Figure: Radial and axial positions of 32 Paul-trapped particles--- ( left): Radial projection of positively charged aluminum particles experimentally observed by Wuerker, et al. ( center, right): Computer simulation of 32 Mg
ions, showing ( center) instantaneous radial (XY) and (
right) axial (XZ) positions. source file: paul32cr.trp.
In 1959, R.F. Wuerker, H. Shelton, and R.V. Langmuir used the theory of ``alternating gradient focusing'' and the ``strong focusing principle'' to confine electrically charged particles in a quadrupole trap to which oscillating and static electric potentials were applied. Charged aluminum particles with dimensions of about 
m were observed to form a crystalline array or a radially-concentric crystalline structure
which melted and reformed as a function of the applied potentials and vacuum pressure of the electromagnetic trap.[39]
Table: Experimental parameters for the 1959 work of Weurker, Shelton, and Langmuir.
Since the pioneering experiments of Wuerker, et al., electromagnetic traps have been used to confine thousands of ions as well as single atoms and even single elementary particles.