Geoscience Reference
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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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