By Richard Fitzpatrick
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Sample text
In particular, the first-order perpendicular drift differs fundamentally from the E × B drift, since it is not the same for different species, and, therefore, cannot be eliminated by transforming to a new inertial frame. We can now understand the motion of a charged particle as it moves through slowly varying electric and magnetic fields. The particle always gyrates around the magnetic field at the local gyrofrequency Ω = eB/m. The local perpendicular gyration velocity u⊥ is determined by the requirement that the magnetic moment µ = m u⊥2/2 B be a constant of the motion.
In other words, the conservation of J prevents charged particles from spiraling radially in or out of the Van Allen belts as they rotate around the Earth. This helps to explain the persistence of these belts. 13 Third Adiabatic Invariant It is clear, by now, that there is an adiabatic invariant associated with every periodic motion of a charged particle in an electromagnetic field. Now, we have just demonstrated that, as a consequence of J-conservation, the drift orbit of a charged particle precessing around the Earth is approximately closed, despite the fact that the Earth’s magnetic field is non-axisymmetric.
It follows from Eqs. 95) where Bm is the magnetic field-strength at the mirror points, and ϑm is the latitude of the mirror points. Clearly, the latitude of a particle’s mirror point depends only on its equatorial pitch-angle, and is independent of the L-value of the fieldline on which it is trapped. Charged particles with large equatorial pitch-angles have small parallel velocities, and mirror points located at relatively low latitudes. 10 Van Allen Radiation Belts 2 CHARGED PARTICLE MOTION particles with small equatorial pitch-angles have large parallel velocities, and mirror points located at high latitudes.
The Physics of Plasmas by Richard Fitzpatrick
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