Modulational Instability of Ion Acoustic Waves in a Magnetized Plasma Consisting of Isothermally Distributed Hot and Cold Electrons

Using the standard Reductive Perturbation Method a nonlinear Schr¨odinger equation is derived to study the modulational instability of small amplitude ion acoustic waves in a collisionless magnetized plasma composed of adiabatic warm ions, Maxwell-Boltzmann distribution of hot electrons as well as Maxwell-Boltzmann distribution of cold electrons, and the plasma system immersed in an external uniform static magnetic field (B0 = B0ˆz) propagating along the z-axis.
The instability condition and the maximum growth rate of instability have been investigated analytically as well as numerically. We have studied the effect of each parameter of the present plasma system on the maximum growth rate of instability. In particular, it is found that the maximum growth rate of instability decreases with the increasing value of the ion cyclotron frequency with some set of values of the parameters associated with the present plasma system. Again, we have seen that the instability region decreases with the increasing value of the ion cyclotron frequency.