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.