# Pad\'e-based arbitrary wavelength polarization closures for full-F gyro-kinetic and -fluid models

## TL;DR

This paper introduces Padé-based polarization closures for full-F gyro-kinetic and gyro-fluid models, improving accuracy and energy conservation across arbitrary wavelengths, addressing a key limitation in existing models.

## Contribution

It presents a novel quadratic form and Padé approximations for polarization closures that enhance accuracy and energy conservation in gyro-fluid models.

## Key findings

- Achieves polarization charge density with desired accuracy
- Retains linear polarization effects at arbitrary wavelengths
- Ensures proper energy conservation and correct long wavelength limits

## Abstract

We propose a solution to the long-standing short wavelength polarization closure shortfall of full-F gyro-fluid models. This is achieved by first finding an appropriate quadratic form of the gyro-fluid moment over the polarization part of the gyro-center Hamiltonian. Secondly, we deduce Pad\'e-based approximations to the latter expression that produce a polarization charge density with the desired order of accuracy and retain linear polarization effects for arbitrary wavelengths. The proposed closures feature proper energy conservation and the anticipated Oberbeck-Boussinesq and long wavelength limits.