Stability dust-ion-acoustic wave in dusty plasma with stream-influence of charge fluctuation of dust grains

There is a rapidly increasing wealth of experimental data on socalled dusty plasma i.e. ionized gases or usual plasmas that contain micron-sized charged particles. Interest in these structures is driven both by their importance in many astrophysical as well as commercial situations. Among them are linear and non-linear wave phenomena. We consider the influence of dust charge fluctuations on stability of the ion-acoustic waves when the stream of particles is present. It is assumed that all grains of dust have equal masses but charges are not constant in time -they may fluctuate in time. The dust charges are not really independent of the variations of the plasma potentials. All modes will influence the charging mechanism, and feedback will lead to several new interesting and unexpected phenomena. The charging of the grains depends on local plasma characteristics. If the waves disturb these characteristics, then charging of the grains is affected and the grain charge is modified, with a resulting feedback on the wave mode. In the case considered here, when the temperature of the electron is much greater then the temperature of the ions and the temperature of electrons is not great enough for further ionization of the ions, we show that stability of the acoustic wave depends only on phenomenological coefficient and relation between.