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 ...
• Compressible solutions – In general incompressibility will not always apply. – Usually this is approached by assuming that the system starts in equilibrium and that perturbations are small. • Assume uniform B 0 , perfect conductivity with equilibrium pressure p 0 and mass density ρ 0 ρ = ρ 0 + ρ p r B r u r J r E T T T T T T = p r = B r = u r = J r = E 0 0 + p r + b
– Continuity – Momentum – Equation of state ∇p = – Differentiate the momentum equation in time, use Faraday’s law and the ideal MHD condition where ∂ρ r = −ρ0( ∇ ⋅u) ∂t r ∂u 1 r r ρ0 = −∇p − ( B0 × ( ∇× b)) ∂t µ 0 ∂p ( ) 0 ∇ρ = Cs ∂ρ 2 ∇ρ r r r E = −u × B0 r ∂b r r r = −( ∇× E) = ∇× ( u × B0 ) ∂t 2 r ∂ u 2 r r r r − C ∇( ∇ ⋅ ) + × ( ∇× ( ∇× ( ∇× ( × 2 s u CA u C ∂t r r = C A B 1 0 ) 2 ( µ ρ A ))) = 0
- Page 3 and 4: Space Plasma Physics • Space phys
- Page 5 and 6: - Galileo theorized that aurora is
- Page 7 and 8: The Plasma State • A plasma is an
- Page 9 and 10: • B acts to change the motion of
- Page 11: • The electric field can modify t
- Page 14 and 15: • The change in the direction of
- Page 16 and 17: • Maxwell’s equations - Poisson
- Page 18 and 19: • Maxwell’s equations in integr
- Page 20 and 21: • For a coordinate in which the m
- Page 22 and 23: B r • The force is along and away
- Page 24: - As particles bounce they will dri
- Page 27 and 28: The Properties of a Plasma • A pl
- Page 29 and 30: • For monatomic particles in equi
- Page 31 and 32: • What makes an ionized gas a pla
- Page 34 and 35: • The plasma frequency - Consider
- Page 36 and 37: • A note on conservation laws - C
- Page 38 and 39: - Momentum equation r ∂us r r r r
- Page 40 and 41: • Energy equation ∂ ( ∂t 1 2
- Page 43 and 44: - Often the last terms on the right
- Page 45 and 46: F B • Magnetic pressure and tensi
- Page 47 and 48: •Some elementary wave concepts -F
- Page 49 and 50: • When the dispersion relation sh
- Page 51 and 52: - Incompressible Alfvén waves •
- Page 53: 1 2 2 C ⎛ B ⎞ A ⎜ ⎟ ⎝ µ
- Page 57 and 58: • The fluid velocity must be alon
- Page 59: - Arbitrary angle between k r and B
– Continuity<br />
– Momentum<br />
– Equation <strong>of</strong> state ∇p<br />
=<br />
– Differentiate the momentum equation in time, use Faraday’s<br />
law and the ideal MHD condition<br />
where<br />
∂ρ<br />
r<br />
= −ρ0(<br />
∇ ⋅u)<br />
∂t<br />
r<br />
∂u<br />
1 r r<br />
ρ0 = −∇p<br />
− ( B0<br />
× ( ∇× b))<br />
∂t<br />
µ<br />
0<br />
∂p<br />
( ) 0<br />
∇ρ<br />
= Cs<br />
∂ρ<br />
2<br />
∇ρ<br />
r r r<br />
E = −u<br />
× B0<br />
r<br />
∂b<br />
r r r<br />
= −(<br />
∇× E)<br />
= ∇× ( u × B0<br />
)<br />
∂t<br />
2 r<br />
∂ u 2 r r<br />
r r<br />
− C ∇(<br />
∇ ⋅ ) + × ( ∇× ( ∇× ( ∇× ( ×<br />
2 s<br />
u CA<br />
u C<br />
∂t<br />
r r<br />
=<br />
C A<br />
B<br />
1<br />
0 ) 2<br />
( µ ρ<br />
A<br />
))) = 0
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