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Solar Wind Energy Coupling Through The Cusp

Solar Wind Energy Coupling Through The Cusp. Robert Sheldon NASA/MSFC/NSSTC/XD12 Ted Fritz, Jiasheng Chen, BU. ABSTRACT.

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Solar Wind Energy Coupling Through The Cusp

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  1. Solar Wind Energy Coupling Through The Cusp Robert Sheldon NASA/MSFC/NSSTC/XD12 Ted Fritz, Jiasheng Chen, BU

  2. ABSTRACT • Three variants of solarwind-magnetosphere energy coupling are well-known: the rectified solar wind electric field Ey (Dungey, Akasofu e); the viscous interaction (Axford & Hines); and the shock-driven inductive electric fields (1991 event). We suggest a fourth, intermediate category active during high speed solar wind streams, corresponding to “recurrent magnetic storms”. Such streams do not have a good impedance match to the dipole magnetosphere, and therefore neither supply electric nor viscous energy. However, they are well-matched to the quadrupole cusps, with several promising mode conversion mechanisms available. This may explain the correlation with MeV electrons, highest not for internal (AE, Dst), or external drivers (ram pressure, Ey) but for “mixed” drivers such as Kp and Vsw. We present POLAR data and simulations showing good agreement with statistical studies, diffusive gradients, energetic particle spectra, elemental composition, and dynamical development consistent with a cusp transducer. The major difficulty is the lack of historical data, since few missions excepting POLAR have flown through the cusp with energetic particle instruments. Still, even equatorial s/c such as CRRES or AMPTE or the proposed RBSP, can see the cusp source as a “butterfly” pitchangle distribution diffusing into the equatorial plane.

  3. Transducers: The Oldest Physics Problem How does point A influence point B? • 500BC Aristotle: mind, “spooky action-at-a-distance” • 500BC–2000AD Democritus to Descartes: particles • 1690AD Newton: “action-at-a-distance” gravity (tides) • 1650AD Huygens: waves • 1840AD Faraday: fields How does the Sun transfer energy to Earth? • Photons+protons (DC equil.): heat,pressure (Chapman) • Electric+Magnetic fields (AC/DC): currents (Alfven) • Waves+impulsive events (AC mechanical): compressional, shocks, viscous (Axford) Can you connect A-E with 1-3?

  4. SunEarth Transducers None work for MeV electrons! • Proton pressure  Bow shock, hot plasma (100eV electron, 1 kev/nuc ion), thermalized ram energy “Frictional” or “viscous” (rV5/2) • Impulsive  SSC, shock acceleration, Fermi, radial diffusion, Kp, “mechanical” (rV, rV2) • Fields  Polar cap potential, convection, ring current, Dst, AE, “electrical” (V*Bz) [ICME] • What transducer powers Outer Radiation Belt MeV Electrons (ORBE)? Poor correlation with all of the above! V correlates best all by its lonesome. Why?

  5. Springs & Shock Absorbers:The importance of matching impedances • Why does a car have BOTH springs & shocks? • Springs are “reversible”, adiabatic, they “bounce back” ruining the tire tread as the energy dissipates in the tires. • Shock absorbers are “irreversible”, non-adiabatic, they convert the energy to heat. But with too slow a response. • Springs match the impedances of potholes to shocks • ORBE/Vsw energy transducer must be irreversible. • Cannot be too “stiff”, ideally it is “critically damped” • Magnetic fields are “springs”, what are “shocks”? • Something responding to Vsw, yet dissipative…

  6. The Dipole Trap in Lab & Space Electrons  • Great Trap • Poor accelerator • Best for producing ENA of E >1 keV particles outside trap. 2.2cm Ions ↑Sheldon 2002: Lab magnetosphere with NIB magnet @–400V McIlwain 1963

  7. TOP Quadrupole Trap in the Laboratory(Two, 1T, parallel NIB magnets, -400V, 50mTorr) cusp separatrix 2.2cm 2.2cm SIDE

  8. Maxwell solved the “image dipole” problem, plotting the quadrupoles. Chapman used it 50 years later to explain the magnetosphere. T87 Maxwell 1880 Chapman 1930

  9. The 2nd (Cusp) Invariant Bouncing on a field line without crossing the equator Near the nose, a single equatorial B-maximum, near both cusps N. & S., a double local B-maxima. |B| CF currents N.Ionosphere Equator S.Ionosphere 3 wells 2 wells s-distance

  10. T96Cusp TopologyDot marks the spot of quadrupole null point as a function of season/UT.“UFO” is ionospheric footprint of null, darker smaller |B| Solstice 4UT Solstice 16UT Equinox 16UT Equinox 16UT,-Bz

  11. Ionospheric Footpoint of the HiLatitude Minima: Tilt vs Press +1.75deg +7.3deg -3.67deg 5dyn Null Point Poleward Minima 3.3dyn Equatorward Minima 1.7dyn

  12. Ionospheric Footpoint of HiLatitude Minima: Tilt vs Dst +1.75deg +7.3deg -3.67deg -50nT Both sunward (positive) tilt and/or high solar wind pressure are needed to produce the poleward “dome” cusp minima. -30nT -10nT

  13. Ionospheric Footprint of HiLatitude Minima: Press v Dst 3.3dyn 5dyn 1.7dyn -50nT -30nT |Dst| alone doesn’t develop the poleward side of the cusp, but it amplifies or magnifies what is already there. (Significant for statistical correlations.) -10nT

  14. Dotted B-field lines Cusp Equator(min |B| on fieldline) Solid |B|-mag contours Trapped particle orbits on several C-shells Cshell=1 Side Front C=1.5 C=2

  15. Tracing in a T96 Quadrupole Trap Quad null pt B-field lines Trapped e- trajectory Quasi- Chaotic

  16. H+ Trapping in T96 Cusp Hi E cutoff Numerical Roundoff Loss-cone cutoff Red= None Green=Quasi- Blue= Yes

  17. e- Trapping in T96 Cusp Hi E cutoff Numerical Roundoff Loss-cone cutoff Red= None Green=Quasi- Blue= Yes

  18. Cusp Provisional Invariant Limits • Energy Limits (1st invariant at 100nT) • Minimum energy, Emin, is defined by cusp “separatrix” energy (ExB = B) ~ 30 keV in the dipole? • Max energy, Emax, defined by rigidity.~ 4 MeV e- (20keV H+) • Consequently, no protons are expected to be trapped. • Pitchangles locally 40-90o, (2nd invariant) • Low C-shells are empty below 1 Re for all energy, with a high-Cshell cutoff ~6 inversely dependent on Energy. 1 < C <~6 Re

  19. Mapping Cusp to Dipole • Conserving the 1st invariant, and pitchangle scatter the particles into the cusp-loss cone (<40o), then the particles can appear in the dipole trap, or radiation belts. What would their distribution look like? • Energy limits to the rad belts, give ~ 0-100 keV for protons, and 1-15 MeV for electrons. • C-shell limits to the dipole give ~5<L<∞? very close to the PSD “bump”. • Mapping pitchangles  50o < a < 90o at dipole eq? • Cusp particles look like ORBE injections.

  20. POLAR: Oct 12-16, 1996

  21. Sheldon et al., GRL 1998 POLAR/ CAMMICE data 1 MeV electrons PSD in outer cusp

  22. POLAR 4/1/97 Cusp Traversal

  23. The Dipole Trap “Accelerator” • The dipole trap has a positive B-gradient that causes particles to trap, by B-drift in the equatorial plane. Three symmetries to the Dipole each with its own “constant of the motion” 1)Gyromotion around B-field Magnetic moment, “”; 2) Reflection symmetry about equator Bounce invariant “J”; 3) Cylindrical symmetry about z-axis Drift invariant “L” Betatron acceleration by E┴ compression, violation of 3rd invariant, L-shell

  24. The 1-D Fermi-Trap Accelerator Waves convecting with the solar wind, compress trapped ions between the local |B| enhancement and the planetary bow shock, resulting in 1-D compression, or E// enhancement. Pitchangle diffusion keeps it in.

  25. The 2-D Quadrupole Trap • A quadrupole is simply the sum of two dipoles. • Quadrupoles have “null-points” which stably trap charged particles (eg. Paul trap) • Motion of the dipoles results in a 2D constriction of the volume. This is just a generalization of 1D Fermi-acceleration to 2D. • 1D Fermi acceleration increases E//, violating the 2nd invariant. • 2D betatron acceleration increases E┴ , violating the 1st & 3rd invariants • Efficiency Product: hT = h1 h2 h3 h4 h5 h6…

  26. Model • Fast solar wind is trapped in the cusp • 27 day recurrence, non-linear with Vsw • High Alfvenic turbulence of fast SW heats the trap • Low Q-value, compressional, BEN • 2nd Order “Fermi” accelerates electrons • Low energy appear first, then high w/rigidity cutoff. • Trap empties into rad belts simultaneous L=4-10 • “gentle” evaporation, or “rapid” topology change • Initially “butterfly” around 70-deg equatorial

  27. 1. Non-Linear Vsw Dependence 30keV 100eV 10keV 1keV Vsw Flux Flux seed trap seed trap E E The Reason that Vsw interacts non-linearly is that it does several things at once. It heats the seed population, while also making the trap deeper.

  28. Kolmogorov, Arnol’d, Moser (applied to Jupiter perturbation of Earth)……… Earth orbit as Perturbed by Jupiter. Poincaré slice x vs. vX taken along the E-J line. Earth orbit if Jupiter were 50k Earth masses.

  29. Real Life • Up to this point, we have developed the theory of cusp trapping and acceleration in an ideal, vacuum quadrupole. • However, real life is far more interesting. POLAR data, which triggered this investigation, shows trapped ion flux and a highly modified magnetic field, which we argue is a Cusp Diamagnetic Cavity. • The positive feedback between the quadrupole and trapped ions, suggests that CDC are ubiquitous and important.

  30. Cusp Diamagnetic Cavitiesa.k.a Magnetic Bubbles

  31. Turbulence, Power, Spectra…

  32. Schematic Cusp Diamagnetic Cavity POLAR sees thick (1-6 Re) CDC, whereas Cluster sees thin (< 1Re). We interpret this as a radial dependence on the thickness of the CDC.

  33. Stability of Infinitesimal Dipole

  34. Stability of Finite Ring

  35. Cusp Energetic Particles (Ions) Spectra at 2 times Ratio of Spectra

  36. McIlwain, 1966

  37. ORBE (McIlwain 1966)

  38. McIlwain 1966

  39. Correlations • Highest SW correlation for energetic particles in the radiation belts is: velocity. R=.7-.8 during high-speed streams) • V is NOT an energy. Not a density. Nor a Force(mv) • Multiplying by density  ram or mechanical energy, makes the correlation worse. • Multiplying by Bz  Electrical energy, makes the correlation worse. • There is a Dst signature with ORBE, but magnitudes are uncorrelated, only occurrence.

  40. Empirical Prediction • McIlwain 1966: Geo MeV e increases • Paulikas & Blake 1979: Vsw best external • Nagai 1988: Kp best internal predictor • Baker 90 LPF, Koons&Gorney 90 NN • Dmitriev&Chao03 Log-Linear • Ukhorskiy et al., 04 NonLinear

  41. Cusp Scaling Laws • Maximum energy from rigidity cutoffs, scaled by distance of planetary cusp to surface of planet. • Assuming: • Brad ~ Bsurface= B0 • Bcusp ~ B0/Rstag3 • Erad= 5 MeV for Earth • Ecusp ~ v2perp~ (Bcuspr)2 ~ [(B0/Rstag3)Rstag] • m = E/B is constant EPlanet~ EEarth(RPBPlanet/REBEarth)2 (RE-Stag/RP-Stag)4

  42. Scaled Planetary ORBE Planet Mercury Earth Mars Jupiter Saturn Uranus Neptune R STAG 1.4 10.4 1.25 65 20 20 25 B0 (nT) 330 31,000 < 6 430,000 21,000 23,000 14,000 ERAD 0.66 MeV 5 MeV < .5 eV 7.1 MeV 1.6 MeV 0.81 MeV 0.12 MeV

  43. 1996

  44. Conclusions • The quadrupole is a nearly universal trap and cosmic accelerator more efficient than Fermi (and shocks). • The quadrupole cusp has ideal properties to couple AC mechanical energy from SW into the magnetosphere. • The peculiar correlations of ORBE with SW can be explained by requiring an intermediate stage of the non-linear cusp. • A test of the mechanism using comparative magnetospheres shows the correct energy scaling. Soli Deo Gloria

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