Variational hydrodynamics of the classical Yukawa one-component plasma

TL;DR

This paper extends a variational hydrodynamic approach to the Yukawa plasma, deriving equations that match well with simulations across various regimes, especially at weak to moderate screening.

Contribution

It introduces a generalized variational hydrodynamics framework for Yukawa plasmas, including finite length scale effects and deriving new dispersion relations.

Findings

Excellent agreement with numerical data in weak to moderate screening regimes.

Discrepancies observed at strong screening.

Finite-wavelength dispersion relations match simulations across parameters.

Abstract

We consider a recently developed variational approach to the hydrodynamics of strongly coupled plasmas [D. Krimans and S. Putterman, Phys. Fluids 36, 037131 (2024)] and extend it to the Yukawa one-component plasma. This approach generalizes the ordinary hydrodynamic equations to finite length scales by explicitly including terms that depend on the pair distribution function. After discussing the form of the Lagrangian, we derive equations of motion and explicit formulas for the momentum and energy conservation laws. After demonstrating consistency with thermodynamics, we consider the simpler linear regime and the dispersion laws. By comparing the longitudinal speed of sound to existing numerical data, we find excellent agreement in the weak to moderate screening regimes, while discrepancies arise at strong screening. The finite-wavelength behavior of the longitudinal dispersion relation also shows excellent agreement with simulations across a wide range of coupling and screening parameters, even when the wavelength is comparable to the average interparticle spacing. In addition to the linear regime, our variational approach has potential for application to nonlinear problems and other physical systems.