Modified two-stream instabilities in dusty space plasmas

Modified two-stream instabilities are investigated in dusty plasmas in which electrons and/or ions drift across an external magnetic field. The usual high requency instability (ωce ⪢ ω ⪢ ωci) driven by treaming electrons is modified due to ni ≠ ne. Low frequency instabilities in the regime ωci ⪢ ω ⪢ ωcd (ωcd is the dust gyrofrequency) are considered for both long wavelengths, kϱi ⪡ 1, and short wavelengths, kϱi ⪢ 1 (ϱi is the ion gyroradius). It is found that low frequency instability can occur even when Ti ⪢ Te. Applications of the results to dusty plasmas in protostellar clouds and planetary rings are discussed.