Variational hydrodynamics of the classical Yukawa one-component plasma.

Area of Science:

• Plasma Physics
• Fluid Dynamics
• Statistical Mechanics

Background:

• Strongly coupled plasmas exhibit complex behaviors not fully captured by standard hydrodynamic models.
• Existing models often neglect finite length scale effects crucial for understanding plasma dynamics.

Purpose of the Study:

• To extend a variational approach for ideal hydrodynamics to the Yukawa one-component plasma.
• To generalize hydrodynamic equations to finite length scales by incorporating pair distribution functions.
• To derive equations of motion and conservation laws for strongly coupled plasmas.

Main Methods:

• Developed a variational approach based on a Lagrangian formulation.
• Derived equations of motion, momentum, and energy conservation laws.
• Analyzed the linear regime, including dispersion laws and longitudinal speed of sound.

Main Results:

• Achieved excellent agreement between the derived longitudinal speed of sound and numerical data in weak to moderate screening regimes.
• Observed discrepancies at strong screening, indicating limitations of the model in highly screened environments.
• Demonstrated excellent agreement of finite-wavelength dispersion relations with simulations across various coupling and screening parameters.

Conclusions:

• The extended variational approach provides a robust framework for describing hydrodynamics in finite-length scale plasmas.
• The model shows high accuracy for dispersion relations, even when wavelengths approach interparticle spacing.
• The approach holds promise for applications in nonlinear plasma dynamics and other physical systems.