Solitary waves in interstellar plasma with Cairns distributed electrons in the presence of negative ions

Plasma with both negative and positive ion species and electrons is called negative ion plasma. This type of plasma has a great importance in various fields of plasma science and technology. Among the nonlinear structures, ion-acoustic solitons present the most important aspect of nonlinear phenomena in modern plasma research. When the velocity of the ions and the electrons is much smaller than that of the light, an ion-acoustic soliton exhibits the non-relativistic behavior in the plasmas. But, when the electron and the ion velocities approach the velocity of light in the plasma, relativistic effects dominantly change the soliton behavior. Relativistic plasmas can be found in many situations. Nonlinear structures are usually investigated by using some form of perturbation method. In small amplitude approximation, we usually derive nonlinear partial differential equation like Korteweg–de Vries (KdV) or modified KdV and etc.
A great numbers of authors used the reductive perturbation technique, Bharuthramand and Shukla (1986); Yadav and Sharma (1991) studied ion-acoustic solitons. Rizzato (1988) showed that plasmas with components such as positrons in addition to electron and positive ions behave differently. The positrons can be used to probe particle transport in tokamaks and since they have sufficient lifetime, the two-component (e-i) plasma becomes a three-component (e-i-p) one (Surko and Murphy 1990). We know that when the ion velocity approaches the velocity of light, relativistic effects may significantly modify the behavior of the solitary waves. Relativistic plasmas occur in a variety of situations, such as, space plasma phenomena (Grabbe 1989), laser–plasma interaction (Arons 1979), plasma sheet boundary layer of earth’s magnetosphere (Vette 1970) and describing the Van Allen radiation belts (Ikezi 1973). The weakly relativistic effects on ion-acoustic wave propagation in one dimension using the KdV equation for cold plasma without electron inertia have been investigated (Das and Paul 1985). Nejoh (1987) has investigated the same results in the warm plasmas. Kalita et al. (1996) have investigated the existence of solitons considering the complete fluid equation of electrons. EL-Labany (1995) investigated the contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non-isothermal electrons by using reductive perturbation theory. EL-Labany et al. (1996) have investigated ion-acoustic solitary waves in weakly relativistic warm plasma at the critical phase velocity by reductive perturbation theory. Large amplitude Langmuir and ion-acoustic waves in relativistic two fluid plasmas deriving the pseudo potential has been considered by Nejoh (1987). The oblique propagation of nonlinear ion acoustic solitary waves (solitons) in magnetized collision less and weakly relativistic space plasma with positive and negative ions and non-thermal (Cairns distributed) electrons is examined by using reduced perturbation method to obtain the Korteweg-de Vries (KdV) equation that admits an obliquely propagating soliton solution. We investigated the effect of ions velocity and non-thermal electrons on amplitude and width of solitary waves and also other effective parameters on them. We find out that four modes exist in our plasma model but the numerical analysis showed that only two types of ion acoustic modes (fast and slow) exist in the plasma. The fast mode corresponds to the propagation of compressive solitons, whereas the rarefactive solitons exist for the slow mode. We also calculated the energy of soliton and discussed the effect of plasma parameters on it. The amplitude of both types of solitons increases with the angle between the wave vector and magnetic field, the relativistic ion drift velocity, negative ion density and also with non-thermal parameter. The strength of the magnetic field doesn’t change the amplitude of soliton (for both types) but makes its width smaller. With increasing relativistic ions drift velocity the amplitudes of solitons become larger but their widths become smaller.