SLIDE SHOW 3

€

∂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

€

∂B∂ t

= η∇2B

B is governed by a diffusion equation --> field variations on a scale L0

diffuse away on time * *

€

vd = L0 / td

€

=ηL0

€

td =L0

2

η

with speed

(b) If Rm >> 1

The induction equation reduces to

€

∂B∂ t

= ∇× (v × B)

€

E + v × B = 0

and Ohm's law -->

Magnetic field is “* *”frozen to the plasma

1. Diffusion

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.

Start with field B0(x) and watch diffuse.

Current density

2. Diffusion heats the corona

X-ray bright points, coronal holes, coronal loops

Coronal loops -- many tiny diffusion locations

3. Diffusion allows magnetic connections to change -- eg when flux emerges

QuickTime™ and aVideo decompressor

are needed to see this picture.

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)

QuickTime™ and a decompressor

are needed to see this picture.

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

1. If magnetic

field static, then

plasma can flow

only along B

QuickTime™ and aVideo decompressorare needed to see this picture.

Example of Plasma Motions

along Loops

Covered with turbulent

convection cells:

(1 Mm)

(15 Mm)

2. Photosphere

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture. Granulation

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

In close-up:

B is even concentra

ted at edges of granules

3. When a magnetic

field erupts, the plasma is carried

with it

e.g. Erupting Prominence

E.g. Coronal Mass Ejection

The SUN

TODAY

The photo sphere

(SOHO-MDI)

Magnetic field

(SOHO-MDI)

Movie of magnetic

fieldQuickTime™ and a

YUV420 codec decompressorare needed to see this picture.

Chromosphere (Ha - Big

Bear)

Chromosphere

(SOHO-EIT)

Corona at 1.3 MK

(EIT)

Corona at 1.6 MK

(EIT)

Corona at 2.3 MK

(EIT)