Particle dynamics

Reviewartikel, 2026

This article provides an introduction to kinetic plasma physics through the theory of charged particle motion in prescribed, inhomogeneous, and time-dependent electromagnetic fields. Starting from the exact solution in uniform, static fields, we identify the fundamental spatial and temporal scales of magnetized motion—the Larmor radius and cyclotron frequency—which enable systematic expansions when the electromagnetic fields vary slowly compared with these intrinsic scales. Under this drift (adiabatic) ordering, particle dynamics separates into rapid gyromotion and slower guiding-centre motion. We derive the guiding-centre equations by progressively incorporating spatial and temporal field variations and examine the emergence of adiabatic invariants, including conservation of the magnetic moment and higher-order corrections obtained perturbatively. Applications to tokamak geometry illustrate the implications for magnetic confinement. Finally, we briefly discuss extensions beyond the ideal collisionless picture, including Debye shielding, radiation reaction, and the effects of collisions and turbulence.