1. Induction Equation Clare E Parnell School of Mathematics and Statistics

2. Induction Equation Diffusion term Advection term
 If Rm >> 1 then magnetic field advected:
 If Rm << 1 then magnetic field diffuses:

3. Diffusion Equation Consider what happens to the following magnetic
field after diffusion

4. Diffusion Equation Solution for magnetic field:
Solution for current density:

5. Diffusion - Evolution of the magnetic field lines

6. Diffusion - Evolution of Bz versus x

7. Diffusion - Evolution of jy versus x

8. Advection Equation Consider what happens to the following magnetic
field B moved by the flow v

9. Advection Equation Solution for magnetic field:
Solution for current density:

10. Advection - Evolution of the magnetic field lines

11. Advection - Evolution of Bz versus x

12. Advection - Evolution of jy versus x

13. Importance
On Sun vast majority of plasma is advected except where small length scales are created, e.g., in current sheets.
Combination of advection and diffusion known as magnetic reconnection

14. Importance Magnetic reconnection important in: Powering solar flares
Heating solar corona
Driving solar wind
Triggering CMEs