&Bullet; physics 14, 53
In order to accurately measure the magnetic moment of the muon, the physicists first had to precisely measure the field of the 680-tonne magnet that guides the muons.
The basic idea of the muon
An experiment at the Fermi National Accelerator Laboratory (Fermilab), Illinois, is to detect the wobble of microscopic magnets that move around a 15-meter-wide ring-shaped magnet. The tiny magnets are elementary particles called muons, and the wobbles show the magnetic strength or moment of the muons. The results reported today do not match the predictions of the Standard Model, which makes the muon the talk of the town (see Viewpoint: Muon’s Escalating Challenge to the Standard Model). There is one less discussed aspect of this development, however, and that is the giant magnet that corrodes the muons. The muon
Scientists constantly monitor this 1.45 Tesla magnet using hundreds of nuclear magnetic resonance (NMR) sensors, some of which ride on a small cart that rolls around the experiment. The effort has helped reduce the field measurement uncertainties to 114 parts per billion – an almost two-fold improvement over the previous muon experiment, which first observed the magnetic moment discrepancy.
This experiment, conducted at Brookhaven National Laboratory in New York, used the same giant magnet as Muon
used today. The magnet was shipped 3,200 miles from Brookhaven to Fermilab in 2013. The main components of the magnet are a combination of iron chunks and superconducting coils that create a vertical field within the muon storage ring – a 45 m long circular path that is located in the metal of the magnet structure. The field directs the muons along a circular path, while their magnetic moments wobble or move at the same time. To get the magnetic moment of the muon, the muon
The collaboration divides the frequency of this precession by the strength of the magnetic field. “The spin precession frequency is the better known part of the experiment,” says Peter Winter of Argonne National Laboratory, Illinois. “But measuring the magnetic field is just as important.”
Winter and his colleagues have developed sophisticated protocols for measuring the magnetic field, which they quantify not using the Tesla, but using the precession frequency of a proton exposed to the same field while sitting in the center of a water sample
. “It’s a mouthful,” admits David Kawall of the University of Massachusetts, Amherst. However, this proton-in-water frequency is a frequently used standard in NMR measurements. Kawall compares it to the metal cylinder in Paris, which until recently was the kilogram standard. “We know how to measure what our probes measure and how to interpret them using this NMR standard,” says Kawall.
One of the complications of measuring the giant magnet’s field is that it varies in both space and time due to structural inhomogeneities and temperature fluctuations. “If the storage ring were completely homogeneous, you could just insert a probe, measure the field, and that’s it,” says Kawall. The spatial variations around the ring are on the order of 14 to 17 ppm – which isn’t terrible for a giant iron magnet, he says. In fact, the deviations are three times smaller than in the Brookhaven experiment, which is partly due to a careful “shimming” process in which 8,000 hand-cut strips of iron foil were glued onto the magnetic structure in 2016. The strips of film have evened out the field – like a sheet of paper placed under the legs of a wobbly table. “These little pieces can change the magnetic field significantly,” says David Flay of the Jefferson Lab in Virginia.
Despite all the adjustments made to the magnet, the researchers need a detailed map of the field. To do this, they installed a number of 378 NMR probes around the magnetic ring. These solid probes can provide continuous readings of the field, but they are located a few inches from the muon beam. To measure the actual field experienced by the muons, Winter and his colleagues placed 17 NMR probes in a 50 cm long car. Every three days – when the muon beam is switched off – the cylindrical carriage is pulled out of a small garage and pulled around the beam path with a cable set. Although it does not carry passengers, the car has a full itinerary with 9,000 “destinations” where field measurements are recorded. “The car can map the field at finer intervals than the fixed probes, which means that we can better measure the field distribution in which the muons move.” Winter says. The car hits at a speed of about 1 cm / s and takes about an hour to complete a one-way trip over the 45 m circumference.
The probes in the cart and the fixed probes are 10 cm long cylinders filled with a swab of Vaseline. Protons in the jelly are precessioned by the application of a radio pulse, and this precession is recorded to determine the magnetic field around the probe. “We use Vaseline because the proton precession recovery time is faster than in water, so we can measure the field every 1.4 seconds,” explains Flay. To convert the proton-in-jelly frequency measurement to the standard proton-in-water frequency, Flay and Kawall developed a water-based NMR probe that they station at a single stop along the carriageway. During the calibration process, the car moves in, takes a measurement at a precisely defined position, and then moves out. Then the calibration probe performs exactly the same maneuvers and the readings are compared. This “hokey pokey dance” is repeated for six hours in order to obtain a reliable conversion factor for each probe in the car.
“I think the magnetic field measurement is sometimes underestimated in this experiment because you might think that only one sensor has to be placed somewhere,” says Winter. “In reality it is a long chain of complex measurements.” The researchers are continuing to work on reducing the measurement uncertainties with the aim of achieving an accuracy of 70 parts per billion for the magnetic field and 140 parts per billion for the muon magnetic moment. The experiment is a rich mix of high energy physics, atomic physics, and beam dynamics, says Kawall, who worked on the Brookhaven experiment before joining the Fermilab project. “It’s so interesting that you could spend a career working on it to understand it,” he says.
Michael Schirber is the corresponding editor for physics based in Lyon, France.