Fundamentals of Plasma Physics

184 Chapter 6. Cold plasma waves in a magnetized plasma

1
c

2

vA^2

n^2
L

n^2
R

1

ci

|
ce|

n

2

Figure 6.1: Propagation parallel to the magnetic field.

Having determined the eigenvalues forθ= 0,the associated eigenvectors can now
be found. These are obtained by substituting the eigenvalueback into the original set of
equations;for example, substitution ofn^2 =Rinto Eq.(6.21) gives





−D −iD 0

iD −D, 0

0 0 P



·





Ex

Ey

Ez



=0, (6.32)

so that the eigenvector associated withn^2 =Ris

Ex

Ey

=−i, foreigenvaluen^2 =R. (6.33)

The implication of this eigenvector can be seen by considering the rootn=+

√

Rso that