Experimental demonstration of a tomographic 5D phase-space reconstruction

Detailed knowledge of particle-beam properties is of great importance to understand and push the performance of existing and next-generation particle accelerators. We recently proposed a new phase-space tomography method to reconstruct the five-dimensional (5D) phase space, i.e., the charge density distribution in all three spatial directions and the two transverse momenta. Here, we present the first experimental demonstration of the method at the FLASHForward facility at DESY. This includes the reconstruction of the 5D phase-space distribution of a GeV-class electron bunch, the use of this measured phase space to create a particle distribution for simulations, and the extraction of the transverse 4D slice emittance.

💡 Research Summary

The authors present the first experimental demonstration of a five‑dimensional (5D) phase‑space tomography for ultra‑relativistic electron bunches, performed at the FLASHForward facility at DESY. The method combines a polarizable X‑band transverse‑deflection structure (PolariX TDS) that streaks the bunch in a selectable transverse direction with a conventional four‑dimensional (4D) transverse tomography based on a set of nine quadrupoles. By varying the phase advance between a reconstruction point and a measurement screen in ten steps for each transverse plane (total 180°) and simultaneously streaking the beam at ten different angles, a total of 1 000 projection images were planned; 960 of them were successfully recorded over 28 h.

The raw images were processed with a Simultaneous Algebraic Reconstruction Technique (SART) implemented in Python’s scikit‑image library, using two iterations. First, a three‑dimensional charge‑density distribution was reconstructed for each phase‑advance setting. These distributions were transformed into normalized coordinates (x_N, x′_N, y_N, y′_N) using Courant‑Snyder parameters obtained from beam‑line simulations. The PolariX TDS provided a shear parameter (average 18.7 ± 2.5) measured via RF‑phase scans, allowing the longitudinal coordinate to be resolved into 72 slices of 20 fs each (≈19 fs longitudinal resolution). For each time slice the four‑dimensional transverse phase space was assembled from the ten phase‑advance settings, yielding a full 5D distribution (x_N, x′_N, y_N, y′_N, t).

Visualization of the reconstructed 5D data revealed clear non‑linear correlations among all transverse planes and the time coordinate. In particular, (x_N, t) correlations are attributed to coherent synchrotron radiation (CSR) generated in the two horizontal bunch‑compressor chicanes upstream of FLASH, while (y′_N, t) correlations likely stem from residual vertical dispersion combined with the energy chirp introduced during compression. The (x′_N, y′_N) plane shows a non‑circular, non‑Gaussian shape with centroid and momentum offsets that evolve along the bunch, indicating collective effects beyond simple linear optics.

From the 5D reconstruction the authors generated a synthetic particle distribution containing five million macroparticles. By sampling each time slice according to the reconstructed probability density (retaining only voxels above 5 % of the slice maximum to suppress reconstruction noise) they obtained realistic particle ensembles. These ensembles were used to compute slice‑by‑slice covariance matrices Σ_4D, from which normalized emittances ε_nx, ε_ny, Courant‑Snyder β and α functions, and the four‑dimensional slice emittance ε_4D = √det Σ_4D were extracted. The measured β functions (≈10 m) and α functions (≈0) agree with the design within the estimated uncertainties, while the sliced 4D emittance matches the product ε_nx·ε_ny to within 5 % on average (minimum 1 % near the bunch core), confirming that transverse‑plane correlations are modest.

Uncertainty analysis was performed by repeating the reconstruction 100 times with random variations of the shear parameter according to its measured Gaussian spread. Additional systematic contributions were evaluated: a 1 % beam‑energy error leads to a 5 % emittance error; a 1 % RMS energy spread (including a linear chirp and 0.1 % uncorrelated spread) adds ≈2 % error; and the finite number of projection angles (ten per plane) can overestimate emittance by up to 13 %. The larger discrepancy observed in the vertical emittance is attributed to an incomplete vertical phase‑advance scan, reducing the number of usable projections for that plane.

To validate the reconstruction, the synthetic particle distribution was tracked from the reconstruction point to the measurement screen using the exact beam‑line settings employed during the experiment. Simulated screen images were compared with the measured ones in the (v, t) coordinates (v being the transverse direction orthogonal to the streaking direction). The centroid deviation of each time slice, normalized to the measured RMS size, yielded an average weighted discrepancy of 32 % ± 15 % across all recorded projections, indicating reasonable qualitative agreement.

In summary, this work demonstrates that 5D tomography can provide a complete, time‑resolved picture of an ultra‑relativistic electron bunch, revealing hidden correlations that affect beam quality in free‑electron lasers and future colliders. The method enables the generation of high‑fidelity particle distributions for start‑to‑end simulations and opens the path toward real‑time diagnostics and correction of transverse‑plane correlations. Future improvements—more projection angles, higher‑resolution screens, and integration into feedback loops—are expected to further reduce uncertainties and make 5D tomography a routine tool for next‑generation accelerator facilities.