1. Consequences of Cusp Trapping Rob Sheldon National Space Science & Technology Center J. Chen, T.Fritz Boston University May 28, 2002

2. History •We discovered a high-altitude MeV electron population trapped in the cusp (GRL 98) •We also discovered diamagnetic cavities or trapped low-energy plasma in the cusp. (JGR98) •What is the relationship between high & low energy plasma? (Think rad belt & plasmasphere) –Topology  Waves/Energy 1 energization •In this talk, we want to relate these two aspects of the cusp, as a possible source of rad belt MeV e-

3. Necessity of Quadrupolar Trap •Maxwell (~1880) showed that a perfect conductor adjacent to a dipole formed an image dipole •Chapman (~1930) realized that a neutral plasma was like a perfect conductor •Two dipoles have some quadrupole moment •Therefore, every dipole embedded in a plasma, MUST form a quadrupolar region, which is also a trap. (Nobel prize for Paul trap) •This trap is embedded in the high latitude cusp

4. Maxwell

5. Parallel Dipoles w/ ring current - High latitude minimum, and Shabansky orbits -Bistable distributions - Quadrupolar regions of magnetosphere are important for trapping and feeding dipole.

6. Sheldon et al., (GRL 98) observed 1MeV electrons at L~12, adiabatically (but not diffusively) connected to the MeV radiation belt population. It had a trapped, 90- degree pitch angle dependence.

7. High Latitude MinimumTrap? •The high-latitude minimum can trap a bouncing particle, which then possesses a 2nd invariant •But will the ions stay in this region, bouncing forever, or drift away? Does the 3rd invariant also exist?  The literature didn ’ t say, but certainly minima exist on both sides of the cusp. We did a particle tracing simulation to investigate this possibility.

9. Plasma Entry @ Cusps - One magnet grounded, other biassed -Plasma generated by electrons on one magnet, feed into other trapping field due to diffusion though "x-line" -Like northward Bz, this feeding happens at the cusps -The cusps themselves hold the plasma long enough to glow, "Sheldon orbits"

10. But Diamagnetic Cavities? •Since this region has weak fields, trapped plasma will distort the field.  As the plasma drifts around the minimum |B|, it produces a “ cusp ring current ” that opposes the cusp field and makes a diamagnetic cavity. •How are these diamagnetic cavities related to the quadrupole trapped plasma? –These cavities are filled with mirror mode waves and high turbulence.

11. Cusp Diamagnetic Cavities

12. Plasma is Diamagnetic B B D

13. MLT/MLAT/Radial Occurrence The CDC occur near the outer cusp. Not surprising, because the cusp is the region of weakest field. The cusp is also a diverging field.

14. Diamagnetic Levitation The University of Nijmegen shows how all substances are diamagnetic, and can be levitated harmlessly by the diverging (cusp-like) field in the 32mm bore of a 16 T Bitter magnet. water drop live frog small frog

15. Stability calculation algorithm •1) Place small dipole in the cusp, anti-aligned •2) Calculate B = B DIPOLE + B t96 for a 1 Re bubble around the little dipole.  3) Since E=  B 2 and F X = dE/dx, we repeat this calculation for a little dx, dy, dz motion and take differences to get F. (We also get dF/dx too.) •4) Finally we adust the strength of B DIPOLE until we can get a zero force. •5) We plot these quantities to find a force free solution

16. Force-free dipole conditions

17. More Simulations a B 2 - D 6 8 r r Minimum energy found for test dipole at ~1e-8 of Earth, placed between MP-2 Re, and MP-4 Re. Schematically, MP currents form a “ hard ” outer boundary, so larger CDC have centroids earthward.

18. Force free condition

19. 4/800km/s, +/0/- 10nT, Day 172/294,300/10 Dst

20. Log scale

21. The Quadrupole Cusp x x

22. How do we map topology?  Since H =Total Energy= K.E. + P.E then we can write H =  B + qU for this region, where U is the electrostatic potential, B is magnetic field. •Then all trapped orbits conserve H, and contour maps of H delimit the trapping regions.  Once we have a model for (B, U) all the energies can be analyzed for trapping by adjusting . •This mapping transformation with GUI at: –http://cspar181.uah.edu/UBK/

23. http://cspar181.uah.edu/UBK

24. Scaling Laws •B rad ~ B surface = B 0 •B cusp ~ B 0 /R stag 3 •E rad = 5 MeV for Earth  E cusp ~ v 2 perp ~ (B cusp  ) 2 ~ [(B 0 /R stag 3 )R stag ]   E/B is constant E rad-planet ~(R stag-Earth /R stag-planet )(B 0-planet /B 0-Earth ) 2 E rad- Earth

25. Scaled Radiation Belts Planet Mercury Earth Mars Jupiter Saturn Uranus Neptune E RAD 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 25 B 0 (nT) 330 31,000 < 6 430,000 21,000 23,000 14,000

26. Conclusions •The Cusp is a stable quadrupole trap. •Diamagnetic bubbles are stable in the cusp. •Non-linear relation between bubble size & penetration into the magnetosphere •These bubbles may enhance high-Energy trap.  Scalings based on a Cusp accelerator produce a reasonable estimate of Jupiter ’ s radiation belt energy, predict that Mars will not have a radiation belt, and lead to predictions for the other planets.  Heliosphere cusp 0 cosmic rays?