In particle accelerators, quadrupole magnets are used to focus beams
of charged particles.
They are designed to create magnetic fields whose
magnitude grows linearly with the radial distance from its longitudinal axis,
which is usually centered around and parallel to the main motion of
the charged particles. The net result of these fields is a focusing force
in one plane and a defocusing one in the plane perpendicular to it.
Several quadrupole magnets can be arranged in sequence such that they create
a net focusing effect in both planes.