Astronomy & Celestial Mechanics
the sky, computed
Concept

Radial diffusion — where it appears

The slow random walk of trapped radiation-belt particles across drift shells, driven by fluctuations of the magnetic field on the timescale of their drift. Its coefficient grows as the tenth power of distance, and because it conserves the first two invariants it heats particles carried inward.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Three motions, three decades apart, and that is the point. The three periods of a trapped 1-MeV electron's motion against the shell it is trapped on, on a logarithmic time axis. It gyrates about a field line in 0.22 milliseconds, bounces between its mirror points in 0.33 seconds, and drifts right round the planet in 16 minutes — ratios of 1498 and 3015 at L = 4. Each motion carries a conserved quantity: the magnetic moment, the longitudinal invariant, and the magnetic flux the drift shell encloses. The separation is what makes them conserved. An invariant survives anything that changes slowly compared with its own period, so a disturbance lasting minutes destroys the third and leaves the first two untouched — and a particle that keeps its magnetic moment while being moved inward to a stronger field must gain energy. That is not a loophole; it is how the belts are filled.

Three clocks and nothing to fall onto

A charged particle in a dipole field gyrates, bounces and drifts, on timescales a millisecond, a second and a quarter of an hour. The three periods are three decades apart, and that separation is not a curiosity — it is the reason each motion has a conserved quantity, and the reason a magnetic storm can accelerate particles rather than merely stir them.

spaceflight · Radiation belts Two clocks for a radiation-belt electron, at Kp 2. Two times against drift shell L, on a logarithmic scale, for electrons of about 1 MeV. The first is how long radial diffusion takes to move an electron by one Earth radius, the inverse of an empirical diffusion coefficient that grows as the tenth power of L — at Kp 2, 550 years at L = 2, 10 years at L = 3, 21 days at L = 5. The second is how long the electron survives before it is scattered into the loss cone. Inside the plasmapause, here at L = 4.7, that is set by plasmaspheric hiss: years at L = 1.3, 14 days at L = 2.5, 5.2 days at L = 3; outside it a single lifetime of 30 days stands for every other loss. Inside L = 4.8 the electron is lost before diffusion can carry it further in, which is the shaded region; outside, diffusion wins and the belt is fed. The two curves cross at a single place, and that crossing is the inner edge of the outer belt.

The gap between the belts is a race between two clocks

Electrons reach the inner magnetosphere by diffusing inward from the outer edge, and they are lost there to waves that scatter them into the atmosphere. The diffusion slows as the tenth power of distance and the loss does not, so the two clocks cross at one sharp place. Inside it lies the slot, and at megaelectronvolt energies the inner electron belt is not a steady population at all but what the last great storm left behind.

spaceflight · Radiation belts

Named alongside it

The objects these essays reach for when they reach for this one.

Adiabatic invariantGeomagnetic stormLoss coneMagnetosphereRadiation beltsBremsstrahlungDrift shellMagnetic mirrorMagnetic momentPitch anglePlasmaspherePlasmaspheric hiss

All concepts