A particle beam in an accelerator is like a swarm of gnats: each one flies at its own speed and angle. To keep the swarm from scattering and to hit the target, engineers need to know exactly how all particles move at once — all six coordinates of their motion. But conventional sensors only show a flat shadow of the swarm on a screen, like a smudge on glass after an impact.

The neural network in this work learns to reconstruct the full swarm from sixteen such shadows. The images are taken on a screen where the beam is slightly deflected, and between frames the magnet settings and the phase of the accelerating field are changed. This way, each particle leaves its own trace on the screens at different angles, and from these traces the network assembles a three-dimensional picture.

The method was tested on the injector of the KEK-ATF complex in Japan. The network was trained on computer simulations and then fed real images. The reconstructed beam sizes at the cathode and its duration matched direct measurements. This means that from the shadows on the screen, one can judge the swarm as a whole.

Now accelerator tuning can become simpler: instead of bulky tomography, it is enough to take sixteen images and run them through the neural network. This saves time and computational power, so the method will be useful at operating facilities.