Universal instability of dust ion‐sound waves and dust‐acoustic waves

It is shown that the dust ion‐sound waves (DISW) and the dust‐acoustic waves (DAW) are universally unstable for wave numbers less than some critical wave number. The basic dusty plasma state is assumed to be quasineutral with balance of the plasma particle absorption on the dust particles and the ionization with the rate proportional to the electron density. An analytical expression for the critical wave numbers, for the frequencies and for the growth rates of DISW and DAW are found using the hydrodynamic description of dusty plasma components with self‐consistent treatment of the dust charge variations and by taking into account the change of the ion and electron distributions in the dust charging process. Most of the previous treatment do not take into account the latter process and do not treat the basic state self‐consistently. The critical lengths corresponding to these critical wave numbers can be easily achieved in the existing experiments. It is shown that at the wave numbers larger than the critical ones DISW and DAW have a large damping which was not treated previously and which can be also measured. The instabilities found in the present work on their non linear stage can lead to formation of different types of dust self‐organized structures.