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. 2017 Sep 11;7:11159. doi: 10.1038/s41598-017-11547-9

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© The Author(s) 2017

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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Linear-field electron acceleration in unbounded free space by an ultrafast radially-polarized laser pulse, a process illustrated schematically in (a). As an example, (b) shows the net acceleration to a final energy of 7.7 MeV of a 30 keV electron pulse with charge −0.2 fC, by a 25 mJ, 3 fs laser pulse of wavelength 0.8 μm focused to a waist radius of 1.6 μm. The initial electrons are randomly distributed in a sphere of diameter 1 μm. More details of the interaction in (b) are given in Fig. 2.