High Speed Streams & Earth’s Quadrupole Cusp:

Implications for ORBE

R. B. Sheldon, NASA/MSFC/NSSTC

T. Fritz & J.-S. Chen, CSP/BU

Manaus, Brazil

Feb 10, 2005

The Oldest Physics Problem• How does point A influence point B?

– Aristotle: mind, “spooky action at a distance”– Democritus to Descartes: particles– Newton: gravity (e.g. tides)– Huygens: waves– Faraday: fields

• How does the Sun transfer energy to Earth?1. Photons & protons (DC equilibrium): pressure, heat2. Waves & impulsive events (AC mechanical): Alfvenic,

compressional, shocks3. Electric & Magnetic fields (AC/DC): currents

Sun-Earth Transducers

• Proton pressure Bow shock, hot plasma (100eV electron, 1 kev/nuc ion), thermalized ram energy “Frictional” or “viscous” (V5/2)

• Impulsive SSC, shock acceleration, Fermi, radial diffusion, Kp, “mechanical” (V2)

• Fields Polar cap potential, convection, ring current, Dst, AE, “electrical” (V*Bz) [ICME]

• What transducer is CIR ORBE? Poor correlation of ORBE with all of the above! Best with Vsw.

Springs & Shock Absorbers• Why does a car have BOTH springs & shocks?

– Springs are “reversible”, adiabatic, they “bounce back” (and ruin the tire tread).

– Shock absorbers are “irreversible”, non-adiabatic, they convert the energy to heat.

– Ex: manual dynamo with lightbulb or with 1F capacitor.

• Vsw energy transducer must be irreversible.– Cannot be too “stiff”, ideally it is “critically damped”

• Magnetic fields are “springy”, what are “shocks”?– Something responding to Vsw, yet not stiff…

The Quadrupole Cusp -- Static Equilibrium

The Dipole Trap

• Great Trap

• Poor accelerator

• ENA of E >1 keV

particles outside trap.

Quadrupole Trap in the Laboratory

(Two 1-T magnets, -400V, 50mTorr)

Maxwell 1880 Chapman 1930

QuadrupolarT87 Magnetosphere

• All modern B-models have high latitude cusps.

• Since Chapman & Ferraro 1937, we’ve known the magnetosphere is a quadrupole, yet all the trapping models to the present have assumed a dipole.

Cusp Equator

B-field lines

|B|

C=2

C=1

C=1.5

The Simulated T96 Quadrupole Trap

• Lousy Trap

• Great Accelerator

• Can be made to trap better though.

Chaotic, nearly trapped

H+ Trapping in T96 Cusp

e- Trapping of T96 Cusp

Cusp Provisional Invariants• Minimum energy, Emin, is defined by “separatrix”

energy (ExB = B) ~ 30 keV

• Max energy, Emax, defined by rigidity.~ 3 MeV e-

• Mapping cusp Energy limits to the rad belts, give ~ 0-100 keV for protons, and 1-5 MeV for electrons.

• Mapping C-shell limits to the dipole give ~4<L<∞. very close to the PSD “bump”

• Mapping pitchangles 50o < < 90o at dipole eq.

• Cusp particles have all the right properties ORBE

The Outer Radiation Belt Electrons (ORBE)

McIlwain, 1966

ORBE (McIlwain 1966)

McIlwain 1966

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

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.• Whatever the mechanism, it is not energy-starved

(2nd moment) or density starved (0th moment).

1996

The Discovery of Cusp MeV Electrons

POLAR: Oct 12-16, 1996

Sheldon et al., GRL 1998

POLAR/ CAMMICE data

1 MeV electron

PSD in outer cusp

POLAR 4/1/97 Cusp Traversal

Accelerator Efficiency

Why would the cusp accelerate at all? Why not just use standard well-

known accelerators?

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

The 1-D Fermi-Trap Accelerator

Waves convecting withthe solar wind, compresstrapped ions between the local |B| enhancementand the planetary bow shock, resulting in 1-Dcompression, or E// enhancement. Pitchangle diffusion keeps it in.

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

PROPERTY DIPOLE FERMI QUADRUPOLE

Stochasticity .001:1:1000 s .001:>103:>104 s 0.1:1:10 s

Process Flow rim>ctr>blocked end>side>diffus ctr>rim>open

Wave Coupling hi E weak all E same hi E best

Accel. in trap Traps Detraps Trap/Release

Diffusion Essential Helpful Neutral

Adiabatic Heat 2D pancake 1D cigar 2D pancake

Energy Source SW compress SW Alfven SW+internal

e- Max Energy 900MeV@10Re 1.8 MeV@.1Re 280 MeV@3Re

e- Min Energy 45 keV 2.5 keV 30 keV

Trap Volume 1024 m3 1020 m3 1022 m3

Trap Lifetime > 1013s 104s 109:105s

Accel. Time > 300,000s 8,000s 25,000s

Trap Power < 5x108W 106W 5x107W

Model1. Fast solar wind is trapped in the cusp

– 27 day recurrence, non-linear with Vsw

2. High Alfvenic turbulence of fast SW heats the trap– Low Q-value, compressional, BEN

3. 2nd Order “Fermi” accelerates electrons– Low energy appear first, then high w/rigidity cutoff.

4. Trap empties into rad belts simultaneous L=4-10 – “gentle” evaporation, or “rapid” topology change – Initially “butterfly” around 70-deg equatorial

1. Non-Linear Vsw Dependence

E

Flux

EFlux

30keV100eV 1keV 10keV

Vsw

seed trap seed trap

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.

Kolmogorov, Arnol’d, Moser (applied to Jupiter perturbation of

Earth)………Earth orbit as Perturbed byJupiter.

Earth orbit if Jupiter were 50k Earth masses.

Poincaré slicex vs. vX takenalong the E-J

line.

T96 Cusp Topology

Solstice16UT

Solstice4UT

Equinox16UT Equinox

16UT,-Bz

Cusp Feedback

But the cusp is turbulent! How can the REAL cusp trap anything for 2 days!?

It doesn’t.

Usually.

Cusp Diamagnetic Cavitiesa.k.a Magnetic Bubbles

Diamagnetic Effect of Cold Plasma

An Interplanetary Test

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~ (Bcusp)2 ~ [(B0/Rstag

3)Rstag]

• E/B is constant

Erad-planet~(Rstag-Earth/Rstag-planet)(B0-planet/B0-Earth)2Erad-Earth

Scaled Planetary ORBE

Planet

Mercury

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

ERAD

4 keV

5 MeV

< 1.5 eV

150 MeV

1.2 MeV

1.4 MeV

0.42 MeV

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

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