Geoscience Reference
In-Depth Information
Alfven Waves
=
E
(
i,r
)
=
k
(
i,r
)
Ax
k
(
i,r
)
Ay
,
c
A
ck
(
i,r
)
A
E
(
i,r
)
A
Ax
E
(
i,r
)
Ay
∓
E
Az
=0
,
⊥
=
b
(
i,r
)
=
,
k
(
i,r
)
Ay
k
(
i,r
)
Ax
−
1
k
(
i,r
)
A
b
(
i,r
)
A⊥
Ax
b
(
i,r
)
Ay
Az
=0
,
(7.66)
−
' refers to the '
i
'-wave, while '+' refers to the '
r
'-wave.
Now the upper sign '
FMS-Waves
=
E
(
i,r
)
=
k
(
i,r
)
Sy
,
k
0
k
(
i,r
)
E
(
i,r
)
S⊥
Sx
E
(
i,r
)
Sy
E
Sz
=0
,
S,z
k
(
i,r
)
k
(
i,r
)
Sx
−
S
=
b
(
i,r
)
=
k
(
i,r
)
Sx
k
(
i,r
)
Sy
,
k
Sx
+
k
Sy
k
(
i,r
)
Sz
1
k
(
i,r
)
S
b
(
i,r
)
S
Sx
b
(
i,r
)
Sy
Sz
=
−
.
(7.67)
⊥
k
(
i,r
)
S
In (7.66)-(7.67)
=
2
1
/
2
+
2
k
(
i,r
)
α,x
k
(
i,r
)
α,y
k
(
i,r
)
α
,
and
α
='
A
' r
α
='
S
'
.
Vectors
b
(
i,r
)
A⊥
and
b
(
i,r
)
S⊥
are orthogonal to
B
0
and normalized to unity. The
scalar products are
=
b
(
i,r
)
1
/
2
b
(
i,r
)
A⊥
b
(
i,r
)
A⊥
A⊥
·
=1
,
=
b
(
i,r
)
S
1
/
2
b
(
i,r
)
S
b
(
i,r
)
S
⊥
·
=1
.
(7.68)
⊥
⊥
Normalization of
E
(
i,r
)
A
and
E
(
i,r
)
S
are given by
⊥
⊥
=
E
(
i,r
)
1
/
2
=
c
A
c
E
(
i,r
)
A⊥
E
(
i,r
)
A⊥
A⊥
·
,
=
E
(
i,r
)
1
/
2
k
0
E
(
i,r
)
S⊥
E
(
i,r
)
S⊥
S⊥
·
=
.
k
(
i,r
)
Sz
Here the dot denotes the scalar product which for the example for two vectors
A
=(
A
x
,A
y
,A
z
)and
B
=(
B
x
,B
y
,B
z
)is
B
)=
A
x
B
x
+
A
y
B
y
+
A
z
B
z
.
(
A
·
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