Coupling parameter lower bound in Yukawa-Vlasov plasmas

TL;DR

This paper investigates the conditions under which collective excitations can exist in Yukawa plasmas by establishing lower bounds on the coupling parameter, providing insights into plasma behavior across different dimensions.

Contribution

It introduces a rigorous lower bound for the coupling parameter in Yukawa plasmas and derives a general formula for acoustic phase velocity in the weakly damped regime.

Findings

Established a lower bound for the coupling parameter preventing real solutions.

Derived a formula for the acoustic phase velocity in the plasma.

Identified parameter domains where collective excitations are allowed or forbidden.

Abstract

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.