Low-frequency electrostatic waves in self-gravitating dusty plasmas with dust-ion collisions

The influence of dust-ion collisions on low-frequency modes in a self-gravitating dusty plasma is studied. The stability of the system is easily determined using elementary principles of rootlocus theory. It shows that collisions between ions and dust grains do not change the criteria for gravitational collapse at any value of their collision frequency, but diminish the growth rate of unstable dusty plasmas. Moreover, the rootlocus plots visualize qualitatively the evolution of the real frequencies and damping decrements of the dust-acoustic and ion-acoustic modes as the dust-ion collision frequency increases