Reference

Particles acceleration: Electric field • Particles can be accelerated by an electric field: f=qE • Electrostatic accelerators use this principle. • One of the most common type of electrostatic accelerator is called "Van de Graaff" accelerator. • Tandem accelerators are a modified type of electrostatic accelerators where the charge is

Particles see voltage In case of no acceleration, synchronous particle has ϕs = 0 Particles arriving early see ϕ< ϕs Particles arriving late see ϕ> ϕs energy of those in advance is decreased relative to the synchronous particle and vice versa. To accelerate, make 0 < ϕs< π so that synchronous particle gains energy V0 sin 2πω rf t =V0 ...

Lawrence’s student M.S. Livingston demonstrated the principle of the cyclotron in 1931, producing 80-keV ions; in 1932 Lawrence and Livingston announced the acceleration of protons to more than 1 MeV. Later in the 1930s, cyclotron energies reached about 25 MeV and Van de Graaff generators about 4 MeV. In 1940 Donald W. Kerst, applying the results of careful orbit calculations to the design of magnets, constructed the first betatron, a magnetic-induction accelerator of electrons, at the University of Illinois. The progress in research made possible by raising the energies of protons led to the building of successively larger accelerators; the trend was ended only by the cost of fabricating the huge magnet rings required—the largest weighs approximately 40,000 tons. The difference in electric potential between the position where the electron begins moving through the field and the place where it leaves the field determines the energy that the electron acquires. In the simplest case a charged particle moving in a direction at right angles to the direction of a uniform magnetic field feels a force at right angles both to the particle’s direction and to the field. The key with a particle accelerator is to set up the wave so that, when the particles arrive, the electric field is in the direction needed to accelerate the particles.