A Brief Introduction to Space Plasma Physics.pdf - Institute of ...

– For a plane wave solution
– The dispersion relationship between the frequency ( ) and
the propagation vector ( ) becomes
This came from replacing derivatives in time and space by
– Case 1
r
r
r
r
r
u
r
~ exp[ i(
k
r ⋅ −ω
t)]
ω
k r r r r r r r r r r r
k )[( C ⋅ k ) u − ( C ⋅u)
k − ( k ⋅u
C ] = 0
2 2 2
− ω u + ( Cs
+ CA)(
k ⋅u)
k + ( CA
⋅
A
A
)
A
k
r ⊥
r
B 0
2 r
ω u
∂
→ −iω
∂t
r
∇ → ik
r
∇⋅ → ik ⋅
r
∇× → ik ×
= ( C
2
s
+
C
2
A
r r r
)( k ⋅u)
k