As a member of the ATLAS Collaboration, doctoral students are generally required to perform a Qualification Task (QT), which is a year-long project dedicated to the overall operations, maintenance, or future success of the experiment, which is rewarded by receiving authorship status upon completion. This is the collaboration's way of managing the politics of academic authorship in an experiment shared by over 5,000 collaborators which publishes hundreds of papers each year.
My own QT focused on mapping the toroidal magnetic fields used for the ATLAS Muon Spectrometer, which I completed in the second year of my PhD. This page presents an overview of the details associated with my project, aimed at an audience with less exposure to collider experiments.
Rather than detail the specific results from my project which are largely internal, this page presents an overview of the general purpose and design behind ATLAS' magnetic fields, their role in experiments, and the associated challenges for this goal addressed by my QT.
In collider physics, one of the most important observables for event reconstruction is the momenta of particles produced in our collisions. Combining these momentum measurements with energy deposits and spatial information from other detector components helps us develop a full kinematic picture of our collision, enabling us to perform the precision measurements which drive particle physics forward.
In most modern detectors, this momentum information is obtained for charged particles by exploiting the fact that they arc when traveling through a magnetic field. By placing our particle detector components within a strong magnetic field, we can derive the momentum of charged particles as a function of the field strength and the radius of curvature (specifically a quantity known as the sagitta).
Implementing this method in practice is met with increasing levels of engineering complexity due to non-ideal components, with the primary challenges being:
1. Creating uniform magnetic fields is difficult in small spaces and nearly impossible across large volumes.
2. In the absence of uniform fields, we need precise knowledge of our field's strength and direction for each point in space. In other words, we need a "map" of our magnetic field at all regions in space we might want to reconstruct tracks.
This first difficulty is a notable concern for the 22,000 m³ ATLAS detector. Instead of relying on a single magnetic field source, ATLAS uses a central solenoid as well as three different toroidal magnets, one in the central region of the detector (known as the barrel) and one in each of the end caps of the detector.
Schematic of the ATLAS magnetic field sources (shown in orange), including the toroidal coils and inner solenoid, which is shown immersed in the calorimeters. Sourced from CDS.
My own picture of the ATLAS detector in early 2026. The gray end cap toroid is easily visible in its retracted position, with the barrel toroidal coils being identified by the orange heating fixtures.
The solenoid magnet is the simplest of the bunch, providing a fairly uniform 2 Tesla magnetic field for the inner detector to track charged particle trajectories. Even if not a perfectly ideal solenoid, we obtain a sufficiently clear idea of how the magnetic field behaves during stable operations by taking physical measurements at various grid points throughout the solenoid using a device known as a Hall sensor.
These grid point measurements can then be stitched together, with interpolation performed between the points, to produce a functionally continuous "map" of the magnetic field within the solenoid. When forming particle trajectories from collision processes, our reconstruction software will continually reference this field map across the particle's path in order to measure the associated momentum using the process we discussed before.
This same procedure can be applied for the toroidal fields which surround the Muon Spectrometer (MS), however generating the map for these components is far more complicated. As a reminder, an ideal toroid produces a circular magnetic field through its coils which is smooth and symmetric in the limit that you have infinitely many coils. With just eight coils in each of our toroids, our resulting magnetic fields are far from ideal and require more finely spaced measurements to produce accurate maps. However, the much wider volume covered by the MS as well as the amount of instrumentation in the space between our toroid coils make repeated direct measurements impractical for producing a precise field map.
The ATLAS detector was designed with a solution to this problem, which begins with looking at magnetic field sources themselves, the toroidal coils. Despite their massive scale and engineering accomplishments, these coils are simply current-carrying wires similar to the ones we often learn about in introductory electromagnetism courses. As such, we can imagine that we can perform a lengthy but straight-forward calculation of how the current from one of these coils contributes to the magnetic field for a given point in space using the Biot-Savart Law. The goal would then be to define a mesh of grid points throughout our detector and calculate each coil's contribution to that point, sum them up, and then we have our toroidal field map.
The complication with this strategy is due to the fact that, as current-carrying wires, our toroidal coils are subject to large magnetic forces from the other coils' magnetic fields. While not enough to break our detector, they are certainly sufficient to deform the coils from the ideal, perfect "race-track" geometry they were designed with. This means that we can't precisely know the distances as required in our Biot-Savart Law calculation.
Thankfully, the designers of the MS accounted for this and included a neat detail into the detector: 1,800+ Hall sensors which are installed in various chambers that form the MS. These sensors actively take magnetic field readings during active periods of detector activity, and have their locations and orientations routinely verified by optical alignment teams. Just plotting out the sensors' locations gives a neat illustration of how they are distributed across the detector's geometry, as seen below:
Magnetic field readings from Hall sensors located across the ATLAS detector. At each point, the arrow directions and color indicate the magnetic field's orientation and strength respectively.
Schematic of ATLAS detector and key components. Sourced from CDS.
The large distances between these sensors, coupled with the rapidly varying toroidal field, mean that we can't just interpolate between the sensors' readings to obtain our field map. Rather, they help us constrain the geometry and locations of our toroidal coils by providing 1,800 known data points which are used to perform a χ² fit. In this procedure we initially calculate the predicted magnetic field for each Hall sensor location using the Biot-Savart Law and an initial guess at the toroid geometries. The differences between our observed Hall sensor readings and our predicted values are then calculated, and we shift the orientations and shape of the toroidal coils to reduce these distances. This is repeated until we converge on a minimal difference between our field predictions and the observed values.
The result of this fit is our best model of the true locations and shapes for each of our toroidal cables, enabling us to perform our aforementioned Biot-Savart approach. From here, we specify a set of finely spaced points throughout the detector, perform our numerical calculation of Biot-Savart for all of our contributing magnetic field sources, and finally combine the solenoid map we described earlier. The result is a complete map of the magnetic field across the ATLAS detector, which is visualized below:
The magnitude of the magnetic field map across the detector, viewed from a transverse and longitudinal view on the left and right respectively. Several defining features can be identified, such as the toroidal coils, the solenoid magnet, and the ferromagnetic elements in the hadronic calorimeter.
This entire process is bit of a rabbit hole of complexity, even barring
