Dynamical properties of random charge fluctuations in a dusty plasma with different charging mechanisms

A dust particle in a plasma acquires electric charge by collecting electrons and ions, and sometimes by emitting electrons. The charging currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value. We developed a model yielding a general expression for the charge fluctuations’ temporal autocorrelation function. Both the magnitude and characteristic time of fluctuations can be obtained, knowing the specific form of charging currents. Numerical results are presented for different charging mechanisms, including charging by thermionic and photoelectric emission. It is shown that for all charging mechanisms the amplitude of fluctuations varies as $\Delta Z=\alpha \sqrt{〈|Z|〉},$ where 〈Z〉 is the equilibrium dust grain charge in units of electron charges.