Weak focusing occurs in

particle accelerators A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...

when charged particles are passing through uniform magnetic fields, causing them to move in circular paths due to the

Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

. Because of the circular movement, the orbits of two particles with slightly different positions may approximate or even cross each other. Because a

particle beam A particle beam is a stream of charged or neutral particles. In particle accelerators, these particles can move with a velocity close to the speed of light. There is a difference between the creation and control of charged particle beams and neu ...

has a finite emittance, this effect was used in

cyclotron A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Janu ...

s and early

synchrotron A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...

s to prevent the growth of deviations from the desired particle orbit. Due to its definition, it also occurs in the

dipole magnet A dipole magnet is the simplest type of magnet. It has two poles, one north and one south. Its magnetic field lines form simple closed loops which emerge from the north pole, re-enter at the south pole, then pass through the body of the magnet. T ...

s of modern accelerator facilities and must be considered in beam optics calculations. In modern facilities, most of the beam focusing is usually done by

quadrupole magnet Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. ...

s, using

Strong focusing In accelerator physics strong focusing or alternating-gradient focusing is the principle that, using sets of multiple electromagnets, it is possible to make a particle beam simultaneously converge in both directions perpendicular to the direction ...

to enable smaller beam sizes and vacuum chambers, thus reducing the average magnet size.

References

Accelerator physics {{accelerator-stub