Single-Particle Motion: Drifts in E and B

A charged particle obeying $m\dot{\vec v}=q(\vec E+\vec v\times\vec B)$, integrated with the Boris pusher, a time-reversible leapfrog that conserves the speed exactly in a pure magnetic field. In a uniform $\vec B$ the orbit is a helix at the cyclotron frequency $\omega_c=|q|B/m$. Add a perpendicular $\vec E$ and the guiding centre drifts at $\vec v_d=\vec E\times\vec B/B^2$, the same for every charge and mass. A gradient or curvature of $\vec B$ gives the grad-B and curvature drifts; a converging field (a magnetic bottle) reflects the particle, conserving the adiabatic invariant $\mu=mv_\perp^2/2B$. The trail is the real 3D orbit drawn in an orthographic Canvas2D projection (deterministic and gate-robust; the 3D motion is honestly a projection, not a WebGL scene). The headline readouts are $|\vec v|$ (constant to $10^{-9}$ in pure $\vec B$) and $\mu$.