Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0603115

Simplified Variational Principles for Barotropic Magnetohydrodynamics

Asher Yahalom·Donald Lynden-Bell
View original source ↗Read source document ↗Export metadata ↓

Abstract

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$ and the density $ρ$. The equations obtained for non-stationary barotropic magnetohydrodynamics resemble the equations of Frenkel, Levich & Stilman \cite{FLS}. The connection between the Hamiltonian formalism introduced in \cite{FLS} and the present Lagrangian formalism (with Eulerian variables) will be discussed. Finally the relations between barotropic magnetohydrodynamics topological constants and the functions of the present formalism will be elucidated.

Explore related subjects

physics.plasm-phastro-phmath-phmath.MPphysics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Asher Yahalom, Donald Lynden-Bell. 2007-11-18. Simplified Variational Principles for Barotropic Magnetohydrodynamics. https://doi.org/10.1017/s0022112008002024

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Entropy stable numerical schemes for divergence diminishing Chew, Goldberger & Low equations for plasma flows

Chew, Goldberger & Low (CGL) equations are a set of hyperbolic PDEs with non-conservative products used to model the plasma flows, when the assumption of local thermodynamic equilibrium is not valid, and the pressure tensor is assumed to be rotated by the magnetic field. This results in the pressure tensor, which is described by the two scalar components. As the magnetic field also evolves, controlling the divergence of the magnetic field is important. In this work, we consider the generalized Lagrange multiplier (GLM) technique for the CGL model. The resulting model is referred to as the GLM-CGL system. To make the system suitable for entropy-stable schemes, we reformulate the GLM-CGL system by treating some conservative terms as non-conservative. The resulting system has a non-conservative part that does not affect entropy evolution. We then propose entropy stable numerical methods for the GLM-CGL model. The numerical results for the GLM-CGL system are then compared with the CGL system without the GLM divergence diminishing approach to demonstrate that the GLM approach indeed leads to significant improvement in the magnetic field divergence diminishing.

physics.plasm-ph↗
arXiv2026

Low-Temperature Co-Fired Ceramics for a Sustainable Planar Plasma Jet with Homogeneous Plasma in Large Treatment Areas for Biomedical Applications

This study presents a portable planar argon-based plasma jet designed for large-area biomedical applications, with an emphasis on uniform discharge, stability, and safety. The device incorporates interchangeable rear and side inlet gas adapters with restriction plates and channels to equalize gas flow, while electrodes are encapsulated in low-temperature co-fired ceramics to reduce degradation and arcing during repeated operation. Flow simulations were conducted for multiple channel configurations to ensure laminar gas distribution and uniform plasma generation. Device performance and safety were evaluated using the kinPen MED as a reference standard. Electrical characteristics, optical emission, discharge uniformity, temperature, gas velocity, ozone generation, UV irradiance, and leakage current were systematically measured. The plasma exhibited stable voltage, current, and power after an initial warm-up period. Temperatures stabilized within minutes, with the rear-inlet configuration demonstrating lower operating temperatures due to higher outlet gas velocity. Ozone levels remained below established safety limits, while UV exposure constrained allowable treatment times. Leakage current decreased with increasing distance and approached safety thresholds at short separations. These results demonstrate that the proposed planar plasma jet provides stable, uniform plasma delivery while meeting key safety requirements, supporting its potential for clinical and biomedical use.

physics.plasm-ph↗
arXiv2026

Thresholdless IBW Emission and Alpha-to-Thermal-Ion Energy Channeling via Pole Resonance of Fusion-Product Ions

Fusion reactions can release a substantial fraction, and in aneutronic reactions nearly all, of their energy as the kinetic energy of fusion-product ions. In magnetized plasmas, these energetic ions can form ring distributions in velocity space. Such distributions can drive Dory-Guest-Harris (DGH) electrostatic instabilities, but these self-instabilities require a finite energetic-ion density and can be stabilized by a thermal background. We show that the same background can instead enable a distinct instability mechanism: a cyclotron pole of the minority energetic-ion susceptibility destabilizes a stable ion Bernstein wave (IBW) eigenmode. When the energetic-ion harmonic is distinct from the thermal-ion harmonics, exact root-pole resonance is thresholdless in the ideal collisionless limit. A species-resolved power balance shows that the energetic ions supply the free energy while the thermal plasma receives it. In the LAPD proton--alpha example, $99.96\%$ of the alpha-particle power loss enters the coherent proton response. This self-excited, ion-directed transfer provides a possible linear building block for alpha-particle energy channeling in proton-Boron11 fusion.

physics.plasm-ph↗