Influence of collisions on development of streaming instabilities in space plasma

Plasma is ubiquitous in the universe along with its intrinsic instabilities. Relative drifts between plasma consistent are prevalent in various space and astrophysical plasma environment. This results in instabilities of two-stream type. Actually, these are the most frequently encountered instabilities in space plasma. Presence of charged dust grains in space plasma leads to large amount of novel peculiarities [1-4]. Collisions play an important role in three component space plasma. Variations of the grains' charge and mass through collisions lead to still more new peculiarities. In particular, dust charge relaxation process leads to instability of Legmuire wave in plasma even on absence of relative drifts [5]. Collisions result in energy dissipation and become deciding factors in the limiting spatial and temporal growth and determining the magnitude of the fields. They can also essentially influence on the mode structure of instability and reduce the growth rates. But dissipation never suppresses streaming instabilities completely. Further increasing of collision frequency transforms physical nature of the instability to dissipative type. Present investigation considers development of ion-dust streaming instability with account of collisions. The transformation of the streaming instability to that of dissipative type with increase in collisions' frequency is traced in detail. The changes of collisions' cross sections depend on system parameters are taken into account. Usual treatment of such problems includes consideration of two various limiting solutions of the respective dispersion relation for instabilities of conventional and dissipative type. We obtained general solution and analyzed gradual transition of one solution to another. Dynamics of instability development in space and time is also investigated. Used approach is similar to that, developed in [6,7]. Other streaming instabilities in space plasma are also considered by the same approach. Application of the results to dusty cosmic environment such as earth's upper atmosphere, collapsing protostellar clouds and planetary rings is discussed.

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