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Dust-acoustic waves and stability in the permeating dusty plasma: I. Maxwellian distribution

The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases that the thermal velocity of the flowing dusty plasma is (a) much larger than, and (b) much smaller than the phase velocity of the waves. We find that the stability of the waves depend strongly on the velocity of the flowing dusty plasma in the permeating dusty plasma. The numerical analyses are made based on the example that a cometary plasma tail is passing through the interplanetary space plasma. We show that, in case (a), the waves are generally unstable for any flowing velocity, but in case (b), the waves become unstable only when the wave number is small and the flowing velocity is large. When the physical conditions are between these two limiting cases, we gain a strong insight into the dependence of the stability criterions on the physical conditions in the permeating dusty plasma.