Study Of Quantum And Semi-Relativistic Effects On Weibel Instability In Anisotropic Plasmas

In space and laboratory plasma, it is a common phenomenon that the velocityspace of particle is nonuniform, this kind of phase space nonuniformity easily induceinstability. Weibel instability is a kind of instability which is caused by the anisotropyof electron temperature or momentum. The development of Weibel instability wouldlead to strong pinch and filamentation, the filamentation is very important in manyunmagnetized plasmas. Meanwhile, with the instability, the plasma can stimulatequasi static spontaneous magnetic field, which is widely used in controlled nuclearfusion, fast ignition. Therefore the investigation of Weibel instability is significantlyimportant. In this paper, we considered the quantum and semi-relativistic effects onWeibel instability in the unmagnetized anisotropic plasma.The dispersion equation of Weibel instability in the unmagnetized plasmasystem with arbitrary degeneracy anisotropic Fermi distribution is presented based onthe Vlasov-Maxwellian kinetic theory. For the arbitrary degeneracy case, thenumerical analysis is used and the growth rate is obtained, which decreases with theloss of the degree of anisotropy; and the result of non-degenerated limit candegenerate to the Maxwellian distribution of high temperate limit. The conclusionmay be responsible for the next-generation intense laser-solid density plasmaexperiments.The short-range collision of plasma particle can cause the change of plasmaproperty, thus resulting in a variety of plasma collective phenomena, such asinstability, fluctuation of plasma. Therfore, considering the electron-ion coulombcollision effect, we discussed Weibel instability in a semi-relativistic anisotropicplasma. Based on classical kinetic theory, we obtain the dispersion relation of Weibelinstability in dense and unmagnetized anisotropic plasma. An analytical expression isderived for the growth rate of the Weibel instability. Then, two limiting cases areconsidered. The results show that the growth rate decreases with the increase ofcollisions frequency, as semi-relativistic effects lead to constraint relaxation, thusweak anisotropy of temperature can stimulate instability as well.