According to the equations of marginally-stable ideal-MHD, the electron number density continuity equation
takes the form
 |
(3.45) |
where use has been made of Equations (2.139), (2.380), and (3.26). Here,
. It follows that
and
.
Thus,
 |
(3.46) |
where use has been made of Equation (3.29).
Now, the equilibrium plasma flow is written
 |
(3.47) |
It follows that
 |
(3.48) |
The linearized form of Equation (3.45) is
 |
(3.49) |
where
is the perturbed plasma velocity, and use has been made of Equations (3.46) and (3.48). Let us write
 |
(3.50) |
It follows that
 |
(3.51) |
where use has been made of Equations (3.8) and (3.19).
Hence,
writing
Equation (3.49) reduces to
![$\displaystyle \delta v = -\frac{m}{r\,F}\left[\phi + \left(\frac{\omega-{\mit\Omega}}{F}\right)\delta\psi\right]\frac{n_e'}{n_e},$](img1516.png) |
(3.54) |
where use has been made of Equation (3.42).