Different approaches employed for dusty plasmas, ranging from single particle description (valid for low dust densities) to models appropriate in the presence of dense dusty clouds, are briefly reviewed. For environments with high dust density, a selection of examples is provided to elucidate phenomena arising in dusty plasmas when the effects of absorption of plasma particles on the dust surfaces and dust charge fluctuations are of importance and cannot be neglected.
A review is given of the theory of charging of a dust particle according to the Orbital Motion Limited (OML) theory. This is followed by a summary of a more complete orbital theory that includes the concept of an absorption radius, or effective potential barrier, for the positive ions. Measurements of the charge acquired by a dust particle are then described, using the method of damped dust oscillations employed at Oxford.
The paper analyses the properties of dusty plasmas in the extreme conditions when the free electrons are absent. The nonlinear Korteveg de Vries equation with a nonlocal (integral) term in a small parameter approximation is derived. The conditions are determined when the integral term is essential hence the Landau damping of two-ion-dusty plasma waves is substantial.
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