Advanced accelerator-based light sources such as free electron lasers (FEL) accelerate highly relativistic electron beams to generate incredibly short (10s of femtoseconds) coherent flashes of light for dynamic imaging, whose brightness exceeds that of traditional synchrotron-based light sources by orders of magnitude. FEL operation requires precise control of the shape and energy of the extremely short electron bunches whose characteristics directly translate into the properties of the produced light.

Control of short intense beams is difficult due to beam characteristics drifting with time and complex collective effects such as space charge and coherent synchrotron radiation. Detailed diagnostics of beam properties are therefore essential for precise beam control. Such measurements typically rely on a destructive approach based on a combination of a transverse deflecting resonant cavity followed by a dipole magnet in order to measure a beam’s 2D time vs energy longitudinal phase-space distribution.

In this paper, we develop a non-invasive virtual diagnostic of an electron beam’s longitudinal phase space at megapixel resolution (1024 × 1024) based on a generative conditional diffusion model. We demonstrate the model’s generative ability on experimental data from the European X-ray FEL (EuXFEL).

We use a vector of non-invasively measured beam and accelerator parameters to guide the diffusion process. These measurements include noisy low-dimensional and very sparse signals which typically cannot be directly mapped to complex beam images: beam loss or position monitors, magnet power supply current, and RF cavity phase and amplitude set points.

We train the method with tens of thousands of such non-invasive measurements paired with direct destructive measurements of the beam's 2D (z,E) phase space projection. We then show that the generative  diffusion process has learned to generate these highly complex high resolution images directly from this sparse data, thereby giving us a virtual view of the electron beam in the EuXFEL. The figure below shows the overall setup. 

In the paper we show that this method has learned a physics-informed image manifold which relates accelerator parameters to beam images and is therefore able to traverse this manifold by simply moving around in the learned latent embedding, to generate physical intermediate beam states between training data examples.

This is a very general approach in which data from a complex physical system is used to condition the diffusion process to then create a non-invasive virtual diagnostic of the state of the process without having to rely on destructive measurements.

Beyond accelerator beam diagnostics, the approach that was developed here can be applied to any complex system to replace destructive measurements with a non-invasive generative model that is conditioned by a sufficiently rich set of non-invasive measurements.