The behavior of streaming instabilities in dissipative plasma

An approach is presented, which allows getting much more information on streaming instabilities (SI) from the dispersion relation (DR) as compared to well-known (and very simplified) initial and boundary problems. The approach is based on general assumptions and does not refer on any particular model and/or type of the stream interaction with background system (Cherenkov, cyclotron etc). The basis of the approach is transformation of the DR to an equation for slowly varying amplitude of the growing waveform. Its solution presents the problem of time evolution of initial pulse. In its turn the expression for the fields¿ space-time evolution gives detailed information on the instability behavior including results of the initial and boundary problems. Most of the information is unavailable by other methods. For particular model only two parameters should be specified. The expressions for the fields¿ space-time structure also show that with increase in dissipation all SI gradually turns to dissipative streaming instability (DSI). A new, previously unknown type of DSI is presented. It develops under overlimiting electron beams and/or under weak coupling of the stream with plasma.