The%20Magnetospheric%20Cusp:%20A%20Quadrupole%20Trap%20and%20Stochastic%20Accelerator%20at%20the%20Planets

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The Magnetospheric Cusp A Quadrupole Trap and
Stochastic Accelerator at the Planets

• Ravi Kinnera, Rob Sheldon
• University of Alabama in Huntsville
• J. Chen, T.Fritz, J. Sullivan
• Boston University
• Richard Denton, Dartmouth College

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Motivation

• We discovered a cusp-altitude MeV electron
  population that was completely unexpected.
• Studying this population produced the surprising
  result that the cusp may determine the energy of
  the radiation belt particles.
• Thus the magnetopause controls the magnetosphere,
  not the other way around. David Beards work
  lives on!

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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 we will
  show is also a trap.

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Maxwell
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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 didnt say, but certainly minima
  exist on both sides of the cusp. We did a
  particle tracing simulation to investigate this
  possibility.

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Yes! But is it stable?

• 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.
• These cavities are filled with mirror mode waves
  and high turbulence.
• Are they stable configurations?

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Scaling Laws

• Brad Bsurface B0
• Bcusp B0/Rstag3
• Erad 5 MeV for Earth
• Ecusp v2perp (Bcuspr)2 (B0/Rstag3)Rstag
• m E/B is constant
• Erad-planet(Rstag-Earth/Rstag-planet)(B0-planet/B
  0-Earth)2Erad-Earth

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Scaled Radiation Belts

• Planet
• Mercury
• Earth
• Mars
• Jupiter
• Saturn
• Uranus
• Neptune

ERAD 4 keV 5 MeV lt 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 lt 6 430,000
21,000 23,000 14,000
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Conclusions

• The Cusp plays an important part of every
  magnetosphere.
• The Cusp is a stable quadrupole trap.
• Scalings based on a Cusp accelerator produce a
  reasonable estimate of Jupiters radiation belt
  energy, predict that Mars will not have a
  radiation belt, and lead to predictions for the
  other planets.