The effect of shear flow and the density gradient on the Weibel instability growth rate in the dense plasma

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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.