Gyrokinetic Vlasov-Poisson model derived by hybrid-coordinate transform of the distribution function

TL;DR

This paper introduces a hybrid-coordinate transform to derive a more accurate gyrokinetic Vlasov-Poisson model, improving the order consistency of the full-orbit density approximation and validating it through numerical simulations.

Contribution

A novel hybrid coordinate frame approach is developed to enhance the accuracy of the gyrokinetic model's full-orbit density approximation.

Findings

The new model achieves the exact order of psilon^{psilons-1} for the full-orbit density.

Numerical simulations show similar performance between the new and standard models.

The hybrid coordinate transform corrects the order inconsistency in the standard model.

Abstract

This paper points out that the full-orbit density obtained in the standard electrostatic gyrokinetic model is not truly accurate at the order $\varepsilon^{\sigma-1}$ with respect to the equilibrium distribution $e^{-\alpha \mu}$ with $\mu \in (0, \mu_{\max})$, where $\varepsilon$ is the order of the normalized Larmor radius, $\varepsilon^{\sigma}$ the order of the amplitude of the normalized electrostatic potential, and $\alpha$ a factor of $O(1)$. This error makes the exact order of the full-orbit density not consistent with that of the approximation of the full-orbit distribution function. By implementing a hybrid coordinate frame to get the full-orbit distribution, specifically, by replacing the magnetic moment on the full-orbit coordinate frame with the one on the gyrocenter coordinate frame to derive the full-orbit distribution transformed from the gyrocenter distribution, it's proved that the full-orbit density can be approximated with the exact order being $\varepsilon^{\sigma-1}$. The numerical comparison between the new gyrokinetic model and the standard one was carried out using Selalib code for an initial distribution proportional to $\exp(\frac{-\mu B}{T_i})$ in constant cylindrical magnetic field configuration with the existence of electrostatic perturbations. In such a configuration, the simulation results exhibit similar performance between the two models.