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Why do proton linear accelerators operate at lower frequencies than electron linear accelerators?

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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.

Proton linear accelerators operate at lower frequencies than electron linear accelerators primarily due to the significantly lower velocity of the heavier protons compared to electrons.1

Because electrons have a very small mass, they reach speeds close to the speed of light at relatively low energies (a few megaelectron volts). Once they reach these relativistic speeds, their velocity remains nearly constant, allowing them to travel along with an accelerating electromagnetic wave at microwave frequencies of about 3,000 MHz.234

In contrast, protons are much heavier and must be accelerated to significantly higher energies before their speeds approach the speed of light. Consequently, their velocity increases gradually throughout the accelerator. To maintain synchronism with the accelerating fields, proton linear accelerators must account for this prolonged increase in speed, typically operating at lower frequencies of approximately 200 MHz. This design often incorporates drift tubes or side-coupled-cavity structures to ensure particles experience the accelerating field while being shielded during decelerating intervals.124