The Two-stream Instability (TSI) generation is studied analytically in the lunar ionosphere. The TSI is a tiny perturbation in the electron plasma density, due to which an electric field grows with time and this growth is facilitated by the electron plasma in the background. In lunar ionosphere, the TSI comes into existence when the solar wind interacts unhindered with the tenuous lunar electron plasma in the surface bound exosphere. In this study, the conditions which allow the TSI to form and the subsequent instability growth with time i.e. the growth factor, is estimated. Initially, the threshold condition for the TSI to take place is determined. Thereafter, the solar wind and lunar plasma parameter contribution to trigger TSI is investigated along with the effect of these parameters in the evolution of TSI. The plasma TSI evolution with the passage of time is also depicted in phase space diagram with Particle-In-Cell simulations.
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