Guiding Center Derivation of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields

TL;DR

This paper derives a generalized Hasegawa-Mima equation for drift wave turbulence in curved magnetic fields using a guiding center kinetic framework, broadening its applicability without restrictive ordering assumptions.

Contribution

It presents a guiding center derivation of the gHM equation, extending its validity to arbitrary magnetic geometries and density profiles without derivative-based ordering constraints.

Findings

Equivalent gHM equation derived from kinetic guiding center theory

Relaxed turbulence ordering allows broader applicability

Applicable to any magnetic field geometry and electron density

Abstract

Recently, a generalized Hasegawa-Mima (gHM) equation describing drift wave turbulence in curved magnetic fields has been derived in [N. Sato and M. Yamada, J. Plasma Phys. (2022), vol. 88, 905880319] for an ion-electron plasma modeled as a two-fluid system. In this work, we show that a mathematically equivalent GHM equation can be obtained within the kinetic framework of guiding center motion, and that the relevant drift wave turbulence ordering can be further relaxed, effectively generalizing the applicability of the equation to any magnetic field geometry and electron spatial density, in the sense that no ordering requirements involve spatial derivatives of the magnetic field or the electron spatial density.