class FluxTubeConcept "Flux tube concept"
extends Modelica.Icons.Information;
annotation (Documentation(info = "<html>\n<h4>Overview of the concept of quasi static magnetic flux tubes</h4>\n<p>\nFollowing below, the concept of magnetic flux tubes is outlined in short. For a detailed description of flux tube elements, please have a look at the listed literature. Magnetic flux tubes enable the modeling of magnetic fields with lumped equivalent circuit networks.</p>\n\n<p>Since quasi static conditions are assumed, each field quantity can be represented by a complex phasor -- which is indicated by underlining the respective variable:\n</p>\n\n<ul>\n<li>Normal component of magnetic flux density,\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/B_n.png\"> </li>\n<li>Normal component of magnetic field strength,\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/H_n.png\"> </li>\n<li>Magnetic flux,\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/Phi.png\"> </li>\n<li>Magnetic potential difference,\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/V_m.png\"> </li>\n</ul>\n\n<p>The figure below and the following equations illustrate the relationships between</p>\n\n<ul>\n<li>the normal component of flux density and magnetic flux, and</li>\n<li>the normal component of field strength and magnetic potential difference.</li>\n</ul>\n\n\n<p>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/magnetic_flux_tube_schematic_qs.png\" alt=\"Magnetic flux tube\">\n</p>\n\n<p>A <strong>flux tube</strong> confines the magnetic flux. Flied lines, and flux tubes, respectively are always closed. So there is no flux entering or leaving a flux tube. The total flux of a configuration can be represented by parallel flux tubes, representing different flux paths. This is considered by connecting the elements of a lumped circuit model, such that the sum of all fluxes of a connection is equivalent to zero.</p>\n\n<p>\nFor a section of a flux tube with length\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/l.png\">\nthe magnetic potential difference is determined by the length integral over the magnetic field strength:</p>\n\n<dl>\n<dd>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/V_m-H_n.png\">\n</dd>\n</dl>\n\n<p>\nThe magnetic flux entering, and leaving a flux tube, respectively, is determined by the surface integral of the normal component\nof the magnetic field strength:</p>\n<dl><dd>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/Phi-B_n.png\">\n</dd></dl>\n<p>The magnetic potential difference and the magnetic flux have the same angle, so the reluctance a real (non complex) quantity:</p>\n\n<dl><dd>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/R_m-V_m-Phi.png\">\n</dd></dl>\n\n<p>\nFor a\n<a href=\"modelica://Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.GenericFluxTube\">generic flux tube</a> reluctance with constant\narea of cross section,\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/A.png\">,\nand length,\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/l.png\">,\nthe magnetic reluctance is:</p>\n<dl><dd>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/QuasiStatic/FluxTubes/R_m_cuboid.png\">\n</dd></dl>\n\n<h4>Assumptions</h4>\n\n<ul>\n<li><strong>Force</strong> interaction is not considered</li>\n<li>Reluctance models are <strong>linear</strong>; so non-linearities can only be taken into account by adapting the constant relative permeability;\nsee example\n<a href=\"modelica://Modelica.Magnetic.QuasiStatic.FluxTubes.Examples.NonLinearInductor\">NonLinearInductor</a></li>\n</ul>\n\n<h4>Notes</h4>\n\n<p>The parameter and variable names are chosen as close as possible to the transient\n<a href=\"modelica://Modelica.Magnetic.FluxTubes\">FluxTubes</a> library, to avoid additional effort when converting transient into quasi static flux tubes models.</p>\n\n<h4>Reference Note</h4>\n\n<p>A similar approach on quasi static flux tube models is published in\n[<a href=\"modelica://Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.Literature\">Raabe2012</a>].</p>\n</html>"));
end FluxTubeConcept;