Abstract
A compact dispersion relation for parametric instabilities of an electromagnetic pump wave is derived, taking into account the dust-particle dynamics and the dust-grain charge fluctuations caused by wave motions in unmagnetized dusty plasmas. Specific results for quasistationary modulational and filamentation instabilities are presented. It is found that thresholds of these instabilities are reduced in the presence of quasistationary plasma slow response involving charged dust grains. The present investigation should be useful in understanding the nonlinear propagation of intense electromagnetic waves through dusty space and laboratory plasmas.
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