Shear stress effect has been often neglected in calculation of the Weibel instability growth rate in laser-plasma interactions. In the present work, the role of the shear stress in the Weibel instability growth rate in the dense plasma with density gradient is explored. By increasing the density gradient, the shear stress threshold is increasing and the range of the propagation angles of growing modes is limited. Therefore, by increasing steps of the density gradient plasma near the relativistic electron beam-emitting region, the Weibel instability occurs at a higher stress flow. Calculations show that the minimum value of the stress rate threshold for linear polarization is greater than that of circular polarization. The Wiebel instability growth rate for linear polarization is 18.3 times circular polarization. One sees that for increasing stress and density gradient effects, there are smaller maximal growth rates for the range of the propagation angles of growing modes π2<θmin<π and 3π2<θmin<2π in circular polarized plasma and for kcωp<4 in linear polarized plasma. Therefore, the shear stress and density gradient tend to stabilize the Weibel instability for kcωp<4 in linear polarized plasma. Also, the shear stress and density gradient tend to stabilize the Weibel instability for the range of the propagation angles of growing modes π2<θmin<π and 3π2<θmin<2π in circular polarized plasma.

Body stress flow can be expected in the fast ignition imploding of the inertial fusion process that strongly damps small-scale velocity structures. The Weibel instability is one of the plasma instabilities that require anisotropy in the distribution function. The body stress effect was neglected in the calculation of the Weibel instability growth rate. In this article, the propagation condition of impinging waves and the growing modes of the Weibel instability on the plasma density gradient of the fuel fusion with the body stress flow are investigated. Calculations show that the minimum value of the body stress rate threshold in the linear polarization is about 2.96 times greater than that of the circular polarization. Increasing 10 times of the density gradient and decreasing 2 times of the wavelength in the linear polarization and the circular polarization, respectively, lead to about 1.78 × 10 6 times increment and 0.019 times decrement in the maximum of the Weibel instability growth rate. Also, the Weibel instability growth rate maximum in the circular polarization is about 10 7 times greater than that of the linear polarization. The body stress flow and the density gradient tend to stabilize the Weibel instability in the circular polarization and act as a destabilizing source in the linear polarization. Therefore, by increasing steps of the density gradient plasma near the relativistic electron beam-emitting region, in the circular polarization, the Weibel instability occurs at a higher stress flow. KEYWORDSbody stress, density gradient, weibel instability INTRODUCTIONFor the inertial confinement fusion, experiments seek to compress a capsule (1.11 mm radius), consisting of deuterium-tritium fuel and an outer plastic (CH) ablator, to sufficient temperatures and densities that a self-sustaining thermonuclear burn is achieved. The flow of the target plasma is induced, which causes the implosion of the target plasma up to high density and temperature. [1][2][3] The fast ignition scenario is a very promising approach to inertial fusion, because it can significantly reduce the required laser energy. The fast ignition is a two-step process implying two drivers. The deuterium tritium pellet is first precompressed by a laser without being ignited. The outer layers of the capsule ablate and launch a series of shocks inward. Then, ignition is performed through a petawatt laser shot on the side of the fuel pellet. Laser impact on the surface of the fuel pellet generates a few tens of mega bars of intense pressure that isentropically compresses the deuterium tritium material to a few eV and a density of the order of 1,000 times the liquid deuterium tritium density. At the time of ignition, the fuel should be assembled into the lower-density region (100 g/cm 3 ), high-temperature (>10 keV) central hot spot surrounded by higher-density region (1,000 g/cm 3 ) deuterium-tritium fuel. The electrons driven by the ponderomotive pressure form. With increasing pressure, the elements of a body are compressed. Such a compression c...