Geoscience Reference
In-Depth Information
4
Magnetohydrodynamic Waves
4.1 MHD Equations
Basic Equations
In Chapter 1 the macroscopic electrodynamic parameters of plasma were ob-
tained in the framework of multifluid hydrodynamics. Taking into account
the multicomponent composition of partly ionized ionospheric plasma is nec-
essary because many important peculiarities of wave perturbations cannot
be studied in the approximation of one-fluid magnetohydrodynamics. In the
magnetosphere, on the other hand, a one-fluid approximation is usually suf-
ficient and it is more important to consider the finiteness of plasma pressure
than its complex composition.
The magnetospheric plasma will be regarded here as a single hydrody-
namic medium characterized by a single hydrodynamic velocity
u
(
r
,t
)and
plasma density
ρ
(
r
,t
). Then their relations with partial velocities
v
k
(
r
,t
)
and concentrations
N
k
(
r
,t
) are given by
u
(
r
,t
)=
m
k
N
k
(
r
,t
)
ρ
(
r
,t
)
v
k
(
r
,t
)
,
ρ
(
r, t
)=
m
k
N
k
(
r
,t
)
.
The variables
ρ
and
u
obey the hydromagnetic equations:
•
Equation of mass conservation
∂ρ
∂t
+
∇
·
(
ρ
u
) = 0 ;
(4.1)
•
Equation of motion for conductive gas
ρ
∂
u
∂t
)
u
=
P
+
1
+(
u
∇
−
∇
c
[
j
×
B
]
.
(4.2)
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