1. CSI 769-001/PHYS 590-001 Solar Atmosphere Fall 2004 Lecture 09 Oct. 27, 2004 Ideal MHD, MHD Waves and Coronal Heating

2. Ideal MHD: Frozen-in Field Considering induction equation in ideal MHD (Eq. 7.61 in P. 222, or Eq. 7.35 in P. 217) Frozen-in field in corona (see P. 216 – 219) The statement is that the total amount of magnetic flux passing through any closed loop circuit moving with the local fluid velocity is constant in time. (Eq. 7.42 in P. 218) In other word, magnetic field moves with the fluid, or the field is said to be “frozen-in” to the fluid.

3. Ideal MHD: Force Free Field Considering momentum equation in ideal MHD (Eq. 7.59 in P. 222) Force Free field in corona Corona in equilibrium, V=0, Lorentz force=0, J must parallel with B, the so called force free field An extreme case: Potential Field (or current free), J=0 everywhere; potential field configuration has minimum energy Coronal field is force free but not potential; Coronal energy is stored in electric currents flowing in coronal loops.

4. Alfven wave, sound wave, MHD waves See text book P.224 to 226, Chap. 7.3) Also see board note for how to derive Alfven wave Alfven wave: V A =(B 2 /4πρ) 1/2 Alfven wave travels along magnetic field due to magnetic tension, similar to a wave traveling along a rope Magnetoacoustic waves: coupling between magnetic wave and sound wave V s =(γP/ρ) 1/2 (text book P.226, eq 7.85) Magnetoacoustic wave velocity depends on the angle between wave propagation direction (K) and magnetic direction (B) Fast mode Slow mode

5. Coronal Heating See text book P.233 to 239, Chap. 7.3.3 Coronal heating should be from mechanic energy, since thermal energy is impossible There are many different heating mechanism: hydrodynamic (wave) heating mechanisms magnetic (wave) heating mechanisms direct current mechanisms: microflares Because the coronal energy budget is only a tiny fraction (~0.01%) of the Sun’s total output, each mechanism is able to deliver the total energy required for coronal heating. On the other hand, simple total energy argument is not sufficient for deciding each mechanism is actually operating.

6. Coronal Heating (cont.) Coronal heating process has three basic elements 1.Generation of mechanical energy 2.Transport of mechanical energy 3.Dissipation of the energy Near-universal agreement that energy is produced by the turbulent fluid motion of the Sun’s outer convective zone But proposed mechanisms differ in energy transport and dissipation

7. Coronal Heating (cont.) Hydrodynamic heating mechanisms Acoustic wave transfer, and shock dissipation Formation of shock (see illustration on the board)

8. Coronal Heating (cont.) Magnetic or magneto-hydrodynamic heating mechanisms Slow mode MHD wave --- shock dissipation Longitudinal MHD tube wave --- shock dissipation Fast mode MHD wave --- Landau damping Alfven waves --- mode-coupling --- resonance heating --- compressional viscous heating --- turbulent heating --- Landau damping Magneto-acoustic surface wave --- mode-coupling --- phase-mixing --- resonant absorption

9. Coronal Heating (cont.) Direct current heating mechanisms: microflare heating Current sheet --- magnetic reconnection (turbulent heating, wave heating)