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

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• 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

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