Longitudinal Phase Space Tomography via Machine Learning at the Los Alamos Neutron Science Center

Inside the massive, fifty-year-old accelerator at the Los Alamos Neutron Science Center, a beam of particles races toward its target. For decades, operators have relied on a limited set of tools to guide this beam, much like driving a car with only a speedometer and no rearview mirror. They can measure how much current the beam carries, but they cannot easily see the beam's internal shape or how its particles are arranged in time and energy. This hidden arrangement, known as the longitudinal phase space, is crucial. If the beam is slightly misaligned or too spread out, it can hit the walls of the machine, causing damage or losing efficiency. To fix these issues, physicists traditionally have to make slow, manual adjustments, guessing at the right settings based on indirect clues. They need a way to see the invisible structure of the beam without stopping the machine to take a direct measurement, which is often impossible.

A team of researchers at Los Alamos National Laboratory has found a new way to see this hidden structure using machine learning. They developed a computer system that can look at a two-dimensional map of the beam's current and instantly reconstruct its full internal shape. Instead of relying on slow, manual tuning, their system uses a type of artificial intelligence called a neural network. This network was trained on millions of simulated scenarios, learning the complex relationship between the raw data the machine collects and the actual beam distribution. When tested, the system produced a clear picture of the beam's condition that matched the results of a painstaking, hours-long manual calibration. The researchers also discovered that the system does not need the entire map to work; by focusing only on the central part of the data, they could cut the time required to collect measurements by two-thirds without losing accuracy. This breakthrough offers a faster, more efficient way to tune one of the world's most important particle accelerators.

The challenge at the heart of this work is an inverse problem. In physics, an inverse problem occurs when you know the result of an event but need to figure out the cause. Here, the scientists can measure the beam's current as it passes through a collector after being adjusted by two different tanks in the accelerator. They know the settings of these tanks, but they do not know the exact shape of the beam before it entered the system. Reconstructing that shape from the current measurement is extremely difficult because the particles interact with each other in complex, non-linear ways. Traditional physics models struggle with this because the calculations are too heavy and the dynamics are too messy to solve quickly. The researchers turned to machine learning, which excels at finding patterns in complex data without needing to solve every equation from scratch.

To build their solution, the team created a digital twin of the accelerator using a simulation code called HPSim. They ran thousands of simulations, varying the settings of the accelerator tanks to generate a vast library of data. For each simulation, they recorded the resulting current map and the corresponding true shape of the beam. They then fed this data into a neural network, specifically a type known as a U-Net, which is designed to translate one image into another. The network learned to map the current measurements directly to the beam's internal shape. To ensure the model would work on real-world data, the researchers added noise to the training simulations, mimicking the random fluctuations and imperfections found in actual experiments. This preparation was vital, as real-world data is rarely as clean as a computer simulation.

When the team tested their models on experimental data collected in May 2025, the results were striking. The machine learning models generated a reconstruction of the beam's shape in less than a second. This speed is a massive improvement over the traditional method, where physicists manually adjust accelerator parameters and run simulations repeatedly until the model matches the experimental data, a process that can take hours. The reconstructed shapes produced by the neural networks were comparable to those obtained through this extensive manual tuning. To verify that the reconstructions were accurate, the researchers performed a self-consistency check. They took the beam shape predicted by the AI and ran it forward through the simulation code to see what the current map would look like. The resulting map closely resembled the actual experimental data they had started with, confirming that the AI had correctly identified the beam's structure.

One of the most practical findings of the study was that the system does not need the full dataset to function. Using a technique called explainable machine learning, the researchers analyzed which parts of the current map were most important for the network's decision. They found that the central core of the data, where the beam current is strongest, contained almost all the necessary information. The outer edges of the map, which often contain noise or less relevant data, contributed very little to the final prediction. This discovery allowed them to test a data reduction strategy. By removing measurements from the corners and edges of the scan, they found that the model could still produce accurate results even when two-thirds of the data was missing. This means that in the future, operators could perform "warm start" scans, where the beam settings are already close to optimal, in just one-third of the time previously required. This efficiency gain is significant for a facility like Los Alamos, where beam time is in high demand and every minute counts.

The study also highlighted the limitations of their approach. The experimental data used for testing was collected at a lower beam current than the machine's typical operating level. Because the particles in the beam push against each other more strongly at higher currents, the researchers noted that their current models might underestimate how spread out the beam becomes during normal operation. Additionally, the models were trained on simulated data, which is an idealized version of reality. Real beams can be more diffuse or have different structures than the simulations suggest. The researchers acknowledged that while their models performed well, they are not a perfect replacement for direct measurement, which is not currently possible at this facility. They suggested that future work should focus on improving the realism of the training data and adding methods to estimate the uncertainty of each prediction, so operators know how much to trust the AI's output.

Despite these caveats, the work demonstrates a clear path forward for using artificial intelligence in accelerator physics. The ability to reconstruct the beam's internal state from limited measurements opens the door to faster tuning and better diagnosis of machine problems. The researchers showed that by combining high-fidelity simulations with robust machine learning techniques, they could overcome the limitations of traditional diagnostics. The success of the U-Net architecture, particularly when combined with data reduction strategies, suggests that similar methods could be applied to other parts of the accelerator or even to different types of particle beams. As the field of accelerator physics continues to evolve, tools like these will likely become essential for maintaining the performance of these complex machines, ensuring they can continue to support the critical research that depends on them.