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

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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.

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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, V0, Lorentz force0, J
  must parallel with B, the so called force free
  field
• An extreme case Potential Field (or current
  free), J0 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.

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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 VA(B2/4p?)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 Vs(?P/?)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

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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 Suns 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.

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Coronal Heating (cont.)

• Coronal heating process has three basic elements
• Generation of mechanical energy
• Transport of mechanical energy
• Dissipation of the energy
• Near-universal agreement that energy is produced
  by the turbulent fluid motion of the Suns outer
  convective zone
• But proposed mechanisms differ in energy
  transport and dissipation

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Coronal Heating (cont.)

• Hydrodynamic heating mechanisms
• Acoustic wave transfer, and shock dissipation
• Formation of shock (see illustration on the
  board)

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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

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Coronal Heating (cont.)

• Direct current heating mechanisms microflare
  heating
• Current sheet --- magnetic reconnection
• (turbulent heating,
  wave heating)