A quadrupole magnet is a type of magnet used primarily in particle accelerators and beamlines for focusing charged particle beams. It generates a magnetic field with a specific spatial variation that can focus or defocus charged particles in two transverse directions, allowing for tighter control of the beam's shape and trajectory.
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A magnet whose transverse field varies linearly with displacement. Its Lorentz force focuses a charged-particle beam in one transverse plane and defocuses it in the other. Oppositely oriented elements provide alternating-gradient focusing.