MHD - Magnetohydrodynamics

        MHD is the study of the interaction between a magnetic field and a plasma, treated as a continuous medium (i.e. a conducting gas).  A magnetic field exerts a force, stores energy, acts as a thermal blanket and provides stability.  A magnetic flux tube is the surface generated by the set of field lines which intersect a simple closed curve.  The flux tube strength is the amount of magnetic flux crossing a section.  The fundamental equations used in MHD are Maxwell's equations:
        Curl  x H = j + dD/dt  (Ampere)
        Curl * B = 0
        Curl x E = -dB/dt (Faraday)
        Curl * D = pc   (p-roe)
              where B = uH (u = mu, magnetic permeability)
                            D = eE (e = electrical permittivity)

  Ohm's Law:
        E = j/b (b = electrical conductivity)

  Fluid Mechanics:
        roe * dv/dt = - Curl * p  (motion)
        droe/dt + roe*Curl*v = 0  (mass continuity)
        p = R * roe * T (perfect gas law)

        In MHD it is assumed that v<<c, therefore dD/dt is negligible.  The total electric field on moving plasma is E + (v x B) = j/b (b = electrical conductivity).  Also, the plasma feels a force j x B in the right side of the equation of motion from Fluid Mechanics.

        Magnetic Helicity (H) is a measure of twisting and kinking of the magnetic tube (self helicity) plus the linkage between different tubes (mutual helicity).  It is a global topological invariant.  It's definition is   Ho = Integral with respect to V(A*B) dV, where B = Curl x A.

        There are other points about Magnetohydrodynamics that were given in the form of lectures during this summer project.  The topics were: magnetohydrostatic equilibria, waves, reconnection, coronal heating, and solar flares.  Some sub-topics were: flux tubes,magnetic pressure and tension forces, magnetohydrostatics, potential fields (where j x B = 0), force-free fields, magnetic flux tubes, MHD waves: sound waves, Alfven waves, magnetoacoustic waves, shock waves; reconnection theories, and magnetic annihilation.

        More information about MHD can be found on the web or through text.
        See http://solar.physics.montana.edu/magara/Research/Research_info_dyna.html - click on MHD waves.
        See http://www-solar.mcs.st-and.ac.uk/~eric/flar.html for some information on solar flares and MHD.
        See http://www-solar.mcs.st-and.ac.uk/~eric/book.html for literature on Magnetic Reconnection and some topics on MHD.
 

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