Charged-particle dynamics · Magnetic traps

Magnetic-mirror particle traps & charged-particle dynamics

A magnet system is ultimately judged by what it does to a charged particle. I trace electron dynamics in magnetic-lens systems with an in-house particle-tracing code (a volume-preserving Boris pusher in the ideal thin-loop Biot–Savart field of the coils), applied here to the magnetic-mirror trap (“magnetic bottle”), a basic building block of plasma confinement and magnetic electron optics.

Watch the magnetic-mirror trap animation →

The physics

In the non-relativistic adiabatic limit, the electron’s rapid gyration makes its magnetic moment μ = mv_⊥²/2B an adiabatic invariant: as B grows toward a coil, v_⊥ must grow with it and, since the magnetic force does no work, v_∥ is exhausted. Reflection occurs where B = B₀/sin²θ₀ (θ₀ is the mid-plane pitch angle); particles inside the loss cone, sin²θ_lc = 1/R, here θ_lc ≈ 43°, escape through the mirror throat. The orbit shown is deliberately fat to keep the gyration visible, so μ wanders by ~10%; at a gyroradius of 0.05a it tightens to ~1.5%.

The model

The ideal thin-loop coil field is evaluated from complete-elliptic-integral expressions, avoiding interpolation from a sampled field map. Trajectories are advanced with the Boris algorithm, the volume-preserving pusher of particle-in-cell plasma codes; in a static magnetic field it conserves kinetic energy to machine precision (~10⁻¹⁴ here). The same pusher runs on COMSOL-computed or measured field maps, and live in the browser below.

Interactive simulation: fly the trap yourself

The same Boris pusher and two-coil field, integrated live in the browser (WebGL). Push the pitch angle below the loss cone (≈43°) and the electron escapes.

Gyration, mirror reflection where v_∥ → 0, and a live readout of the (approximately conserved) invariant μ. If WebGL is unavailable, the animations above show the same physics.

From model to hardware

The same Lorentz-force integration underpins the compact IFEL accelerator work and connects to the applied-magnetism projects: the fields being designed are the fields particles must fly through. Mirror-type magnetic lenses are building blocks of electron sources, beam-transport lines, and plasma-confinement devices.

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