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The shape of the nozzle significantly influences the character of the supersonic flow beyond the aperture, especially the shape and type of shock waves, which are highly dense compared to the surrounding gas. These significantly affect the electron scattering, which influences the resulting image. This paper analyzes the effect of aperture and nozzle shaping under specific low-pressure conditions and its impact on the electron dispersion of the primary electron beam.<\/jats:p>","DOI":"10.3390\/s24113436","type":"journal-article","created":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T09:33:31Z","timestamp":1716802411000},"page":"3436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical-Physics Analyses of the Nozzle Shaping at the Aperture Gas Outlet into Free Space under ESEM Pressure Conditions"],"prefix":"10.3390","volume":"24","author":[{"given":"Pavla","family":"\u0160aback\u00e1","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"},{"name":"Institute of Scientific Instruments of the CAS, Kr\u00e1lovopolsk\u00e1 147, 612 64 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0640-0406","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"Maxa","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"},{"name":"Institute of Scientific Instruments of the CAS, Kr\u00e1lovopolsk\u00e1 147, 612 64 Brno, Czech Republic"}]},{"given":"Jana","family":"\u0160vecov\u00e1","sequence":"additional","affiliation":[{"name":"Faculty of Military Leadership, University of Defence, 662 10 Brno, Czech Republic"}]},{"given":"Jaroslav","family":"Tal\u00e1r","sequence":"additional","affiliation":[{"name":"Faculty of Military Leadership, University of Defence, 662 10 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4426-2857","authenticated-orcid":false,"given":"Tom\u00e1\u0161","family":"Binar","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8528-4430","authenticated-orcid":false,"given":"Robert","family":"Bayer","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9793-9767","authenticated-orcid":false,"given":"Petr","family":"Ba\u010da","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"given":"Petra","family":"Dostalov\u00e1","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 10, 616 00 Brno, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9256-8538","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"\u0160varc","sequence":"additional","affiliation":[{"name":"Faculty of Military Leadership, University of Defence, 662 10 Brno, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Maxa, J., \u0160aback\u00e1, P., Mazal, J., Ned\u011bla, V., Binar, T., Ba\u010da, P., Tal\u00e1r, J., Bayer, R., and \u010cudek, P. 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