For years, accelerator physicists have been working to make sense of a seemingly random rattling of the ground that affects the alignment of their equipment. Now one physicist has taken the most comprehensive look yet at such data from Europe, Japan, and the United States, and reports his results in the 11 June *Physical Review Letters*. The ground’s haphazard jiggling, he says, conforms to a simple mathematical description that was proposed decades ago. Understanding this ground motion may prove useful in the design of future particle accelerators likely to dwarf those in use today.

Accelerator physicists obsess over the stability of the ground, as it is crucial for the proper functioning of their machines. For example, staff at the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois, use a variety of devices to watch for subtle shifts in the position of their Volkswagen-sized magnets that guide particles. One technique uses a horizontal pipe half-filled with water that stretches around much of the Fermilab ring. Sensors measure micron-scale changes in the depth of the water that reflect tiny changes in elevation.

Accelerator facilities accommodate and correct for all sorts of ground motion, including that produced by seismic activity, the pull of the moon’s gravity, and changing air pressure due to weather. But there is also a random component of the motion that Vladimir Shiltsev of Fermilab has shown follows a simple equation, $<{\text{(\Delta Y)}}_{2}>$ = *ATL*. That is, over time *T*, the square of the change in distance *Y* between two points that are initially a distance *L* apart is *ATL*, where *A* is a number that depends on the local geology.

This equation is similar to one that describes the so-called random walk, the simplest mathematical description of random diffusion of molecules, and it appears in many areas of physics. But the so-called ATL law includes an extra factor of *L*–as the distance between two points increases, so does the rate of displacement between them. The precise reason for this random motion seen across time and distance is a mystery, though Shiltsev says it might result from the “fractal” nature of the ground, as reported by geoscientists. If the ground is essentially a collection of blocks that vary over a wide range of sizes, and they all jiggle at random, that might produce the ATL law, Shiltsev speculates.

Shiltsev previously showed that the law explains ground motion at Fermilab, but he has now spent years looking through much more data from around the world and from various of sources, such as beam position monitors and laser trackers. Shiltsev compiled records collected over two decades from 15 accelerator facilities [1]. He fully confirmed the ATL law and overall found that a 30-meter stretch of ground moves at random about a hundred nanometers in any direction each minute. Or in more human terms, if a soccer field was level 30 years ago, today it might be a millimeter higher at one end than the other.

That’s small enough to be largely ignored at current accelerator facilities, but it might be significant if future accelerators such as the International Linear Collider (ILC) are built. These colliders may stretch 30 kilometers or more and focus their particle beams to just a few nanometers across.

The analysis is probably the most exhaustive ever done and “fits to a number of observations taken at various laboratories for years,” says Katsunobu Oide, of the KEK laboratory in Tsukuba, Japan. “The formula is simple and easily applicable anywhere.”

### References

- Vladimir Shiltsev, “Space-Time Diffusion of Ground and Its Fractal Nature,” arXiv:0905.4194v1 (2009).