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In this work, the Weibel instability (WI) due to inverse bremsstrahlung (IB) absorption in a laser fusion plasma has been investigated. The stabilization effect due to the coupling of the self-generated magnetic field by WI with the laser wave field is explicitly shown. In this study, the relativistic effects are taken into account. Here, the basic equation is the relativistic Fokker-Planck (F-P) equation. The main obtained result is that the coupling of self-generated magnetic field with the laser wave causes a stabilizing effect of excited Weibel modes. We found a decrease in the spectral range of Weibel unstable modes. This decreasing is accompanied by a reduction of two orders in the growth rate of instable Weibel modes or even stabilization of these modes. It has been shown that the previous analysis of the Weibel instability due to IB has overestimated the values of the generated magnetic fields. Therefore, the generation of magnetic fields by the WI due to IB should not affect the experiences of an inertial confinement fusion.

The present work has the aim to investigate the Weibel instability induced by inverse bremsstrahlung in laser fusion plasma, where the effect of the self-generated magnetic field is induced. Specifically, we have considered the generated static magnetic field effect on the inverse bremsstrahlung absorption. For this, we consider a homogeneous under dense plasma in interaction with a high-frequency and low-magnitude laser electric field. In our investigation, the unperturbed anisotropic distribution function which takes into account the plasma heating due to inverse bremsstrahlung absorption of laser energy is calculated from the Fokker-Planck equation. By using this distribution function, we have established the dispersion relation of the Weibel modes taking into account the coupling term of quasi-static magnetic fields with high frequency fields of the laser wave. The main obtained result is that the inclusion of the self-generated magnetic field in the inverse bremsstrahlung absorption causes a decrease of the spectral range of the Weibel unstable modes and a reduction of the growth rate of the instability by two orders. This result shows clearly that the previous analyses of the Weibel instability due to inverse bremsstrahlung have an over estimated for the values of the generated static magnetic fields. Therefore, inverse bremsstrahlung overestimated the values of the generated static magnetic fields should not affect the experiences of inertial confinement fusion.

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In this work, have put forward a philosophy of the Weibel instability in laser fusion plasma; these instabilities generated by several mechanisms, namely: the heat transport, the expansion of the plasma and the inverse bremsstrahlung absorption (IB). Several research papers have been presented as well as theoretical models for the relaxation and stability of these modes, which are considered to be very flammable and peaceful on the interaction yield between lasers and plasma. To resolve these modes must be combined with the magnetic field. The stabilization effect due to the coupling of the self-generated magnetic field by Weibel instability with the laser wave field is explicitly showed in recently paper. In these studies, the relativistic and non-relativistic or linear and non-linear effects are taken into account here; the basic equation is the Fokker-Planck (F-P) or Vlasov equation. The best result is that the coupling of self-generated magnetic field with the laser wave causes a stabilizing effect of excited Weibel modes in the all states. Found a decrease in the spectral range of Weibel unstable modes. This decreasing is accompanied by a reduction of orders in the growth rate of instability or even stabilization of these modes. It has been shown that the previous analysis of the Weibel instability due to IB have overestimated the values of the generated magnetic fields.