Magnetic Bottle
A charged particle spirals along converging magnetic field lines. As the field strengthens, the particle's pitch angle steepens until it reflects at the mirror point — the principle behind magnetic confinement in plasma physics and the Van Allen radiation belts.
About this lab
Magnetic mirroring is a fundamental phenomenon in plasma physics. When a charged particle moves along a magnetic field line into a region of increasing field strength, the component of its velocity perpendicular to the field increases (to conserve the magnetic moment, an adiabatic invariant), while the parallel component decreases. If the field becomes strong enough, the parallel velocity drops to zero and the particle reverses direction — it is "mirrored."
A magnetic bottle uses two converging field regions (mirrors) at either end to trap charged particles between them. The critical parameter is the mirror ratio R = B_max / B_min. A particle with initial pitch angle alpha (the angle between its velocity and the field direction) will be trapped if sin\u00b2(alpha) > 1/R. Particles with smaller pitch angles — those traveling nearly parallel to the field — escape through the "loss cone." This is the same mechanism that traps charged particles in Earth's Van Allen radiation belts, where the converging field near the poles acts as a natural magnetic bottle.
In this simulation, the particle's guiding-center motion is computed from the conservation of the first adiabatic invariant (magnetic moment mu = mv_perp\u00b2 / 2B). The field geometry is a simple axisymmetric bottle with a smooth B(z) profile increasing toward both ends. You can adjust the initial pitch angle to see whether the particle mirrors or escapes through the loss cone, and change the mirror ratio to alter the trapping threshold.