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. 2019 Jul 17;9:10391. doi: 10.1038/s41598-019-45024-2

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Microbunching instability in a relativistic electron bunch. (a) Illustration: at accelerator locations where curved trajectories are present, each electron interacts with the coherent synchrotron radiation emitted by the others. (b,c) Numerical simulation: resulting spontaneous appearance of a pattern in phase space, which evolves in a complex way (computation using KARA storage ring parameters, see Method Section, and Supplementary Video 1). (c) Corresponding longitudinal density profile. Note that the fast modulation in (c) – thought apparently small – is responsible for a particularly intense emission of coherent synchrotron radiation (typically 10³–10⁵ times the normal synchrotron radiation) ranging from the millimeter-wave to THz domains.