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Four bar magnets configured to produce a quadrupole.

Quadrupole magnets are designed to create a magnetic field whose magnitude grows linearly with the radial distance from its longitudinal axis, which is usually centered on 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.

In a quadrupole electromagnet there are four steel pole tips: two opposing magnetic north poles and two opposing magnetic south poles. The steel is magnetized by a large electric current that flows in the coils of tubing wrapped around the poles.

In a particle accelerator, the various magnets required to bend, steer and correct the particle beam make up 'the lattice'. The quadrupoles in the lattice are of two types: 'F quadrupoles' (which are horizontally focusing but vertically defocusing) and 'D quadrupoles' (which are vertically focusing but horizontally defocusing). This situation is due to the laws of electromagnetism (the Maxwell equations) which show that it is impossible for a quadrupole to focus in both planes at the same time.

If an F quadrupole and a D quadrupole are placed immediately next to each other, their fields completely cancel out. But if there is a space between them (and the length of this has been correctly chosen), the overall effect is focusing in both horizontal and vertical planes. A lattice can then be built up enabling the transport of the beam over long distances - for example round an entire ring. A common lattice is a FODO lattice consisting of a basis of a Focusing quadrupole, 'nothing' (often a bending magnet), a Defocusing quadrupole and another length of 'nothing'.

• Particle accelerator
• Linear particle accelerator
• Electron optics

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