A Model for Nonlinear Waves in Space Plasma with Generalized (r, q) Distribution

In this paper, Burger's equation has been derived to study nonlinear ion acoustic waves in space plasma. We write the basic set of governing equations and lay down the stretching and perturbation scheme to derive the Burger's equations for the ion acoustic waves in which electrons follow a nonthermal distribution known as generalized (r, q) distribution function. The generalized (r, q) distribution successfully fits the distribution functions that have been frequently observed in space plasmas. The spectral index r controls the shape of the distribution function at low energy and by increasing its value, shoulders in the profile of the distribution increases. The spectral index r can also have negative values due to which distribution becomes spiky at low energies. The spectral index q, on the other hand, controls the shape of the tail of distribution function and by increasing its value, number of high energy particles reduces. In the limit, when r = 0 and q -> infinity, (r, q) distribution function becomes Maxwellian distribution. It has been shown that when electrons are modelled by the generalized (r, q) distribution function the nonlinear ion acoustic waves admit both compressive and rarefactive shock structures in contrast to Maxwellian distribution. A comparison has also been made between the shock structures obtained by employing the Maxwellian distribution and generalized (r, q) distribution.