Ion temperature gradient mode modulational stability analysis with cairn’s distribution

In this manuscript, we have studied electron-ion plasma with inhomogeneity in equilibrium number density and temperature. Ions are the dynamic species, and lighter particles in plasma obey the cairn’s distribution. We introduce Brajinskii’s equation for dynamic species and get the linear dispersion relation and the nonlinear Schrodinger equation by the reduction perturbation method. From the linear dispersion relation, we found the mode frequency and phase velocity, while from the nonlinear Schrodinger equation, we obtained the stability and instability of the ion temperature gradient mode modulation. Findings show that phase velocity is dependent on the superthermality coefficient and other plasma parameters like ion temperature, ion density, and mode parameter η i . Further, the modulational stability and instability of the mode vary with the superthermality coefficient and other plasma parameters, especially the η i . We can apply these observations equally to the laboratory as well as to the space plasma.