Generalized Bohm sheath criterion in dusty plasma of space environment

Abstract

By introducing the Kappa distribution function ( κ ) and considering the dimensionless variables and applying them to the Poisson equation, the Bohm sheath equation in a plasma is obtained. We know the above distribution function has two important factors: 1-the invariant kappa spectral index ( κ 0 ), 2-the number of degrees of freedom ( d e , Φ ). In this regard, we considered soliton with positive and negative potentials in the two areas of the solar structure Heliosphere (positive potential: near equilibrium areas κ 0 > 1 and negative potential Heliosheath: out of equilibrium areas 0 < κ 0 < 1 ). Then, the Korteweg-de-Vries equation (KdV) is obtained using the Bohm criterion and applying the Sagdeev pseudo potential method and effects of the spectral index κ 0 , the potential degrees of freedom d e , Φ via perturbation are studied numerically.