Investigation of the Magnetosphere of Ganymede with Galileo's Energetic Particle Detector
Ph.D. dissertation by Shawn M. Stone, University of Kansas,
1999.
Copyright 1999 by Shawn M. Stone. Used with permission.
2.3 Adiabatic Invariants
The guiding center equation is an approximation to the
Lorentz force equation. It simplifies matters enough to
deduce the three basic periodic motions that charged
particles perform in magnetospheres: gyration, bounce, and
drift. However, the drift [2.16] and mirror [2.13] equations
must still be integrated over several degrees of drift and
many bounce periods to predict the future state of the
particles. This is still a problem even with today’s
computational power for most cases.
Fortunately, each of the three typical, nearly periodic, motions have associated with them an adiabatic invariant. These adiabatic invariants are conditional on the fact that the forces providing the motion must vary infinitesimally slowly when compared to the time scales of the particle motion. The quantity called action remains invariant for slow changes in the system:
|
|
[2.17] |
where p is the conjugate momentum and q is the generalized coordinate. Each of the three invariants is derived from Equation [2.17].
- 2.3.1 The First Adiabatic Invariant
- 2.3.2 The Second Adiabatic Invariant
- 2.3.3 The Third Adiabatic Invariant
Next: 2.4 Pitch Angle Diffusion
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Updated 8/23/19, Cameron Crane
QUICK FACTS
Mission Duration: Galileo was planned to have a mission duration of around 8 years, but was kept in operation for 13 years, 11 months, and 3 days, until it was destroyed in a controlled impact with Jupiter on September 21, 2003.
Destination: Galileo's destination was Jupiter and its moons, which it orbitted for 7 years, 9 months, and 13 days.