Small amplitude ion-acoustic double layers in multicomponent plasma with positrons

Abstract

Ion-acoustic double layers has been studied in multicomponent plasma with positrons. Using the reductive perturbation method, the modified Korteweg--de Vries (mKdV) equation is derived for the system. The double-layer solution of the mKdV equation is discussed in detail. It is found that there exist two critical concentrations of positrons, ${\ensuremath{\alpha}}_{R}$ and ${\ensuremath{\alpha}}_{Q}$, which decide the existence and nature of the ion-acoustic double layers. It is also found that the system supports ion-acoustic double layers only when the positron concentration $(\ensuremath{\alpha})$ is less than the critical concentration ${\ensuremath{\alpha}}_{R}$ (i.e., $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{R}$). It is also investigated that for the given set of parameter values, if ${\ensuremath{\alpha}}_{R}<{\ensuremath{\alpha}}_{Q}$, the system supports only rarefactive double layers for the values of $\ensuremath{\alpha}$ lying in the range $0<\ensuremath{\alpha}<{\ensuremath{\alpha}}_{R}$. However, for the given set of parameter values ${\ensuremath{\alpha}}_{R}>{\ensuremath{\alpha}}_{Q}$, the system supports rarefactive double layers for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{Q}$, and for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{Q}$, compressive double layers exist. The present theory also predicts that for a given set of parameter values on increasing the positron concentration, the amplitude of the rarefactive (compressive) double layer decreases (increases), whereas as positron concentration is increased, the width of the rarefactive (compressive) double layer increases (decreases). The effects of positron concentration and temperature ratio on the characteristics of the double layers (namely amplitude and width) are discussed in detail.