Is the Vlasov equation valid for Yukawa plasmas?

Abstract

We analyze the Vlasov dispersion relation for Yukawa plasmas in three dimensions for the purpose of identifying
coupling parameter domains where the Vlasov approach is justified and the existence of a well-developed RPA
type collective excitation is allowed. We establish a rigorous lower bound for the coupling parameter, below
which there can be no real solution to the Vlasov dispersion relation. In the coupling domain, where weakly
damped solutions do exist, we have focused on the long-wavelength acoustic regime where we establish more
restrictive estimates for the lower bound of the coupling parameter. We also derive a general formula for the
corresponding acoustic phase velocity, valid over a wide range of coupling parameter/screening parameter ratios
above the lower bound. We conclude that the Vlasov approach is tenable only above a critical coupling value.
Comparison with Molecular Dynamics simulation results further highlights the limitations of the Vlasov
approximation for weakly coupled Yukawa plasmas.