Follow a field line of a planet's dipole magnetic field from where it crosses the…
PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · The plasma state and single-particle motion
Action and Symmetry, Ch Adiabatic invariants, canonical perturbation theory and integrable systems
Problem
Follow a field line of a planet's dipole magnetic field from where it crosses the magnetic equator, at L planetary radii from the centre, to where it meets the planet's surface. The field strength at that foot is L34−3/L times its value at the equatorial crossing. Treat the top of the atmosphere as the surface.
((a)) Geostationary satellites sit on the field line with L=6.6. Evaluate the mirror ratio Bfoot/Beq for this line.
((b)) Estimate the equatorial pitch angle α0 below which a proton on this line is not turned back before it reaches the atmosphere.
((c)) State, in one sentence, what happens to a proton whose equatorial pitch angle is below this α0, and say why α0 is smaller here than on a line closer to the planet.