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How does alternating-gradient focusing make high-energy synchrotrons smaller and more practical?

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Diagram of a linear proton resonance accelerator, or linac, showing protons entering from a source, passing through a series of labeled drift tubes powered by a radio-frequency source, and exiting as a beam through a cavity. — particle accelerator The accelerator is a large-diameter tube within which an electric field oscillates at a high radio frequency. Within the accelerator tube are smaller diameter metallic drift tubes, which are carefully sized and spaced to shield the protons from decelerating oscillations of the electric field. In the spaces between the drift tubes, the electric field is oriented properly to accelerate the protons in their direction of travel.

Alternating-gradient focusing—also known as strong focusing—revolutionized synchrotron design by allowing for significantly smaller and more practical high-energy machines.1

In early synchrotrons, "weak focusing" required magnets with large gaps to maintain the particle beam, leading to massive, expensive magnet rings as energy requirements increased. Alternating-gradient focusing solves this by using a series of magnets with alternating pole-tip shapes. One type of magnet focuses the beam in the vertical direction while defocusing it radially, while the next magnet in the sequence does the opposite. By pairing these effects, the overall system provides strong, stable focusing in both directions.2

This technique allows the beam to be confined within a vacuum chamber of much smaller cross-section, meaning the magnets required are only about 1/100th the size of those needed for weak-focusing designs. Consequently, this development enabled the construction of much higher-energy synchrotrons without the prohibitive costs associated with building massive magnet rings.21