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

2025/06/30 by Pinto, F. W., Burby, J. W. · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2506.23991

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.

Citations

• Incomplete Dirac reduction of constrained Hamiltonian systems
• The momentum map in Poisson geometry
• Integrability of Poisson brackets
• Generalized Hamiltonian Dynamics

Cited by

• On the Poisson brackets of hybrid plasma models with kinetic ions and massless electrons
• Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints
• Hamiltonian formulation of the quasineutral Vlasov-Poisson system

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