SLIDE SHOW 3 B changes due to transport + diffusion III -- * * magnetic Reynold number INDUCTION EQUATION B moves with plasma / diffuses through it

(a) If R m << 1  The induction equation reduces to  B is governed by a diffusion equation --> field variations on a scale L 0 diffuse away on time * * with speed

(b) If R m >> 1 The induction equation reduces to and Ohm's law --> Magnetic field is “**”frozen to the plasma

1. Diffusion Start with field B 0 (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

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) 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

Example of Plasma Motions along Loops

Covered with turbulent convection cells: (1 Mm) (15 Mm) 2. Photosphere 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 field

Chromo sphere (Ha - Big Bear)

Chromo sphere (SOHO- EIT)

Corona at 1.3 MK (EIT)

Corona at 1.6 MK (EIT)

Corona at 2.3 MK (EIT)