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The magnetic force (per unit volume) in the equation for
fluid motion () may be reexpressed as

(3.46) 
The first term corresponds to the magnetic pressure,
with
.
An important diagnostic of a plasma is the plasma beta, defined
as the ratio of plasma thermal pressure to the magnetic pressure:

(3.47) 
The second term can be further decomposed into two terms:

(3.48) 
where
is a unit vector in the direction of and
is the normal pointing towards the centre of curvature,
defined by (
,
where R_{c} is the radius of curvature of the field
line. The first term cancels out the magnetic pressure
gradient term in () in the
direction along the field lines. This
implies that the magnetic pressure force is not isotropic;
only perpendicular components of
exert force on the
plasma.
The second term in ()
corresponds to the magnetic tension force which is directed
towards the centre of curvature of the field lines and thus acts to
straighten out the field lines. A suitable analogy is the tension force
transferred to
an arrow by the stretched string of a bow. In this case the
tension force pushes the plasma in the direction that will reduce
the length of the field lines.
Next: MHD waves
Up: Fluid & MHD Theory
Previous: Final MHD equations
Iver Cairns
19990809