Complex Burgers’ Equation: Evolution of Shock Waves with a Pair of Non-isothermal Ions in an Arbitrarily Charged Dusty Plasma

Abstract

The evolution characteristics of dust-acoustic shock wave phenomenon in an arbitrarily charged dusty plasma in presence of pair-ion are investigated by deriving modified Complex Burgers’ equation. In this work, the effect of state of both the ions on the shock wave potential is analysed and discussed in detail. It has been observed that the variation of the non-linear coefficient is more consistent with the non-isothermal positive ions moving toward thermal equilibrium than with non-isothermal negative ions. A significant effect on the amplitude of the shock wave potential is observed as the distribution of the non-isothermal positive and negative ions changes from a hump shape through the flat-topped to Boltzmann type. A weighty effect on the height of the shock wave is observed as and when the Mach number of positive and negative ions changes. The shock wave potential shows a greater (lesser) value with negative (positive) ions moving ahead for thermal equilibrium.