MHD course, Last lecture (repetition) ===================================== Chapter 3 (MHD) ---------------- - 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) --------------------- - 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) -------------------------- - 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) ----------------------- - 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) ----------------------- - 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) ------------------------- - 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) ------------------------- - 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) ----------------------------------- - 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?