Charge variation effects on low-frequency electrostatic waves in dusty plasmas

A general formula for the dispersion characteristics of electrostatic waves in dusty plasmas in the presence of charge fluctuation of dust particles is derived based on the linear response theory. The formula is applicable to arbitrary plasma models and waves. Charging equation due to plasma current on the dust surface is employed to describe the charge fluctuation effect. In particular, temperature fluctuation associated with the space charge fluctuation is taken into account in the charging equation and is found to make an important contribution to the damping or growth of the wave. Stability of low frequency waves where the electron response can be treated as static is discussed in detail. It is shown that the dust charge fluctuation contributes to damping when the dust is negatively charged, but to growth when the dust is positively charged. Results are applied to ion waves with positive dust charge.