Van Allen belts: gradient and curvature drift on dipole L-shells, mirror latitude, equatorial loss cone α_lc(L); electrons west, protons east.
About this model
Earth’s radiation belts trap energetic charged particles on dipole magnetic field lines. In the adiabatic (guiding-center) picture, the first invariant μ = mv⊥²/(2B) is conserved, so a particle’s equatorial pitch angle α sets where it mirrors as B grows along the line. Particles with α below the equatorial loss cone α_lc strike the atmosphere and are lost; larger α are stably trapped on an L-shell (equatorial crossing radius r = L R_E in the dipole approximation). Superimposed on rapid gyration and bounce motion is a slow azimuthal drift from magnetic field gradients and line curvature: in a dipole, protons drift eastward and electrons westward around Earth. The teaching model uses a centered dipole B-field, equatorial drift speed v_d ∝ K L² (with relativistic γ at high energy), animated motion on a circular L-shell in the top view, a meridional slice showing the field line, mirror point, pitch angle, and loss-cone wedge, and a plot of α_lc versus L from footpoints at ~100 km altitude. It does not include wave diffusion, realistic magnetosphere asymmetry, or slot-region dynamics.
Who it's for: Space physics or upper-level E&M students after dipole fields and before ring-current or wave-particle interaction modules.
Key terms
Van Allen radiation belts
L-shell
Gradient drift
Curvature drift
Loss cone
Pitch angle
Magnetic mirror
How it works
Van Allen radiation belts: gradient and curvature drift on dipole L-shells, mirror points, and equatorial loss cone — electrons west, protons east.
Frequently asked questions
Why do electrons and protons drift opposite ways?
Gradient and curvature drifts depend on charge sign. In Earth’s dipole, protons drift east and electrons west around the planet.
What is the loss cone?
At the equator, particles with pitch angles below α_lc have mirror points below the atmosphere and precipitate; larger angles are trapped.
What is an L-shell?
In the dipole approximation, L is the equatorial crossing distance in Earth radii: r_eq = L R_E. Constant-μ drift orbits follow L-shells at low pitch angles.
What is omitted?
Offset dipole, local time asymmetry, radial diffusion, plasmasphere, and electromagnetic wave scattering are not modeled.