Weak focusing

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A particle bunch with position variance gets focused in a magnetic field. In reality, the beam will not get focused to a point, but keeps a finite spot size due to divergence. Weak focusing dipole sketch.svg
A particle bunch with position variance gets focused in a magnetic field. In reality, the beam will not get focused to a point, but keeps a finite spot size due to divergence.

Weak focusing occurs in particle accelerators when charged particles are passing through uniform magnetic fields, causing them to move in circular paths due to the Lorentz force. 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 has a finite emittance, this effect was used in cyclotrons and early synchrotrons to prevent the growth of deviations from the desired particle orbit. Due to its definition, it also occurs in the dipole magnets 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 magnets, using Strong focusing to enable smaller beam sizes and vacuum chambers, thus reducing the average magnet size.

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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. A cyclotron accelerates charged particles outwards from the center of a flat cylindrical vacuum chamber along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying electric field. Lawrence was awarded the 1939 Nobel Prize in Physics for this invention.

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Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields.

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Betatron

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The Future Circular Collider (FCC) is a proposed post-LHC particle accelerator with an energy significantly above that of previous circular colliders. The FCC project examines scenarios for three different types of particle collisions: hadron collisions in a collider design known as FCC-hh, electron–positron collisions in a collider design known as FCC-ee, and proton–electron collisions in a collider design known as FCC-eh.

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