Conservative formulation of the drift-reduced fluid plasma model

TL;DR

The paper presents a conservative drift-reduced fluid model for multispecies magnetised plasmas by non-perturbatively inverting the implicit polarisation-velocity relation $\bm{v}_{ps}$ as a function of the electric-field time derivative. This inversion yields a closed set of equations that exactly conserve total energy and momentum to leading order, valid in arbitrary magnetic geometry and including electromagnetic fluctuations. The core advance is the explicit, basis-independent expression $\bm{v}_{ps} = \bm{Q}_s(\bar{\bm{v}}_s) \cdot \bm{U}_s$ with $\bm{U}_s = \frac{\bm{b}}{\Omega_{cs}} \times (\partial_t \bar{\bm{v}}_s + \bar{\bm{v}}_s \cdot \nabla \bar{\bm{v}}_s + r_s \bar{\bm{v}}_s)$ and a determinant-based $\bm{Q}_s$ ensuring invertibility, which is then used to construct a drift-reduced system that preserves the leading-order energy $\mathcal{\overline H}$ and momentum $\bm{\mathcal{\overline M}}$. The resulting framework includes a vorticity equation, a Poisson equation for the electrostatic potential, and Ampère’s equation, forming a conservative, quasi-neutral, Maxwell-fluid model applicable to complex geometries and multispecies closures such as Braginskii's. The work also clarifies how neglecting the polarisation-advection term recovers the traditional non-conservative drift-reduced form, highlighting the practical impact for long-time turbulence simulations.

Abstract

A conservative formulation of the drift-reduced fluid plasma model is constructed by analytically inverting the implicit relation defining the polarisation velocity as a function of the time-derivative of the electric field. The obtained model satisfies exact conservation laws for energy, mass, charge and momentum, in arbitrary magnetic geometry, also when electromagnetic fluctuations are included.