Poisson-Dirac Submanifolds as a Paradigm for Imposing Constraints in Non-dissipative Plasma Models

TL;DR

This paper generalizes Dirac constraint theory using Poisson-Dirac submanifolds, providing a coordinate-free approach that relaxes invertibility conditions, with applications to plasma models like ideal MHD.

Contribution

It introduces a novel, coordinate-free framework for constraints in plasma models based on Poisson-Dirac submanifolds, extending standard Dirac theory.

Findings

Applied to eliminate electron density via Gass' Law

Demonstrated ideal MHD as a slow manifold constraint

Relaxed invertibility condition in Dirac constraint theory

Abstract

We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously relaxing the invertibility condition as seen in standard Dirac constraint theory. We illustrate the the method with two examples: elimination of the electron number density using Gass' Law and ideal MHD as a slow manifold constraint in the ideal two-fluid model.