Analytical and Numerical Study of Weibel Instability in Non-thermal Plasma
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GENERAL AND APPLIED PHYSICS
Analytical and Numerical Study of Weibel Instability in Non-thermal Plasma H. Rashid1 · F. Hadi2 · U. Zakir1 · A. Zeeshan1 Received: 20 July 2020 © Sociedade Brasileira de F´ısica 2020
Abstract The dispersion relation and growth rate γ of the parallel propagating Weibel mode in an unmagnetized, anisotropic nonthermal plasma are investigated using Cairns distribution function. The real and imaginary frequencies, considering Cairns distribution function in the limits of ξ >> 1 and ξ > 1), the real frequency of the wave under consideration is obtained, while in the lower limit (ξ and as a result a non-ceasing and exponentially growing magnetic field is produced [9]. The temperature anisotropy has an imperative role in many situations such as in an auroral ionosphere, solar wind, solar corona, and laboratory plasma. The magnetic field originated in the vicinity of cosmic rays, and supernova and gamma-ray bursts are also elucidated by temperature anisotropy [10–13]. A comprehensive interpretation of this instability was investigated by Fried in 1959 taking two streams of cold plasma as a distribution function [14]. In 1983, Davidson [15] for the first time named this instability as a filamentation instability. The said instability has been investigated by several authors considering Maxwellian and non-Maxwellian distributions [1, 16, 17]. The exact model describing classical Weibel instability was elaborated by Yoon and Davidson [18] in 1987, taking relativistic and anisotropic plasma and clarified different aspects of the mode by taking specific distribution function other than Maxwellian. The more simplified description of the investigation of Yoon and Davidson was enlightened by Yoon [19] in 1989, for relativistic plasma. The growth rate and instability condition were calculated by taking bi-Maxwellian distribution function. In 2006, kinetic Weibel instability was explained by Rolffs et al.
Braz J Phys
[20] in a relativistic plasma generalizing the work on biGaussian distribution, and the condition for the survival of unstable mode was derived. Further investigations of this instability in non-linear limit were presented by Califano at al. [21] in 2002, assuming the anisotropy as two opposite propagating beams with ion dynamics. In 2003, multi-species Weibel instability having large temperature anisotropy was investigated by Davidson et al. [22] using a sharp electron-ion beam traveling through electron-ion plasma. In 2003, Schilickeiser et al. [23] considered an unmagnetized plasma incorporating electron-ion collisions and presented their investigations taking opposite electronion beams leading to the threshold value for the mode. In 2007, Sadia et al. [1] considered three different distributions, i.e., bi-Maxwellian, Kappa, and generalized (r,q), to investigate the behavior and growth rate of the unstable wave. Mathematical relations are calculated for the unstable mode containing real and imaginary parts in the limits ξ >> 1 and > 1 and > 1 The plasma dispersion function is expande
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