in the growth rate of the Weibel instability when the energy transportation of the energetic particles to the fusion plasma systems decreases. The growth rate of the Weibel instability will increase through decreasing the Coulomb collisional frequency and also increasing the temperature anisotropic parameter within a strong relativistic limit.
