Contribution of the generalized (r, q) distributed electrons in the formation of nonlinear ion acoustic waves in upper ionospheric plasmas

The properties of ion acoustic solitary and periodic structures are studied in magnetized two-ion component (O+ − H+ − e) plasmas with (r, q) distributed electrons. It is found that two modes of ion acoustic waves, namely, fast and slow modes, can propagate in such a plasma. The nonlinear Zakharov–Kuznetsov equation is derived using the well-known reductive perturbation method. Employing the theory of planar dynamical systems, the system under consideration is found to admit compressive (hump) and rarefactive (dip) solitary structures and periodic wave solutions. It is found that behavior of propagation of nonlinear ion acoustic solitary structures is different for fast and slow modes owing to the difference in physics of the two modes. The effect of the double spectral indices r and q is thoroughly explored. It is shown that altering the shape of the distribution function through these indices radically alter the propagation characteristics of nonlinear ion acoustic waves. The ratio of concentration of heavy (O+) to light ions (H+) is found to change the fast mode, whereas the temperature ratio is observed to alter the slow mode. We have applied our study to the upper ionosphere where bi-ion plasmas and the presence of non-Maxwellian electrons have been observed by various satellite missions.