Resonance and Resonant Cavities

What is Resonance?

Resonance is a very common phenomenon which occurs in many types of physical systems. A familiar example is pushing a child on a swing. You can make the swing go higher and higher with relatively little effort if you time your push just right. The swing has a natural frequency of vibration and pushing "just right" means you are putting energy into it at a frequency known as the fundamental frequency. The system is said to be in resonance and the amplitude of the motion increases rapidly.

Probably the most dramatic example of resonance caught on film is the Tacoma Narrows Bridge collapse in 1940.

This photograph shows the twisting motion of the center span
of the Tacoma Narrows bridge just prior to failure in 1940.

Shape and Resonant Behavior

Musical instruments also operate on the principle of resonance. Just as the length of an organ pipe helps determine the musical tone at which it resonates, so the shape and size of a microwave cavity determines the frequency and mode for which it resonates. All the many cavities in the accelerator structure must resonate at the same frequency. This requires good temperature control since the metal cavities expand as they warm up.

Cavity Contortions -- Getting Rid of Unwanted Modes

Many frequencies or modes of vibration, other than the fundamental, may be present at the same time. In a musical instrument these modes are known as overtones. The design of any instrument is chosen to give it the desired "voice" by controlling which overtone modes are strong resonance's and which are quickly damped out.

In an accelerating cavity, additional resonant modes can reduce operating efficiency and disturb the desired beam motion. Just as an instrument can be designed for a desired "voice" so the cavity can be designed by adding features to its shape that reduce the response for the undesired modes. Vibrations of the beam itself will induce many modes in the cavity. In a modern storage ring, the accelerating cavities are placed at intervals around the ring and are designed to make such modes die out very quickly so they don't disturb the later bunches coming through.

The cavities pictured above are designed for the high energy storage ring of the PEP-II B Factory project. All the odd grooves that make this cavity look like a Mayan pot are added to connect extrusions that help remove unwanted electromagnetic field pattern vibrations.