Linear and Non-linear Analysis of Dust Acoustic Waves in Electronegative Halley Comet Plasma

Abstract

In this thesis, we have discussed lineariandinon-linear effectskonkdust acousticiwaves (DAWs) inia magnetized electronegative dusty plasma. By electronegative dusty plasma, we mean the plasmaihaving electrons, positive ions, negative ions, and dust particulates constituents. In theilinear analysisiregime, initheiabsence of dusticharge fluctuations, the Doppler’s frequency and growth rate are our main focus. The Doppler’s frequency variation has been discussed with the effects of Cairns distributed positive ions, obliqueness of the magnetic field, densityiratio of electrons versus energetic positive ions, and normalized dust cyclotron frequency or magnitude of the magnetic field. It was found that for dust acoustic waves these parameters affect the Doppler’s frequency. Similarly, the growth rate variations have been discussed with the effects of Cairns distributed positive ions, obliqueness of the magnetic field, normalized dust cyclotron frequency, density ratio of electrons versus energetic positive ions, and density ratio of negative ions versus energetic positive ions. It was observed that for dust acoustic waves these parameters affect the growth rate. While in the same regime we also considered the dust charge fluctuation and derived a linear expression. Onithe otherihand, inithe non-lineariregime, DAWs have been investigated. Since we are studying the low-frequency wave, therefore, we have to enlarge the space and time coordinates by stretching the coordinates. By using the Reductive Perturbation Technique (RPT), the Korteweg-de Vries Burger equation isiderived for theismall butifinite amplitudeinon-linear dust acoustic wave (DAWs) bearing non-thermality (Cairns distributed) in the positive ions. In our case, the non-linear KdVB equation in the absence of the dust charge fluctuation, the dissipative term vanishes, and the non-linear KdVB equation is reduced to the KdV equation which admits solitary wave solution. While