Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

Dust particles in typical laboratory plasma become charged largely by collecting electrons and/or ions. Most of the theoretical studies in dusty plasma assume that the grain charge remains constant even though it fluctuates due to the discrete nature of the charge. The rates of ions and electrons absorption depend on the grain charge, hence its temporal evolution. Stochastic charging model based on the standard Langevin equation assumes that the underlying process is Markovian. In this work, the memory effect in dust charging dynamics is incorporated using fractional calculus formalism. The resulting fractional Langevin equation is solved to obtain the amplitude and correlation function for the dust charge fluctuation. It is shown that the effects of ion-neutral collisions can be interpreted in phenomenological sense through the nonlocal fractional order derivative.