## Flux Freezing

An important nature of the ideal MHD is derived from equatio (B.4), that is, the matter and the magnetic field is coupled with each other. Consider a gas parcel threaded with the magnetic field . The magnetic flux anchored to the gas parcel is changes

 (B.5)

where . The first term of the lhs of the equation comes from a time derivative of the magnetic flux density, while the last term represents the change of the integral region due to gas motion (see Fig.B.1). ( ) Using the Stokes' theorem , the last term is reduced to . Finally, we obtain
 (B.6)

where we used equation (B.4). This means that the magnetic flux anchored to a gas parcel does not change in the ideal MHD regime.

Kohji Tomisaka 2009-12-10