Variational principles for hydrodynamics of strongly coupled plasmas

Strongly coupled plasmas represent a challenging regime in plasma physics, where the dynamics are dominated by particle interactions and correlations. As an alternative to direct particle-based simulations—which require significant computational resources for macroscopic systems—we present a novel hydrodynamic approach derived using the least action principle. Our proposed Lagrangian explicitly incorporates the pair distribution function to capture correlation effects and ensures the conservation of both momentum and energy.

We demonstrate how our framework extends conventional hydrodynamics into the strongly coupled regime and to small length scales by applying it to Coulomb and Yukawa one-component plasmas. By linearizing the hydrodynamic equations, we derive both longitudinal and transverse modes. The resulting dispersion relations show very good agreement with molecular dynamics simulations across a broad range of coupling strengths and screening parameters, including at finite wavelengths comparable to the interparticle spacing.

These promising results motivate further development of this variational approach, including investigations into its nonlinear behavior—such as during plasma expansion or shock wave propagation—and the incorporation of quantum effects. Such advancements could benefit a wide range of strongly coupled plasma applications.