Lepton spin motion in a weak electromagnetic trap

Averaging methods are used to discuss the spin and orbital motion of charged leptons confined in a trap formed by perturbing a strong uniform magnetic field with a weak nonuniform magnetic or electric field. The principal result is an expression for the gyromagnetic difference frequency correct up to second order in the perturbing field. The motion is also discussed in the resonant case where the difference frequency is an integral multiple of the longitudinal oscillation frequency of the orbital motion. The two most recent precision measurements of the electron g-factor anomaly are reanalyzed, resulting in the removal of the apparent discrepancy between them and yielding a corrected value for the electron gyromagnetic anomaly: a = (1 159 656.7 +- 3.5) x 10-9