Excitation of the dust ion-acoustic and dust acoustic-like perturbations by plasma density ripples

It is shown that the dust ion-acoustic (DIA) and dust acoustic (DA)-like perturbations can be excited by the electron density and ion density ripples, respectively. For this purpose, we use the relevant equations for the DIA and DA-like disturbances and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that both the DIA and DA-like mode can be driven on account of the free energy in the plasma density ripples.