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

∂p
∂x
• Since = 0 , = 0 and = 0 the x-component of
momentum becomes
• Faraday’s law gives
• The y-component of the momentum equation
becomes
J y
J z
∂ux
∂p
ρ = −
∂t
∂x
r
u = uj ˆ
r
E = −uB iˆ
∂
u y
∂t
0
∂b
∂t
+ ( J
∂E
= −
∂z
• Differentiating Faraday’s law and substituting the y-
component of momentum
2
∂ b
=
2
∂t
x
y
1 r r
= − J × B
B
0
B
=
0
=
− b
B
0
0
ρ
0
2
∂ u
∂z∂t
y
J
∂u
∂z
z
B0
∂b
µ ρ ∂z
2 2
⎛ B ⎞ ∂ b
=
⎜
⎟
2
⎝ µ
0
ρ ⎠ ∂z
) = 0