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Coupling parameter lower bound in Yukawa-Vlasov plasmas

We have analyzed the Vlasov dispersion relation for Yukawa plasmas in three and two dimensions primarily for the purpose of identifying coupling parameter domains where the existence of well-developed collective excitations is forbidden or allowed. First, we have established a rigorous lower bound for the coupling parameter, below which there can be no real solution to the dispersion relation. In the coupling domain where weakly damped solutions do exist, we have focused on the long-wavelength acoustic regime where we have established more restrictive lower-bound estimates of the coupling parameter. We have also derived a general formula for the corresponding acoustic phase velocity, valid over a wide range of coupling parameter/screening parameter ratios above the more restrictive lower bound.