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

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-

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

Maxwell

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

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.

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.

Plasma 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"

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.

Cusp Diamagnetic Cavities

Plasma is Diamagnetic B B D

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.

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

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

Force-free dipole conditions

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.

Force free condition

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

Log scale

The Quadrupole Cusp x x

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: –

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

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 B 0 (nT) ,000 < 6 430,000 21,000 23,000 14,000

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?