To achieve ion confinement in a Paul trap, an oscillating electric potential
difference, 
, is applied in place of or in addition to a static potential, 
:
The resultant Paul trap potential alternates between: (1) a focusing potential well in the axial direction with a defocusing inverted radial potential; and
(2) a focusing potential well in the radial direction with a defocusing axial potential. By focusing particles in one direction and then in the other, the dynamic Paul trap potential creates a stable equilibrium whereas the static quadrupole potential was capable of only unstable equilibrium.