Van Allen Beltinator
3D Fokker-Planck Radiation Belt Explorer
Rendering
T+0.0h
Phase space density f evolves via diffusion in the three adiabatic invariants (J₁, J₂, J₃), corresponding to gyration, bounce, and azimuthal drift motion.
Separates radial diffusion (L*), momentum diffusion (p), and pitch-angle diffusion (y = sin α₀) with bounce-averaged coefficients. DL*L* is now time-dependent via Kp(t).
Dα₀p is the mixed energy–pitch angle diffusion coefficient. Cross-diffusion terms couple momentum and pitch-angle evolution.
Approximation for the normalized bounce period (Schulz & Lanzerotti 1974). Particles near the loss cone have T ≈ 1.38; those near 90° have T ≈ 0.74.
Radial diffusion coefficient parameterized by Kp index and L-shell. Higher Kp dramatically increases radial transport, driving inward diffusion and energization during storms. Kp is updated every 3 hours in this simulation.
Relativistic electrons (>500 keV) undergo three periodic motions: gyration (μ), bounce (J), and azimuthal drift (Φ = L*). ULF waves drive radial diffusion, chorus waves produce local acceleration, and magnetopause shadowing causes loss on the dayside.
What this means in layman's terms: High-energy particles get trapped by Earth's magnetic field and form two donut-shaped belts around the planet. These particles constantly spiral around magnetic field lines, bounce back and forth between the north and south poles, and slowly drift around the Earth. During magnetic storms, powerful waves can push particles deeper into the belts (making them more energetic and dangerous to satellites), while other processes can knock particles out of the belts entirely. It's a constant tug-of-war between forces that fill the belts and forces that drain them.
The local B-field determines energy from μ. Because electron spectra are steep, small ΔB errors produce large flux errors — especially at high L. At LEO, populations include Trapped, BLC, and DLC electrons requiring accurate magnetic mapping to classify.
What this means in layman's terms: Earth's magnetic field acts like an invisible container that holds these dangerous particles in place. The strength of the magnetic field at any location determines how energetic the particles are. Even small errors in measuring the magnetic field can lead to very wrong estimates of how many particles are present — this matters enormously for predicting radiation damage to satellites and astronauts. At low altitudes where spacecraft like the ISS orbit, some particles are stably trapped, while others are on their way to hitting the atmosphere.