Meridian plane (r, z) — real dipole + RK4 Lorentz force
This is the 2D companion to the 3D Van Allen Belts simulator. It follows a single charged particle through Earth's real dipole magnetic field, integrated with classic 4th-order Runge-Kutta on the full Lorentz-force equation of motion F = q(v × B) in three dimensions, then projects the trajectory onto the meridian (r, z) cross-section for display. Because the underlying integration is genuinely 3D, the projected curve shows real gyration (the tight coiling around the field line), real magnetic-mirror bounce (the particle decelerating, reversing and bouncing between northern and southern mirror points as |B| strengthens toward the poles), and — through the analytic L-shell and altitude readout — the same physics that traps real protons and electrons in the Van Allen belts.
Adjust the particle's energy, initial pitch angle and charge sign, then launch it (or click/tap anywhere in the field) to watch it spiral and bounce. Particles whose pitch angle is too small mirror below the modelled atmosphere (1.03 RE) and are lost; particles launched with too much energy or too shallow a field-aligned component can also escape outward.