In this paper, the Coulomb collision effect of electron-ion is investigated based on the equilibrium bi-Maxwellian anisotropic distribution function in dense and unmagnetized plasma. An analytical expression is derived for the real frequency and the growth rate of the Weibel instability for two limiting cases |ξ=ω′k||θ|||≫1 and |ξ|≪1. In the limit |ξ|≪1, the quantity η that is due to a collisional term will appear in the growth and condition of the rate of the Weibel instability, which leads to a constraining condition of the growth rate. When η increases, the growth rate will increase and the wave instability will be distant from its own damping mode.
In this paper, the Coulomb collisional effect of electron-ion on the growth rate of Weibel instability is investigated based on the semi-relativistic Maxwellian distribution function in dense and unmagnetized plasma. An analytical expression was derived for the dispersion relation of Weibel instability for two limit cases |ξ = ω′/k‖ T‖|≫ 1 and |ξ| ≪ 1. In limit |ξ| ≫ 1 the dispersion relation only includes a real part and in limit |ξ| ≪ 1 the imaginary part of the frequency of waves' instability plays a role in the dispersion relation. In limit |ξ| ≪ 1, the two quantities μ and η, that are due to the relativistic and collisional effects, will appear in the growth rate of Weibel instability. The growth rate of Weible istability will be increased through decreasing the Coulomb collisional frequency and also increasing the temperature anisotropic parameter in strong relativistic limit.
Weibel electromagnetic instability has been studied analytically in relativistic plasma with high parallel temperature, where|α=(mc2/T∥)(1+p^⊥2/m2c2)1/2|≪1and while the collision effects of electron-ion scattering have also been considered. According to these conditions, an analytical expression is derived for the growth rate of the Weibel instability for a limiting case of|ζ=α/2(ω′/ck)|≪1, whereω′is the sum of the wave frequency of instability and the collision frequency of electrons with background ions. The results show that in the limiting conditionα≪1there is an unusual situation of the Weibel instability so thatT∥≫T⊥, while in the classic Weibel instabilityT∥≪T⊥. The obtained results show that the growth rate of the Weibel instability will be decreased due to an increase in the number of collisions and a decrease in the anisotropic temperature by the increasing of plasma density, while the increase of the parameterγ^⊥=(1+p^⊥2/m2c2)1/2leads to the increase of the Weibel instability growth rate.
In the field of fast ignition scheme, self‐generated magnetic fields via beam resistive filamentation have a significant role in the angular divergence of the relativistic electron beam, which can be affected by the intensity of other self‐generated magnetic fields. In this context, the effects of pressure gradient sources arising from temperature and density gradient of the pellet along the beam flow direction are investigated. The results showed that the resistive filamentation instability can be strongly amplified compared to the fully homogeneous plasma. In this respect, for the distance away from the critical surface, the instability is protected for a longer wave number. Also, the beam and plasma properties such as the beam relativistic factor, the beam number density, and the degree of the plasma temperature anisotropy might be effective.
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