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 ...
• A note on conservation laws – Consider a quantity that can be moved from place to place. f r – Let be the flux of this quantity – i.e. if we have an element of area then is the amount of the quantity passing the area element per unit time. – Consider a volume V of space, bounded by a surface S. – If σ is the density of the substance then the total amount in the volume is r r f ⋅δ A ∫σ dV – The rate at which material is lost through the surface is d r r ∫σ dV = −∫ f ⋅ dA dt – Use Gauss’ theorem V – An equation of the preceeding form means that the quantity whose density is σ is conserved. ∫ V V ⎧∂σ ⎨ + ∇ ⋅ ⎩ ∂t ∂σ = −∇ ⋅ ∂t S r⎫ f ⎬dV ⎭ r f = 0 r r ∫ f ⋅dA S δA r
• Magnetohydrodynamics (MHD) – The average properties are governed by the basic conservation laws for mass, momentum and energy in a fluid. – Continuity equation ∂n ∂t s + ∇ ⋅ n – S s and L s represent sources and losses. S s -L s is the net rate at which particles are added or lost per unit volume. – The number of particles changes only if there are sources and losses. s r u – S s ,L s ,n s , and u s can be functions of time and position. – Assume S s =0 and L s =0, ρ s= m sn , s ∫ ρ sdr = M s where M s is the total mass of s and dr is a volume element (e.g. dxdydz) ∂M s r ∂M s r r + ∇ ⋅ sus dr = + sus ⋅ds ∂t ∫ (ρ ) ∂t ∫ ρ where ds r is a surface element bounding the volume. s = S s − L s
- Page 1 and 2: ESS 200C - Space Plasma Physics Win
- 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 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 and 54: 1 2 2 C ⎛ B ⎞ A ⎜ ⎟ ⎝ µ
- Page 55 and 56: - Continuity - Momentum - Equation
- Page 57 and 58: • The fluid velocity must be alon
- Page 59: - Arbitrary angle between k r and B
• A note on conservation laws<br />
– Consider a quantity that can be moved from place <strong>to</strong> place.<br />
f r<br />
– Let be the flux <strong>of</strong> this quantity – i.e. if we have an element <strong>of</strong> area<br />
then is the amount <strong>of</strong> the quantity passing the area<br />
element per unit time.<br />
– Consider a volume V <strong>of</strong> space, bounded by a surface S.<br />
– If σ is the density <strong>of</strong> the substance then the <strong>to</strong>tal amount in the<br />
volume is<br />
r r<br />
f ⋅δ<br />
A<br />
∫σ dV<br />
– The rate at which material is lost through the surface is<br />
d<br />
r r<br />
∫σ<br />
dV = −∫ f ⋅ dA<br />
dt<br />
– Use Gauss’ theorem<br />
V<br />
– An equation <strong>of</strong> the preceeding form means that the quantity whose<br />
density is σ is conserved.<br />
∫<br />
V<br />
V<br />
⎧∂σ<br />
⎨ + ∇ ⋅<br />
⎩ ∂t<br />
∂σ<br />
= −∇ ⋅<br />
∂t<br />
S<br />
r⎫<br />
f ⎬dV<br />
⎭<br />
r<br />
f<br />
= 0<br />
r r<br />
∫ f ⋅dA<br />
S<br />
δA r
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