A THEOREM ON FORCE-FREE MAGNETIC FIELDS

From MaRDI portal
Publication:3249615

DOI10.1073/pnas.44.6.489zbMath0081.21703OpenAlexW2034039186WikidataQ37617857 ScholiaQ37617857MaRDI QIDQ3249615

Lodewijk Woltjer

Publication date: 1958

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.44.6.489




Related Items (only showing first 100 items - show all)

Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crustFinite element approximation of the spectrum of the curl operator in a multiply connected domainHypermagnetic knots and gravitational radiation at intermediate frequenciesA mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations. I: Periodic domainsThe linking number in systems with periodic boundary conditionsOn the asymptotic linking numberOn Woltjer’s variational principle for force-free fieldsHelicity, linking and the distribution of null-homologous periodic orbits for Anosov flows*The kinetic origin of the fluid helicity—A symmetry in the kinetic phase spaceRigorous results on conserved and dissipated quantities in ideal MHD turbulenceBiot-Savart helicity versus physical helicity: A topological description of ideal flowsElectromagnetic fields satisfying the condition \(B\wedge (\nabla \wedge B)=0\)Magnetic reconnection in plasmasGeneralized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows. IIStability of Beltrami flowsWeak solutions of ideal MHD which do not conserve magnetic helicityCross and magnetic helicity in the outer heliosphere from Voyager 2 observationsTransport of magnetic flux in an arbitrary coordinate ALE codeTopological invariants of field lines rooted to planesRelaxed magnetic field structures in multi-ion plasmasA new strategy to microscopic modeling of topological entanglement in polymers based on field theoryBeltrami vector fields with an icosahedral symmetryNeutron spin quantum plasmas -- ferromagnetism as a relaxed stateGeometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spacesThe trunkenness of a volume-preserving vector fieldFormation of large scale structures in dusty magnetoplasmasTopology bounds energy of knots and linksOptical helicity of interfering wavesNumerical computation of the helical Chandrasekhar-Kendall modesEffects of twist on the evolution of knotted magnetic flux tubesA variational formulation for steady surface water waves on a Beltrami flowOn the coalescence of twisted flux tubesTOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORYModel of the symmetry evolution of a nonlinear continuous systemA spectral approach to the linking number in the 3-torusNambu-Lie 3-algebras on fuzzy 3-manifoldsRelativistic vortex dynamics in axisymmetric stationary perfect fluid configurationAn integral equation-based numerical solver for Taylor states in toroidal geometriesBounded solutions of ideal MHD with compact support in space-timeElectromagnetic knotsTime evolving potentials for electromagnetic knotsTaylor states in stellarators: a fast high-order boundary integral solverOptical helicity, optical spin and related quantities in electromagnetic theoryLocal representation and construction of Beltrami fields. II: Solenoidal Beltrami fields and ideal MHD equilibria.A variational interpretation of the Biot–Savart operator and the helicity of a bounded domainEigenfunctions of the curl in annular cylindrical and rectangular geometryA generalized poloidal–toroidal decomposition and an absolute measure of helicityNoether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations lawsConvex integration constructions in hydrodynamicsZero set structure of real analytic Beltrami fieldsExistence and structure of symmetric Beltrami flows on compact 3-manifoldsThe three-dimensional Euler equations: Where do we stand?Kinematic variational principle for motion of vortex ringsIsoperimetric problems for the helicity of vector fields and the Biot–Savart and curl operatorsApplications of beltrami functions in plasma physicsOn the groundstate energy of tight knotsStream Helicity in Toroidal DomainsThe Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluidsOn self and mutual winding helicityTOPOLOGICAL HELICITY FOR FRAMED LINKSHelicity and vortex generationA LINK BETWEEN p-BRANES, NAMBU–POISSON STRUCTURE AND MATROIDSOn a variational principle for Beltrami flowsRelativistic helicity and link in Minkowski space-timeExistence and characterisation of magnetic energy minimisers on oriented, compact Riemannian 3-manifolds with boundary in arbitrary helicity classesStability of Force-Free Magnetic FieldsA new cohomological formula for helicity in \(\mathbb R^{2k+1}\) reveals the effect of a diffeomorphism on helicityEFFECTS OF CHERN–SIMONS CORRECTIONS ON CONSERVED QUANTITIES OF RELATIVISTIC FLUIDTypical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundaryGeometric gradient-flow dynamics with singular solutionsRemark on the dissipation of the magnetic helicity integralInertial magnetohydrodynamicsMagnetic knot cascade via the stepwise reconnection of helical flux tubesMagnetohydrodynamic Relaxation TheoryUsing Magnetic Helicity, Topology, and Geometry to Investigate Complex Magnetic FieldsMagnetic Helicity in fast dynamosA topological theory of the electromagnetic fieldMHD turbulence: Relaxation processes and variational principlesTomographic reconstruction of the Beltrami fieldsПространства Соболева и краевые задачи для операторов ротор и градиент дивергенцииOn the proof of Taylor's conjecture in multiply connected domainsA variational principle for three-dimensional water waves over Beltrami flowsAsymptotic invariants of 3-dimensional vector fieldsOn the relationship between the topology of magnetic field lines and flux surfacesEvolution of helicity in fluid flowsThe third order helicity of magnetic fields via link mapsAn analysis of Taylor’s theory of toroidal plasma relaxationKinetic theory of collisionless relaxation for systems with long-range interactionsThe Biot-Savart operator and electrodynamics on subdomains of the three-sphereA review of relaxation and structure in some turbulent plasmas: magnetohydrodynamics and related modelsStatistical mechanics of a bounded, ideal magnetofluidThe third order helicity of magnetic fields via link maps. IISimultaneous Beltrami conditions in coupled vortex dynamicsClebsch (string) decomposition in \(d=3\) field theoryExact unsteady solutions to the Navier-Stokes and viscous MHD equationsIsoperimetric problem for the first curl eigenvalueHelicity, linkage and dynamo actionEigenfunctions of the curl in cylindrical geometryNumerical approximation of the spectrum of the curl operatorSpectral approximation of the curl operator in multiply connected domains




This page was built for publication: A THEOREM ON FORCE-FREE MAGNETIC FIELDS