Shock waves in dusty plasma with two temperature superthermal ions

An investigation of dust acoustic shock waves in dusty plasma containing two temperature ions is presented. The present investigation is motivated by the observations of Geotail spacecraft that report the occurrence of two temperature ion populations in Earth’s magnetotail. We have derived Burgers equation to study dust acoustic shock structures in an unmagnetized plasma with two temperature superthermal ions. We have also derived the modified Burgers equation at critical values of physical parameters for which nonlinear coefficient (A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A$\end{document}) of Burgers equation vanishes. The numerical analysis is performed in context with observations in Earth’s magnetotail and the influence of various plasma parameters viz. ions temperature ratio, superthermality of hot and cold ions, kinematic viscosity etc. has been observed on characteristics of DA shocks. It is observed that the amplitude of positive shocks via Burgers equation decreases whereas that of modified shocks with higher order nonlinearity increases with increase in superthermality of cold ions.