There are many types of accelerator designs, although all have certain features in common. Only charged particles (most commonly protons and electrons, and their antiparticles; less often deuterons, alpha particles, and heavy ions) can be artificially accelerated; therefore, the first stage of any accelerator is an ion source to produce the charged particles from a neutral gas. All accelerators use electric fields (steady, alternating, or induced) to speed up particles; most use magnetic fields to contain and focus the beam. Meson factories (the largest of which is at the Los Alamos, N.Mex., Scientific Laboratory), so called because of their copious pion production by high-current proton beams, operate at conventional energies but produce much more intense beams than previous accelerators; this makes it possible to repeat early experiments much more accurately. In linear accelerators the particle path is a straight line; in other machines, of which the cyclotron is the prototype, a magnetic field is used to bend the particles in a circular or spiral path.

The early linear accelerators used high voltage to produce high-energy particles; a large static electric charge was built up, which produced an electric field along the length of an evacuated tube, and the particles acquired energy as they moved through the electric field. The Cockcroft-Walton accelerator produced high voltage by charging a bank of capacitors in parallel and then connecting them in series, thereby adding up their separate voltages. The Van de Graaff accelerator achieved high voltage by using a continuously recharged moving belt to deliver charge to a high-voltage terminal consisting of a hollow metal sphere. Today these two electrostatic machines are used in low-energy studies of nuclear structure and in the injection of particles into larger, more powerful machines. Linear accelerators can be used to produce higher energies, but this requires increasing their length.

Linear accelerators, in which there is very little radiation loss, are the most powerful and efficient electron accelerators; the largest of these, the Stanford linear accelerator (SLAC), completed in 1957, is 2 mi (3.2 km) long and produces 20-GeV—in particle physics energies are commonly measured in millions (MeV) or billions (GeV) of electron-volts (eV)—electrons. SLAC is now used, however, not for particle physics but to produce a powerful X-ray laser. Modern linear machines differ from earlier electrostatic machines in that they use electric fields alternating at radio frequencies to accelerate the particles, instead of using high voltage. The acceleration tube has segments that are charged alternately positive and negative. When a group of particles passes through the tube, it is repelled by the segment it has left and is attracted by the segment it is approaching. Thus the final energy is attained by a series of pushes and pulls. Recently, linear accelerators have been used to accelerate heavy ions such as carbon, neon, and nitrogen.

In order to reach high energy without the prohibitively long paths required of linear accelerators, E. O. Lawrence proposed (1932) that particles could be accelerated to high energies in a small space by making them travel in a circular or nearly circular path. In the cyclotron, which he invented, a cylindrical magnet bends the particle trajectories into a circular path whose radius depends on the mass of the particles, their velocity, and the strength of the magnetic field. The particles are accelerated within a hollow, circular, metal box that is split in half to form two sections, each in the shape of the capital letter D. A radio-frequency electric field is impressed across the gap between the D's so that every time a particle crosses the gap, the polarity of the D's is reversed and the particle gets an accelerating "kick." The key to the simplicity of the cyclotron is that the period of revolution of a particle remains the same as the radius of the path increases because of the increase in velocity. Thus, the alternating electric field stays in step with the particles as they spiral outward from the center of the cyclotron to its circumference. However, according to the theory of relativity the mass of a particle increases as its velocity approaches the speed of light; hence, very energetic, high-velocity particles will have greater mass and thus less acceleration, with the result that they will not remain in step with the field. For protons, the maximum energy attainable with an ordinary cyclotron is about 10 million electron-volts.

Two approaches exist for exceeding the relativistic limit for cyclotrons. In the synchrocyclotron, the frequency of the accelerating electric field steadily decreases to match the decreasing angular velocity of the protons. In the isochronous cyclotron, the magnet is constructed so the magnetic field is stronger near the circumference than at the center, thus compensating for the mass increase and maintaining a constant frequency of revolution. The first synchrocyclotron, built at the Univ. of California at Berkeley in 1946, reached energies high enough to create pions, thus inaugurating the laboratory study of the meson family of elementary particles.

Further progress in physics required energies in the GeV range, which led to the development of the synchrotron. In this device, a ring of magnets surrounds a doughnut-shaped vacuum tank. The magnetic field rises in step with the proton velocities, thus keeping them moving in a circle of nearly constant radius, instead of the widening spiral of the cyclotron. The entire center section of the magnet is eliminated, making it possible to build rings with diameters measured in miles. Particles must be injected into a synchrotron from another accelerator. The first proton synchrotron was the cosmotron at Brookhaven (N.Y.) National Laboratory, which began operation in 1952 and eventually attained an energy of 3 GeV. The 6.2-GeV synchrotron (the bevatron) at the Lawrence Berkeley National Laboratory was used to discover the antiproton (see antiparticle).

The 500-GeV synchrotron at the Fermi National Accelerator Laboratory at Batavia, Ill., was built to be the most powerful accelerator in the world in the early 1970s, with a ring circumference of approximately 4 mi (6 km). The machine was upgraded (1983) to accelerate protons and counterpropagating antiprotons to such enormous speeds that the ensuing impacts delivered energies of up to 2 trillion electron-volts (TeV)—hence the ring was been dubbed the Tevatron. The Tevatron was an example of a so-called colliding-beams machine, which is really a double accelerator that causes two separate beams to collide, either head-on or at a grazing angle. Because of relativistic effects, producing the same reactions with a conventional accelerator would require a single beam hitting a stationary target with much more than twice the energy of either of the colliding beams.

Plans were made to build a huge accelerator in Waxahachie, Tex. Called the Superconducting Supercollider (SSC), a ring 54 mi (87 km) in circumference lined with superconducting magnets (see superconductivity) was intended to produce 40 TeV particle collisions. The program was ended in 1993, however, when government funding was stopped.

In Nov., 2009, the Large Hadron Collider (LHC), a synchroton constructed by CERN, became operational, and in Mar., 2010, it accelerated protons to 3.5 TeV to produce collisions of 7 TeV, a new record. The LHC's main ring, which uses superconducting magnets, is housed in a circular tunnel some 17 mi (27 km) long on the French-Swiss border; the tunnel was originally constructed for the Large Electron Positron Collider, which operated from 1989 to 2000. Designed to produce collisions involving protons that have been accelerated to 7 TeV (and collisions of lead nuclei at lower energies), the LHC will not reach its full potential until after improvements are made. The LHC will be used to prove (or disprove) the existence of the Higgs boson and investigate quarks, gluons, and other particles and aspects of physics' Standard Model (see elementary particles).

The synchrotron can be used to accelerate electrons but is inefficient. An electron moves much faster than a proton of the same energy and hence loses much more energy in synchrotron radiation. A circular machine used to accelerate electrons is the betatron, invented by Donald Kerst in 1939. Electrons are injected into a doughnut-shaped vacuum chamber that surrounds a magnetic field. The magnetic field is steadily increased, inducing a tangential electric field that accelerates the electrons (see induction).