Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework

Abstract

The study of X-point collapse in magnetic reconnection has witnessed extensive research in the context of space and laboratory plasmas. In this paper, a recently derived mathematical formulation of X-point collapse applicable in the regime of extended magnetohydrodynamics (XMHD) is shown to possess a noncanonical Hamiltonian structure composed of five dynamical variables inherited from its parent model. The Hamiltonian and the noncanonical Poisson bracket are both derived, and the latter is shown to obey the requisite properties of antisymmetry and the Jacobi identity (an explicit proof of the latter is provided). In addition, the governing equations for the Casimir invariants are presented, and one such solution is furnished. The above features can be harnessed and expanded in future work, such as developing structure-preserving integrators for this dynamical system.

Published in Physics of Plasmas; 37 pages; 0 figures

References in corpus (41)

• Reconnection in a Weakly Stochastic Field
• Fast Reconnection in High-Lundquist-Number Plasmas Due to Secondary Tearing Instabilities
• High order symplectic integrators for perturbed Hamiltonian systems
• Two-scale structure of the electron dissipation region during collisionless magnetic reconnection
• Atmospheric escape from the TRAPPIST-1 planets and implications for habitability
• 3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
• Global Properties of Solar Flares
• General Theory of the Plasmoid Instability
• Magnetic reconnection in the era of exascale computing and multiscale experiments
• X-point collapse and saturation in the nonlinear tearing mode reconnection
• Atmospheric Escape Processes and Planetary Atmospheric Evolution
• Structure and structure-preserving algorithms for plasma physics
• Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration
• Turbulent Reconnection and Its Implications
• Reconnection-Driven Energy Cascade in Magnetohydrodynamic Turbulence
• Plasmoid Instability in Forming Current Sheets
• On the Value of the Reconnection Rate
• Classification and Casimir Invariants of Lie-Poisson Brackets
• Magnetic Reconnection as a Mechanism for Energy Extraction from Rotating Black Holes
• Hamiltonian formulation and analysis of a collisionless fluid reconnection model
• Magnetic reconnection during collisionless, stressed, X-point collapse using Particle-in-Cell simulation
• Physical constraints for the evolution of life on exoplanets
• Hamiltonian Formalism of Extended Magnetohydrodynamics
• On energy conservation in extended magnetohydrodynamics
• Action Principles for Extended MHD Models
• Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory
• Extended MHD turbulence and its applications to the solar wind
• Derivation of the Hall and Extended Magnetohydrodynamics Brackets
• Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime
• Variational Integrators in Plasma Physics
• Magnetohydrodynamic motion of a two-fluid plasma
• Nonlinear Alfvén waves in extended magnetohydrodynamics
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• Structure and computation of two-dimensional incompressible extended MHD
• Nonlinear Resistivity for Magnetohydrodynamical Models
• Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
• Octupolar out-of-plane magnetic field structure generation during collisionless magnetic reconnection in a stressed X-point collapse
• Steady Hall Magnetohydrodynamics Near a X-type Magnetic Neutral Line
• Notes on the exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics