Wave-number-dependent closure condition for fluid moment equations

TL;DR

This paper introduces a wave-number-dependent closure condition for fluid equations that accurately captures kinetic effects like Landau damping across all spatial scales by mapping Padé approximants to kinetic roots.

Contribution

It proposes a novel analytical closure derived from kinetic roots, improving the fidelity of fluid models in representing kinetic plasma effects across wave numbers.

Findings

The closure preserves the primary dispersion relation.

It accurately captures Landau damping effects.

The framework extends to collisional plasmas with BGK model.

Abstract

Fluid models offer crucial computational efficiency for plasma simulations, yet accurately capturing kinetic effects like Landau damping remains a fundamental challenge. While conventional closures (e.g., Hammett-Perkins and Hunana) are widely used, their fidelity relative to exact kinetic response degrades significantly depending on the perturbation wave number. Here, we propose a novel wave-number-dependent closure condition for the three-moment fluid equations that explicitly preserves the primary dispersion relation. By mapping Pad\'e approximant coefficients directly to the kinetic roots of the collisionless Vlasov-Poisson system, we derive an analytical closure that rigorously embeds exact kinetic scaling across all spatial scales. We further demonstrate that this framework readily extends to collisional plasmas via the BGK model. This deterministic approach precisely captures the long-term macroscopic evolution of fluid moments and field energy, offering a rigorous foundation for high-fidelity fluid modeling.