Muon Tomography

Muon tomography is a non-invasive method for the determination of the inner density distribution of massive objects. It has been used successfully in many expeditions where the remote examination of an object is preferable to other on-site techniques. It has been proven most successful in volcanology either as a standalone method or in cooperation with other geophysical techniques, like gravimetry (Fig. 1) and electric resistivity. Since 2008, the Diaphane collaboration has been performing studies on the La Grande Soufrière volcano in Guadeloupe while simultaneously expanding its scope to other domains like civil engineering and, most recently, archaeology.

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Figure 1: Joint measurements with three muon detectors and several gravimeters, with the final goal being the determination of the dome's density distribution. (a) Location of muon telescopes (diamonds) and gravity stations (circles). Gravity stations are coloured according to their divergence from the theoretically expected gravity acceleration value. Red cones indicate the region of the dome sampled by each telescope. (b – d) Muon radiographies obtained with the three telescopes. Each pixel corresponds to a particular line of sight of the telescope. The average density is computed from the opacity, which is inferred from the number of muons detected, and the total length of rock crossed by the muons. (e) The muon telescope at the “Parking” site. (10.1002/2017GL074285)

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Introduction

The principle is relatively simple and it brings to mind the clinical radiography done with X-rays. When we go to the hospital and a doctor wants to examine the condition of a limb, they put us under an X-ray machine. Behind our limb there is a photographic plate. When an X-ray photon strikes the photographic plate it paints it black. The parts of our body that absorb all photons appear white on the plate (bones) and those parts that are fully transparent to photons appear black, while everything in between appears as shades of grey. The machine produces photons and sends them towards the direction of our body and the photographic plate behind it. The bones absorb most of the X-rays, while muscle and other soft tissue let them pass without absorbing that much.

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Figure 2: The first human X-ray, taken by Wilhelm Conrad Roentgen (right), was of the left hand of his wife, Anna Bertha (center), in the year 1895.

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Muon tomography operates in a very similar manner but, instead of photons, it uses muons and, instead of a photographic plate, it uses a particle detector. Moreover, there is no muon-production machine, our particles are provided for free, by Mother Nature herself.

They are the final product of down-going particle showers that start at altitude in the atmosphere with protons and heavier nuclei coming from outer space. These initial particles are called cosmic rays and have incredible energies that dwarf those of the best particle accelerators. For instance the "Oh-My-God" particle, detected in 1991, had energy of 320 x 10^18 eV (51.2 Joules), that's like dropping an apple from 50 meters! Of course these kinds of events are extremely rare, so in our line of work we deal with more modest energies most of the time, but again it still is remarkable.

Two types of muon tomography exist. Absorption (or transmission) tomography involves the study of the inner density of large structures, like volcanos, the overburden of underground facilities, large archeological monuments like pyramids. Absorption is our focus in Diaphane.

The second type is scattering tomography. It concerns objects with smaller dimensions, like cargo containers and focuses on identifying compartments of high mass number A, that is characteristic for radioactive materials and the shielding commonly used to conceal them. It appears to be very promising for homeland security applications, among others, against the smuggling of radioactive materials.

Cosmic-Ray Showers

The study of cosmic rays goes back to the birth of particle physics itself, with many new particles having been discovered in cosmic-ray showers (e.g. the positron, 1932). The field of cosmic-ray physics is vast and primarily investigated through particle physics and astrophysics. It historically evolved from studying the constituents of cosmic-ray showers, to investigating and theorising on the origin of cosmic rays themselves. This in depth study spans more than one hundred years and has led to a very well documented and accurate profiling of the cosmic-ray constituents, their energies, their angular distributions and most of the parameters that govern their showers within the atmosphere.

When a cosmic-ray particle enters the Earth's atmosphere, it reacts with the nuclei of the air molecules, mainly Nitrogen and Oxygen. This interaction gives rise to daughter particles that continue propagating towards the ground. These daughter particles, in their turn, interact with nuclei found in their path, or undergo decay into other more stable particles. These new particles continue this chain of particle production until they reach the ground. The final product of this sequential particle production and destruction leads to what we call a cosmic-ray shower.

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Figure 3: Artist's rendering of a cosmic-ray air shower above a water-Cherenkov detector of the Pierre Auger Observatory in western Argentina. (A. Chantelauze, S. Staffi, L. Bret)

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A cosmic-ray shower, just like an avalanche, starts from a point and becomes larger and larger as it travels through the atmosphere, while producing a multitude of daughter particles (secondaries). When the shower reaches the ground, its footprint will be proportional to the energy of the initial particle (primary) but only the most stable of its daughter particles will be part of this footprint. In order of abundance the final products of a cosmic-ray shower are muons, electrons, photons and protons.

Muons are unstable particles that decay into an electron and two neutrinos (see also: Deep Sea Hunters) 2.2 μs after their creation. So how are they the most abundant if they are unstable?

They may be unstable, but they travel at the speed of light upon creation and this means that in our frame of reference their time passes more slowly. So, in the system of reference of a muon with energy of 2 GeV, a time duration of 2.2 μs translates in our system of reference into a 46 μs duration. This means that, instead of 660m, the muon can now travel several kilometers in our world (13.8 km for this one).

Since cosmic-rays strike the Earth's atmosphere from every direction this also means that muons on ground level are coming from every direction. Their mean rate is 1 muon per cm2 per minute, with a mean energy of 4 GeV and a most probable energy of 2 GeV, the energy used for our last calculation.

This doesn't mean that muons are coming from every direction at the same rate. More muons come from directly above than, let's say, from 45 degrees above the horizon. This in turn means that the more horizontal the viewing angle of an object, the fewer the muons that cross that object before arriving in the same amount of time.

So, even though muons are free, this comes at the price of not having as much as one would like for a specific measurement setup. A direct consequence of this is that the higher the target stands with respect to the detector level, the better for the duration of the measurement.

To take a photograph at night, when there is not much light to be reflected from objects, one has to leave the shutter open for more time, in order for enough photons to come through. In the same manner, a horizontal muon detector has to operate longer in order to collect the amount of muons needed for a tomography. The main difference being that muons cross the studied target while photons reflect off the object of interest.

The Method

Muon absorption tomography (Figure 4) is based on the fact that muons (like all particles) lose energy while traversing matter and the more matter they encounter on their path, the more the energy they lose. And, if they lose all of their energy, they can't exit that block of matter, so they stop and decay inside the object. This means that if I look at a specific direction passing through an object, I will detect only those muons that have higher energy than the minimum energy needed to exit the object. In other words, the amount of matter crossed is linked to a specific energy threshold for a particle.

We already highlighted that cosmic-ray showers and their products, including muons, are very well studied, and this includes their energy distribution as much as their angular distribution. As a result, we know exactly how many muons to expect from every direction (angles) and how many muons to expect for every energy window. For example, if I expect 100 muons from a direction and I get, let's say 30, I can then go to the muon energy distribution and find above which energy threshold I need to be to get these 30 muons. This energy threshold reveals the amount of mass that blocks the muon path in that direction.

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Figure 4: Schematic of a muon tomography setup for the determination of the inner density of a geological structure. Opacity is the amount of matter along the trajectory of the muon, which is considered a straight line.

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The goal of muon tomography, at least in our field of study, is to find the density contrast inside an object for the different directions, and if we are confident enough, to calculate the mean density in each of these directions. This means that having a quantity for the mass in a given direction is not the result we are looking for, instead we need to divide by the length of the muon trajectory inside the object to retrieve the mean density along that direction. This length is calculated by the topographic map of the object.

The Detector

Diaphane detectors are designed to operate in very harsh environments and their design focuses on stability, reliability and remote access, via the internet, to control, monitor and transfer data. The detector geometry is very simple, it comprises three detection planes, placed parallel to each other, which allow for the reconstruction of a particle's trajectory. Each plane is an autonomous detector with its own electronics for control and monitor and all three planes share the same clock.

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Figure 5: (left) A scientist attending to the installation of the detector opposite the La Soufriere volcano dome in Guadalupe. (right) Schematic of the Diaphane detector, showing all of the different compartments: 1 - Front matrix, 2 - Control-box, 3 - Central matrix, 4 -Shielding (steel + lead), 5 - back matrix, 6 - muon trajectory, drawn to visualise the detection principle, and red stars to denote its impact points on the detector matrices, 7 - matrix connections, 8 - mount swing.

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When a particle passes through a plane it deposits energy which is converted into a proportional electric charge and, if that charge is over a certain threshold, then we say that the plane is "triggered". It communicates this "triggered" state to the main electronic board of the detector, and if two out of three planes are triggered during the same time period (Δt~200ns), then we have a "triggered" detector and an output of information is stored in a data file.

The information output is a collection of data, is known as an event and is given a unique identification number. These data let us know when a particle passed through the detection plane, where exactly it passed through and how much energy it deposited on that detection plane. A detector model can be found here.

This is all the information we need to reconstruct the path and direction of the particles that pass through the detector. The direction is important because, depending on the orientation of the detector, particles can be detected coming from both directions and understanding this also helps with background rejection.

The Background

Background is any signal that finds its way into the data recorded by the detector that is not the signal that we are interested in. So, what is considered background depends on what you are looking for. In general. it is best to know exactly what each signal represents and then use this information accordingly, making it possible to distinguish the phenomenon we wish to investigate.

Sometimes background can be identified and removed, while other times it may be indistinguishable from the signal. This doesn't mean that we cannot draw valuable conclusions, even in this latter case. An interesting example is that of the IceCube neutrino telescope, which figured out that the neutrino signal it was seeing was of extraterrestrial origin, even though there was no way to differentiate between those neutrinos created in atmospheric showers and those that were coming directly from outer space.

In the case of muography the signal is high-energy cosmic muons coming from the side of the studied target. The response of our detector to this signal is composed of three points, one on each detection plane, which all fall along the same straight line (Fig. 5). This means that when we find these three collinear points in the data of an event, we are then happy to say that we found an event that is part of our signal.

If only it was that simple...

Background Types

There are other particles that can mimic this kind of behavior. The problem with this mimicking is that they artificially increase the statistics for a certain direction and this leads to an underestimation of the density for that specific direction. Of course, this affects all directions and leads to a smoothing out of the density contrast. It would be nice if we could identify indicators that help us get rid of this background.

We already mentioned that, as well as muons, other particles also arrive at the ground level as part of showers. Hadrons can interact with our target, create a shower of particles themselves, and of those particles, one can trigger our detector (Fig. 6, left).

Alternatively, a hadron can come from above our detector and create a shower of particles just above it (Fig 6., right). These particles will then propagate together, occupying approximately the same plane as they all travel at the speed of light, and even though the planes of the detector are struck by different particles, the points on the detector planes are, to a degree, collinear.

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Figure 6: The two ways a handron can interact with the detector and mimic the straight line signal of a muon.(arXiv: 1906.03934)

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Low-energy muons (soft muons) are more prone to scattering and this means that a down-going soft muon can scatter on our target and find its way into our detector. Furthermore, one such low-energy muon can strike the ground behind our detector and enter it from the rear in an up-going fashion. If the detector is not able to discriminate between the times each plane was crossed, then we will be forced to treat these events as coming from the target and as belonging to the reconstructed direction.

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Figure 7: The two ways a low-energy muon scatters, either on the target or behind the detector. This results in additional events coming from the reconstructed direction.(arXiv: 1906.03934)

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Finally in this category of up-going particles coming from the rear, one can also find high-energy muons. These are part of showers produced parallel to the ground from primaries originating from the furthest parts of the horizon. The more parallel the orientation of the detector the more significant the effect of the up-going muons.

Background rejection

There are a few techniques on the detector level that can help discriminate background events. The solution to up-going muons coming from the rear is the precise timing of the triggering of each detection plane. For soft-muons, electrons/positrons and hadrons, we can place a lead (Pb) segment before the last plane and this will give rise to different effects for different particles. Soft muons are expected to change direction after hitting the lead. This deviation from the initial path is small and not all types of detectors can "see" it. For instance, this technique doesn't work for our detector, because one needs very good angular resolution to capitalise on this effect.

On the other hand, electrons/positrons will be absorbed by the lead and they will never strike the third plane. This means that such events will be 2-fold and not 3-fold coincidences. As for hadrons, they interact strongly with lead and give rise to small showers that show up as multiple points on the rear plane of the detector.

So there are two paths one can take towards background rejection. One is to find ways to stop these background particles from reaching the detector and being recorded. The other is to find patterns in the recorded data that allows for a discrimination between signal and background particles.

In the old days when there was not enough computing power and data storage was very expensive, particle physics was very concerned with getting only the "right" kind of data. Nowadays, and depending on the measurement we perform, we can be more lenient and allow for part of the background to be recorded.

The Task at Hand

Diaphane detectors fall into this more "lenient" kind of detector, in which other particles, as well as muons, find their way into our data and we deal with them during data selection, before the analysis.

Muography is concerned only with muons and the selection process revolves around finding straight lines within our detector and treating them as a muon signal. This leaves out complicated recordings, in which a straight line is not retrieved with confidence. Additionally, if something isn't a muon, but it triggered our detector, it would be good to know what it was exactly. Maybe this finer particle identification can not only improve the tomography results, but also open the door to new applications.

In the workflows you will be presented with events taken from the mission of 2018 at Apollonia where we tried to investigate the discovery potential of buried monuments in collaboration with geophysical techniques. Information on the experimental setup and the data acquisition that took place at the site of the Apollonia Tumulus can be found here .

This was a very difficult measurement, due to the small size of the monument and the small muon flux that we had to work with, but the results returned were very interesting. The lack of statistics presents a great opportunity to test whether we can optimise our muon selection algorithm in order to improve our results. Furthermore, the experimental setup simulation showed that there is a potential way to identify electrons in our detectors.

Your help is Valuable

Since the patterns in our detectors are in their details unknown to us, it is very difficult to program a computer to find them. The human perception is much more capable in such tasks where a categorization of motifs needs to take place and that's the reason why we need citizen scientists to go through these events. This work will help us train our computers to identify these patterns instead of just trying to isolate lines. It will also give us access to the more complicated events which we are now forced to reject before any analysis takes place. Finally the cataloging of these patterns will be used to guide our study towards the identification of the true particles behind these events.

We are on your side

We appreciate your efforts and we are on your side for anything you need. The talk boards can help us communicate and discuss any issues or ideas you may have. Remember that your opinion matters and we look forward to your feedback. We will try our best to respond as soon as possible and to carefully address your concerns and insights. A big THANK YOU from all the members of our team for reading up to this point and we wish you a joyful journey through our "Cosmic Muon Images" project.