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We analyze the Vlasov dispersion relation for Yukawa plasmas in threedimensions for the purpose of identifying coupling parameter domains where theVlasov approach is justified and the existence of a well-developed RPA typecollective excitation is allowed. We establish a rigorous lower bound for thecoupling parameter, below which there can be no real solution to the Vlasovdispersion relation. In the coupling domain, where weakly damped solutions doexist, we have focused on the long-wavelength acoustic regime where weestablish more restrictive estimates for the lower bound of the couplingparameter. We also derive a general formula for the corresponding acousticphase velocity, valid over a wide range of coupling parameter/screeningparameter ratios above the lower bound. We conclude that the Vlasov approach istenable only above a critical coupling value. Comparison with MolecularDynamics simulation results further highlights the limitations of the Vlasovapproximation for weakly coupled Yukawa plasmas.

Is the Vlasov equation valid for Yukawa plasmas?