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Here, we derive the basic equations of magnetohydrodynamics.
Differences from hydrodynamics are the Lorentz force in the equation of motion and the induction equation
of magnetic field.
The Lorentz force is written as

(B.1) 
where we used the Ampere's law
and the displacement current is
ignored.
Thus, the equatin of motion becomes as

(B.2) 
in the Eulerian form.
The Faraday's law
and the Ohm's law
( is the electric conductivity)
lead the induction equation of the magnetic field as

(B.3) 
The factor
is the coefficient of magnetic diffusibility.
When we assume the electric conductivity
,
diffusive MHD equation, equation(B.3), reduces to
the ideal MHD equation as

(B.4) 
Subsections
Next: Flux Freezing
Up: Basic Equations of Magnetohydrodynamics
Previous: Basic Equations of Magnetohydrodynamics
Contents
Kohji Tomisaka
20070708