Fundamental Technologies Galileo Spacecraft Pages

2.3.3 The Third Adiabatic Invariant

The third invariant is associated with the azimuthal drift that charged particles undergo. From the action integral Equation [2.17] and using information provided in Figure 2.8 yields

where p in the direction of dl is assumed negligible since the drift velocity is typically an order of magnitude, or more, less than the particle's total velocity. Using Stoke's theorem gives

where F is the amount of magnetic flux through the drift path. The constancy of F keeps the particles bouncing and drifting along the same L shell.

Figure 2.8 Conservation of the third adiabatic invariant. Magnetic flux enclosed by a particle drifting perpendicular to B and DB remains constant during slow changes in the magnetic field [Walt, 1994].

Next: 2.4 Pitch Angle Diffusion

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Updated 10/18/02, T. Hunt-Ward
tizby@ftecs.com