Geonium theory: Physics of a single electron or ion in a Penning trap

TLDR: In this paper, the theory of a single charged particle in a Penning trap is reviewed, beginning with simple first-order orbits and progressively dealing with small corrections which must be considered owing to the experimental precision that is being achieved.

Abstract: A single charged particle in a Penning trap is a bound system that rivals the hydrogen atom in its simplicity and provides similar opportunities to calculate and measure physical quantities at very high precision. We review the theory of this bound system, beginning with the simple first-order orbits and progressively dealing with small corrections which must be considered owing to the experimental precision that is being achieved. Much of the discussion will also be useful for experiments with more particles in the trap, and several of the mathematical techniques have a wider applicability.