Post on 03-Jan-2016
transcript
SLIDE SHOW 3
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∂B∂ t
= ∇× (v × B) + η∇2B
• B changes due to transport + diffusion
I II
I
II=
L0 v0η
= Rm
• -- *
*
magnetic
Reynold number
INDUCTION EQUATION
η =1
μσwhere is magnetic diffusivity
• B moves with plasma / diffuses through it
(a) If Rm << 1
The induction equation reduces to
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∂B∂ t
= η∇2B
B is governed by a diffusion equation --> field variations on a scale L0
diffuse away on time * *
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vd = L0 / td
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=ηL0
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td =L0
2
η
with speed
(b) If Rm >> 1
The induction equation reduces to
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∂B∂ t
= ∇× (v × B)
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E + v × B = 0
and Ohm's law -->
Magnetic field is “* *”frozen to the plasma
1. Diffusion
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Start with field B0(x) and watch diffuse.
Current density
3. Diffusion allows magnetic connections to change -- eg when flux emerges
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4. Diffusion converts magnetic energy to heat in a
Solar Flare
Sudden brightening in chromosphere & corona near
sunspots
A Solar Flare TRACE -- T = 1.6 MK and 30 MK)
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1. B diffuses & heats plasma to 30 MK !
2. Heat spreads along arcade
of loops, which then cool
through 1.6 MK
3. The loops rise
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Example of Plasma Motions
along Loops
Covered with turbulent
convection cells:
(1 Mm)
(15 Mm)
2. Photosphere
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Supergranulation
This carries magnetic field to edges of cells
Map of Photospheric Magnetic Field
White -- towards you;
Black -- away from you
B is concentrated
around edges of supergranule cells by flow