Charge Fluctuation Instability of the Dust Lattice Wave

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Abstract
Taking into account the statistical charge fluctuations on microspheres embedded in a low-pressure gas discharge, a stochastic differential equation for the one-dimensional dust lattice wave is derived. Using this equation, the nonstochastic differential equations for the mean particle displacement and for the second moments of the displacement and velocity are obtained. The analysis of the equation for the second moments shows that for sufficiently small gas pressure the charge fluctuations can result in exponential growth of the average energy of lattice oscillations.