Electron Spin Motion in a Magnetic Mirror Trap

Averaging methods are used to discuss the electron spin motion in a magnetic mirror trap of the sort used in precision $g-2\mathrm{}$ experiments. An expression is obtained for the difference frequency correct up to second order in the field nonuniformity. When applied to the experiments this result removes the discrepancy between the last two precision $g-2\mathrm{}$ measurements and yields a corrected value for the gyromagnetic anomaly: $a=(1\mathrm{}159656.7\pm 3.5)\times {10}^{-9\mathrm{}}$.