MHD course, Last lecture (repetition)
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Chapter 3 (MHD)
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- Conservative formulation ==> important in numerical methods & theory
- MHD == Euler + jxB + Faraday's law. Other Maxwells identically satisfied:
Ampere is just the definition of j, div B == 0 follows from Faraday,
Gauss's law can be used afterwards to compute charge density.
- Frozen-in theorem: Magnetic flux through a co-moving loop is constant in time.
- Motion of field lines ==> nonsense
- Another related theorem: fluid elements that lie on same field line continue
to do so
Chapter 4 (MHD waves)
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- Entropy, Slow, Alfven, Fast
- Maximum velocity is bounded by sqrt(vA^2 + cs^2)
- Entropy waves: all co-moving phenomena (e.g. auroral arcs if they
drift with ExB velocity). Entropy waves are very common!
- Importance of plasma beta parameter
Chapter 5 (Ionospheric ED)
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- Pedersen, Hall, parallel conductivity
- ionosphere is usually electrostatic
- 3D, 2D continuity equations (2D continuity equation has jPar as source term)
- basically a current distribution problem
Chapter 6 (2D coupling)
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- Current is FAC <==> low-beta plasma
- Current does not stay FA when beta approaches and surpasses unity!
- Resistive scale length lambda = sqrt(SigmaP/K), j=K*DeltaPhi.
Usually lambda = 100 km.
Magnetospheric features smaller than lambda are filtered out.
Chapter 7 (3D coupling)
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- Inertial, P-gradient driven, viscous FAC
- The most important thing to remember from MHD equations: jxB = grad P
- Implementing IM coupling: jPar -> Phii -> Phim -> E -> vPerp (3D)
or Phim -> Phii -> jPar (2D)
** Remember that P is constant along field lines **
Chapter 8 (Boltzmann MHD)
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- To derive Generalized Ohm's law we must start from Boltzmann
- Leading order correction to MHD: Hall term
(Don't confuse with ionospheric Hall!)
Hall term means: B frozen to ve, not vi.
- Classical collision frequencies very tiny in space plasmas
Chapter 9 (Instabilities)
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- Rayleigh-Taylor (cumulus, spread-F, E-region "gradient drift" waves ...)
- Kelvin-Helmholtz (velocity shear)
- Two-stream (two-fluid plasma; Different physics for collisionless/ionospheric)
Ionospheric version is called Farley-Buneman.
- Ballooning and Interchange instability (related to Rayleigh-Taylor).
The role of gravity may be taken by: Pressure gradient, Centrifugal force
on bouncing particles, Corotation of plasmasphere (Jupiter).
In some cases, all 4 mechanism may be simultaneously important!
- Tearing
Chapter 10 (Magnetospheric physics)
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- Bow shock, magnetosheath, current sheet, magnetopause,
plasmapause, plasmasphere
- Magnetopause shape: Magnetic vs. kinetic energy density balance
- Reconnection <== opposite B's at current sheet
- Reconnection ==> plasma flow, convection
- Substorms:
- The basic mode of magnetospheric energy release
- Growth, trigger, expansion, recovery phases
- Trigger (onset) close to (-6.6,0,0)
- Explosive process which taps B^2 energy (mainly)
- Dripping faucet analog "model"
- Often triggered by northward turning of IMF ==> stop of reconnection
==> stop of convection
- May be triggered by some solar wind impulse also (SSC)
- Sometimes triggered internally, with no change in solar wind
- Plasmoids: Correlation with substorms still unclear
- Flux ropes: plasmoids with nonzero By
- Pseudobreakups: small substorm-like phenomena
- Steady Convection Events (SCEs): Strongly negative IMF Bz, Fast reconnection,
Fast plasma flow (convection), Thick auroral oval, No substorms (!)
- Double oval: After recovery phase, sometimes assoc. with SCE
- Substorm progression:
- Growth phase (0.5 h): Current sheet thinning, tail stretching, convection.
Equatorward moving arcs (entropy waves?)
- Trigger (onset) (2 min): Always on most equatorward arc.
- Sometimes: Auroral fading (preceeds substorm onset)
- Sometimes: Auroral horn (propagates with Alfvenic speed)
just after trigger
- Expansion phase (15 min): Expansion in all directions
- Westward traveling surge (WTS)
- Recovery phase (0.5 h)
- Eastward-drifing Omega-bands (<== Kelvin-Helmholtz?)
- Ionosphere: Is small or large conductivity important for onset?
- Does neutral wind sometimes trigger substorms?
- Role of oxygen outflow?