Van Allen Belts: Magnetic Mirroring, Pitch Angle & the Loss Cone

Spiralling along field lines

A charged particle moving through a magnetic field feels the Lorentz force, which curves its path into a helix that spirals around a field line rather than crossing it. Earth's magnetic field is approximately dipolar — about 80% of it can be described as a tilted dipole (roughly 11° from the rotation axis) generated by the geodynamo in the liquid outer core, with a dipole moment of about 8×10²² A·m² and a surface field strength ranging from roughly 25–65 μT depending on location. Because dipole field lines arc from pole to pole, trapped particles get carried toward each pole in turn rather than escaping outward — the basic geometry that creates the Van Allen radiation belts: an inner belt (roughly 1–2 Earth radii, mostly protons from cosmic-ray interactions) and an outer belt (roughly 3–9 Earth radii, mostly electrons from the solar wind), part of the larger magnetosphere that shields Earth from the solar wind.

Magnetic mirroring: bouncing between hemispheres

As a particle spirals toward a pole, it moves into a region of stronger field — and because its magnetic moment is conserved, its perpendicular velocity grows while its parallel (along-the-field) velocity shrinks. If the field becomes strong enough before the particle actually reaches the pole, the parallel velocity hits zero, reverses, and the particle is "mirrored" back toward the opposite hemisphere. This is magnetic mirroring, and it's what lets particles bounce back and forth between the northern and southern hemispheres for days, weeks or longer, drifting slowly around the planet all the while.

Pitch angle and the loss cone

Whether a particle mirrors safely or is lost depends on its pitch angle — the angle between its velocity vector and the local field line. Particles with a large pitch angle (moving mostly perpendicular to the field) mirror high in the magnetosphere, well above the dense atmosphere, and bounce indefinitely. Particles with too small a pitch angle mirror at an altitude that's already deep inside the upper atmosphere, so they collide with air molecules before they can bounce back and are lost — precipitated out of the belt. The range of pitch angles that leads to this fate is the loss cone, and every field line has one.

Why this matters for astronauts and satellites

The Van Allen belts are intensely hazardous to unshielded spacecraft electronics and astronauts, especially during geomagnetic storms driven by coronal mass ejections, when trapped-particle populations spike. Satellites in low-Earth orbit that pass through the South Atlantic Anomaly — a region where the field is anomalously weak, allowing the inner belt to dip unusually close to the surface — must specifically shield their electronics against elevated radiation exposure during each pass.

Frequently asked questions

Try it live

Everything above runs in your browser — open Van Allen Belts, choose a particle species and pitch angle, and watch protons and electrons spiral, mirror near the poles, drift around the planet, and — if their pitch angle is too small — fall into the loss cone. Nothing is installed, nothing is uploaded.