A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
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• The fluid velocity must be along k r and perpendicular <strong>to</strong><br />
0<br />
B r<br />
0<br />
k r u r<br />
• These are magne<strong>to</strong>sonic waves<br />
– Case 2<br />
( k<br />
B r r<br />
1<br />
2<br />
2<br />
v<br />
ph<br />
= k ( ω ) = ± ( C<br />
s+<br />
C<br />
k<br />
k r B r<br />
0<br />
2 2 2 r<br />
r<br />
2 2 2 r r<br />
CA<br />
−ω<br />
) u + (( Cs<br />
CA)<br />
−1)<br />
k ( CA<br />
⋅u)<br />
CA<br />
= 0<br />
r<br />
• A longitudinal mode with u k<br />
r<br />
with dispersion relationship ω<br />
k<br />
(sound waves) r<br />
• A transverse mode with k ⋅u<br />
r<br />
ω<br />
= 0 and = ± C A<br />
(Alfvén<br />
waves)<br />
k<br />
2<br />
A<br />
)<br />
= ±<br />
C s
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