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The Paul trap alternates focusing and defocusing electric forces. Their time average along a moving trajectory need not vanish, even when the electric field averages to zero at every fixed point. A spatial gradient makes the fast displacement correlate with the driving electric field; the RF-averaged trapping potential calculates the resulting restoring force.

Wolfgang Paul's lecture describes hyperbolic ring/endcap electrodes, loading by Electron-impact ionization of low-pressure gas, and resonant ejection through an endcap hole into an electron multiplier. Sweeping RF voltage produces an air mass spectrum.^[ref]