Study of Dust Acoustic Waves and Solutions in Two Ion Temperature Plasmas

Abstract

Dusty plasma is an ionized gas which has ions, electrons and dust particles. The dust particles acquire high charge and interact with particles in the plasma. Based on the relative temperature of the ions, these are classified as hot and cold ions. Here electrons and ions generally follow the Boltzmann distribution. The dust oscillates and excite wave called dust acoustic wave. The equation of motion and continuity equation are used for the dust grains. The mass of ions and electrons is neglected in view of extremely heavy mass of the dust grains. This system of equations is closed with the Poisson s equation. The set of equations initially has been solved using normal mode analysis to see the types of modes possible in the plasma. Further reductive perturbation technique has been used to compare the nature of modes in homogeneous plasma and to verify whether these modes evolve into solitons. Similar study has been carried out for the inhomogeneous plasma and magnetized plasma where the plasma has density gradient. The relevant Korteweg-deVries (KdV) equations are derived and solved in order to find the soliton solution. Conditions are discussed for the evolution of modes into soliton structure. For inhomogeneous plasmas, two situations of weak inhomogeneity and strong inhomogeneity are discussed. Under such situations, the KdV equation assumes its modified form which is solved by finding suitable transformations. The most interesting feature of these plasmas is that a tailing like structure is associated with the soliton, which is discussed in greater details. Since the dust grains are continuously charged, they may attract the electrons in large number, leading plasma with two types of ions and dust grains with a very little number of electrons. This kind of plasma is called electron depleted plasma. Hence, finally this situation is also discussed. The hot ions are found to affect the soliton structure when they are in much larger number with respect to the cold ions.