This simulator integrates single charged particles through Earth's dipole magnetic field in the 2D meridian (r, z) plane, where the field components are Br = 3Mrz/R⁵ and Bz = M(3z²−R²)/R⁵. Each timestep splits the particle's velocity into a part parallel to the local field and two perpendicular parts (in-plane and out-of-plane), then rotates the perpendicular pair by the cyclotron angle Δθ = (q/m)|B|·dt before recombining them — a semi-implicit leapfrog rotation that reproduces gyration around field lines without a full 3D Boris push. Because |B| strengthens sharply toward the poles, the parallel motion decelerates, reverses and bounces the particle between mirror points; any particle whose equatorial pitch angle falls below the analytically computed loss-cone angle strikes the modelled atmosphere and is removed as lost.
Protons (inner belt, injected around L≈1.3–2.7 RE) and electrons (outer belt, L≈4–7 RE) spiralling, bouncing and drifting through Earth's dipole field in the r–z meridian plane, with optional field-line, belt-density and loss-cone overlays plus live trapped/lost particle counts.
Pick a species and set the injection L-shell, pitch angle, particle count and sim speed, then press Inject for a batch or Storm for a randomised burst spread across L 2–6. Toggle field lines, belt density and the loss cone on or off, and use Pause/Reset to freeze or restart the run.
The loss-cone angle here is computed the same way real magnetospheric physics does — from the ratio of the equatorial field strength to the field strength at the particle's atmospheric footpoint — which is why particles with steep, near-90° pitch angles stay trapped far longer than ones injected at shallow angles.
Every particle feels the Lorentz force through a dipole magnetic field with components Br = 3Mrz/R⁵ and Bz = M(3z²−R²)/R⁵ (r, z in Earth radii, dipole moment M normalised so the equatorial surface field equals 1). Each timestep the code splits the velocity into a component parallel to B and two perpendicular components (one in the r-z plane, one out of it), rotates the perpendicular pair by the cyclotron angle Δθ = (q/m)|B|·dt, then recombines them into new r,z velocities — a semi-implicit rotation scheme that reproduces gyration without needing the full 3D Boris algorithm.
For the current L-shell the code finds the magnetic latitude λf where a dipole field line reaches the top of the modelled atmosphere (1.03 RE), then evaluates the dipole field-strength formula B(L,λ) = (1/L³)·√(1+3sin²λ)/cos⁵λ at both the equator and λf. The loss-cone half-angle solves sin²(αlc) = Beq/Batm. Any particle whose equatorial pitch angle is smaller than αlc mirrors below the atmosphere; the simulation detects this the instant a particle's distance from Earth's centre drops under 1.03 RE and removes it as lost.
The code accumulates an azimuthal drift-rate estimate proportional to (vperp²+2vpar²)/(|ωc|·R) with a sign flip of −sign(q): for protons (q=+1) this comes out negative in the code's convention and is reported as eastward, while electrons (q=−1) get the opposite sign and are reported westward. This mirrors the real gradient and curvature drift that separates the inner proton belt from the outer electron belt — though in this 2D meridian-plane view the drift is only tracked as a running number for the stats panel, not rendered as actual azimuthal motion of the dot.
The inner belt (protons, injected around L≈1.3–2.7 RE) and outer belt (electrons, L≈4–7 RE) are simply two different default injection radii and speeds (normalised v = 0.018 for protons versus 0.045 for electrons, with proton mass 1 and electron mass 1/1836), overlaid with two soft radial-gradient bands — amber for the inner belt, blue for the outer — so the density visual matches where each species is seeded. It reflects the real Van Allen structure, where energetic protons dominate close to Earth and electrons dominate farther out, without modelling the source and loss processes that actually create that separation.
No — it's a 2D meridian-plane (r, z) approximation using normalised units rather than real SI velocities, masses or field strengths, and it tracks azimuthal drift only as an analytic rate for the stats panel rather than actually advancing particles out of the plane. It gets the essential physics right — dipole mirroring, gyration, the loss cone, and the correct sign of gradient-curvature drift — making it a solid qualitative teaching tool, but treat exact numbers like the bounce-period readout as illustrative rather than mission-planning-grade.