Shocks and Associated Phenomena in Space

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Shocks and Associated Phenomena in Space

• What are shocks?
• Fluid equations
• Rankine-Hugoniot conditions
• Perpendicular shock
• Associated phenomena
• Heating changing plasma parameters,
• Particle acceleration
• Waves and radiation
• Coronal mass ejections, flares, solar radio
  bursts

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1. Shocks - Qualitative
?

• When disturbance moves faster than speed of
  small amplitude waves, e.g., cs or VA
• Why speed depends on amplitude
• How nonlinear steepening leads to wavebreaking
  dissipation
• What flow deflection, compression, slowing,
  heating, particle acceleration, field
  enhancement, waves, radiation
• Overall excess motion ? dissipation and
  redistribution of energy

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2. Fluid Equations (MHD GD)

• Derived from moments of the Boltzmann Equation

Maxwells Equations
4
Normal incidence frame
5
3. Rankine-Hugoniot (Jump) Conditions 1

• Derived from conservation equations for mass,
  momentum energy with Maxwells equations.
• Conservation law for scalar Q flux F
• Time-steady flow with zero source. Volume
  integral ? surface integral and taking limit as
  box thickness tends to zero ?
• Jump condition for conserved quantity normal
  flux from region 1 into region 2 equal.

Upstream Region 1
Downstream Region 2
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Rankine-Hugoniot (Jump) Conditions 2

• Mass conservation
• Normal momentum
• Tangential momentum
• Energy
• Normal B
• Tangential E

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Rankine-Hugoniot (Jump) Conditions 3

• Shock normal frame has u1 u1n. Shock variables
  are the Alfven and sonic Mach numbers and angle
  ?
• Mass conservation ? compression ratio
• Eliminate Bn, then Bt, ut to find

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Rankine-Hugoniot (Jump) Conditions 4

• Rankine-Hugoniot equation follows on eliminating
  P2
• Cubic in MA2 ?3 solutions
• Weak discontinuity r 1 ? a ? 1 and (17) becomes
  the dispersion equation for the MHD modes
  fast/slow magnetosonic Alfven.
• MA ? 8 find r ? (G 1)/(G 1) 4 for G5/3.
  Limiting compression.
• Fast mode shock B increases, slow mode shock B
  decreases.
• All shocks compression, slowing and heating of
  the flow.

(17)
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3. Perpendicular shock

• ? p/2, so B1nB2n 0, and
• RH solution is
• Find r increases towards (G 1)/(G 1) 4 as
  MA increases.
• Gasdynamic shock (B 0) has
• Flow compression, slowing heating. Field
  increase.

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4. Earths Bow Shock

• Slows deflects flow around magnetopause.
• Once sub-Alfvenic, information (waves) can
  propagate upstream and nonlinearly steepen to
  form the shock.
• Qualitative ram pressure balanced by downstream
  thermal pressure

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B (nT)
?
f
Earths Bow Shock
V (km/s)
?v
fv
Cs (km/s)
N (cm-3)
Pram (nPa)
2230
Time (UT)
2100
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Excellent agreement with Rankine-Hugoniot
conditions
(Lepidi et al., 1997)
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5. Heating of Downsteam Plasma

• Balancing Pram against P2,th often ? Ti 106 K.
• ? thermal emission X-rays from downstream.
• Examples supernova remnants coronal ISM, solar
  system ISM shock interactions.

Hubble BZ Cam
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Particle Reflection Acceleration at Shocks
B1
electron motion
E (y)

• Convection electric field E -u1 x B1 ? E x B
  drift
• plasma drift with
• Shock-drift acceleration
• Magnetic mirror reflection conservation of
  magnetic moment

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Electron beams, Langmuir waves radiation
B ? vExB ?
Kuncic Cairns (2004)
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Flares and Coronal Mass Ejections (CMEs)
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CMEs
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Shock, electrons, waves in situ
f (Hz) Power E(V/m) Electron Flux N(cm-3) B
(nT)
Wind Spacecraft (Bale et al., 1999)
Time (UT)
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Predicted Radio Emission (CME)
Knock Cairns (2004)
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CMEs, radio bursts, Space Weather
Reiner
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Type III Bursts

• Type III solar burst
• Electron beam
• Langmuir waves
• Radio waves fp 2fp
• Earths foreshock radiation

Lin et al., 1981
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6. Summary Shocks in Space Astrophysics

• Shocks nonlinear steepening dissipation
• Rankine-Hugoniot conditions fluid theory and
  mass, momentum etc. conservation.
• Shocks redistribute supersonic flow energy
• Compress, slow, deflect heat plasma.
• Heating balance downstream Pth against Pram.
• Accelerate particles shock-drift Fermi
• Can cause intense plasma radio waves
• Space exciting, fundamental relevant physics.