{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:13:13Z","timestamp":1785413593207,"version":"3.56.0"},"reference-count":73,"publisher":"American Physical Society (APS)","issue":"5","license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,6,6]]},"abstract":"<jats:p>Laser-generated, transient toroidal helium plasma at atmospheric pressure is studied experimentally. Tomographically reconstructed cross-sectional images reveal the gas flow responsible for the formation of the toroidal structure. A splitting of the toroidal plasma during the final phase of its evolution is observed. The plasma dynamics is induced by a two-lobed plasma kernel resulting from a single, focused laser pulse. This kernel generates two shocks that join to form an enhanced third shock, a so-called Mach reflection, in the plane perpendicular to the optical axis. This shock pattern determines the gas flow, which deforms the plasma into a disk, then transforms it into a nonrotating toroid, and finally splits it into two parallel rings. Schlieren imaging, a novel laser scanning-probe imaging technique, thermodynamic modeling, and a deliberately broken flow symmetry confirm this formation mechanism. This study is of interest for the generation of compact toroidal plasma structures in free space, with potential applications in chemical reactors, laser ignition of internal combustion engines, plasma medicine, and linked magnetic field line plasma confinement.<\/jats:p>","DOI":"10.1103\/r96j-1lhd","type":"journal-article","created":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T13:10:52Z","timestamp":1749215452000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Mach reflection and formation of transient toroidal helium plasma"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7962-6297","authenticated-orcid":true,"given":"Vincent L.","family":"Kooij","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/027bh9e22","id-type":"ROR","asserted-by":"publisher"}],"name":"Leiden University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2118-6532","authenticated-orcid":true,"given":"Dirk","family":"Bouwmeester","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/027bh9e22","id-type":"ROR","asserted-by":"publisher"}],"name":"Leiden University"},{"id":[{"id":"https:\/\/ror.org\/02t274463","id-type":"ROR","asserted-by":"publisher"}],"name":"University of California, Santa Barbara"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"r96j-1lhdCc1R1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2014.2308476","type":"journal-article"},{"key":"r96j-1lhdCc2R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1712717114","type":"journal-article"},{"key":"r96j-1lhdCc3R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/ab1ba4","type":"journal-article"},{"key":"r96j-1lhdCc4R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-10457-0","type":"journal-article"},{"key":"r96j-1lhdCc5R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.combustflame.2004.04.002","type":"journal-article"},{"key":"r96j-1lhdCc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.combustflame.2013.12.029","type":"journal-article"},{"key":"r96j-1lhdCc7R1","volume-title":"Proceedings of the 3rd International Conference on the Frontiers of Plasma Physics and Technology","author":"J. Tauer","type":"conference-proceedings"},{"key":"r96j-1lhdCc8R1","doi-asserted-by":"publisher","DOI":"10.1364\/ASSP.2005.812","type":"journal-article"},{"key":"r96j-1lhdCc9R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.372150","type":"journal-article"},{"key":"r96j-1lhdCc10R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4922076","type":"journal-article"},{"key":"r96j-1lhdCc11R1","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3727\/48\/48\/485203","type":"journal-article"},{"key":"r96j-1lhdCc12R1","doi-asserted-by":"publisher","DOI":"10.1021\/acsenergylett.8b00184","type":"journal-article"},{"key":"r96j-1lhdCc13R1","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361:20079043","type":"journal-article"},{"key":"r96j-1lhdCc14R1","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2020.00074","type":"journal-article"},{"key":"r96j-1lhdCc15R1","doi-asserted-by":"publisher","DOI":"10.1002\/jctb.5205","type":"journal-article"},{"key":"r96j-1lhdCc16R1","doi-asserted-by":"publisher","DOI":"10.1186\/s42480-019-0006-8","type":"journal-article"},{"key":"r96j-1lhdCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.095001","type":"journal-article"},{"key":"r96j-1lhdCc18R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112069000991","type":"journal-article"},{"key":"r96j-1lhdCc19R1","first-page":"69","type":"journal-article","volume":"55","author":"A.\u00a0M. Kamchatnov","year":"1982","journal-title":"Sov. Phys. J. Exp. Theor. Phys."},{"key":"r96j-1lhdCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.89.043104","type":"journal-article"},{"key":"r96j-1lhdCc21R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00401864","type":"journal-article"},{"key":"r96j-1lhdCc22R1","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1056","type":"journal-article"},{"key":"r96j-1lhdCc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.150404","type":"journal-article"},{"key":"r96j-1lhdCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.053820","type":"journal-article"},{"key":"r96j-1lhdCc25R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/47\/35\/355205","type":"journal-article"},{"key":"r96j-1lhdCc26R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377818001290","type":"journal-article"},{"key":"r96j-1lhdCc27R1","volume-title":"Radiative Processes in Astrophysics","author":"G.\u00a0B. Rybicki","year":"1979","type":"book"},{"key":"r96j-1lhdCc28R1","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/29\/1\/302","type":"journal-article"},{"key":"r96j-1lhdCc29R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511613630","type":"book","volume-title":"Principles of Plasma Diagnostics","author":"I.\u00a0H. Hutchinson","year":"2002"},{"key":"r96j-1lhdCc30R1","doi-asserted-by":"publisher","DOI":"10.1088\/0143-0807\/32\/5\/002","type":"journal-article"},{"key":"r96j-1lhdCc31R1","doi-asserted-by":"publisher","DOI":"10.1088\/0963-0252\/25\/5\/054003","type":"journal-article"},{"key":"r96j-1lhdCc32R1","doi-asserted-by":"publisher","DOI":"10.1088\/0963-0252\/25\/5\/054004","type":"journal-article"},{"key":"r96j-1lhdCc33R1","doi-asserted-by":"publisher","DOI":"10.18434\/T4W30F","type":"journal-article"},{"key":"r96j-1lhdCc34R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.2821616","type":"journal-article"},{"key":"r96j-1lhdCc35R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1729732","type":"journal-article"},{"key":"r96j-1lhdCc36R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61247-3","type":"book","volume-title":"Gas Discharge Physics","author":"Y.\u00a0P. Raizer","year":"1991"},{"key":"r96j-1lhdCc37R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511541261","type":"book","volume-title":"Laser Induced Breakdown Spectroscopy","author":"A.\u00a0W. Miziolek","year":"2006"},{"key":"r96j-1lhdCc38R1","doi-asserted-by":"publisher","DOI":"10.2514\/6.2019-1250","type":"journal-article"},{"key":"r96j-1lhdCc39R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4073(99)00196-X","type":"journal-article"},{"key":"r96j-1lhdCc40R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112008001468","type":"journal-article"},{"key":"r96j-1lhdCc41R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/ab492a","type":"journal-article"},{"key":"r96j-1lhdCc42R1","volume-title":"8th International Workshop on Radiation of High Temperature Gases for Space Missions","author":"A. Alberti","year":"2019","type":"conference-proceedings"},{"key":"r96j-1lhdCc43R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/aaad87","type":"journal-article"},{"key":"r96j-1lhdCc44R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56640-0","type":"book","volume-title":"Schlieren and Shadowgraph Techniques","author":"G.\u00a0S. Settles","year":"2001"},{"key":"r96j-1lhdCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.12.064015","type":"journal-article"},{"key":"r96j-1lhdCc46R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sab.2004.05.002","type":"journal-article"},{"key":"r96j-1lhdCc47R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1950.0049","type":"journal-article"},{"key":"r96j-1lhdCc48R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1950.0050","type":"journal-article"},{"key":"r96j-1lhdCc49R1","doi-asserted-by":"crossref","DOI":"10.21236\/ADA384954","type":"book","volume-title":"Blast Wave","author":"H.\u00a0A. Bethe","year":"1958"},{"key":"r96j-1lhdCc50R1","volume-title":"Physical Processes in Hot Cosmic Plasmas","author":"D. F. Cioffi","year":"1990","type":"book"},{"key":"r96j-1lhdCc51R1","volume-title":"The Physics of Astrophysics: Gas Dynamics","author":"F.\u00a0H. Shu","year":"1992","type":"book"},{"key":"r96j-1lhdCc52R1","volume-title":"Similarity and Dimensional Methods in Mechanics","author":"L.\u00a0I. Sedov","year":"1959","type":"book"},{"key":"r96j-1lhdCc53R1","volume-title":"Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena","author":"Y.\u00a0B. Zel'dovich","year":"1966","type":"book"},{"key":"r96j-1lhdCc54R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sab.2006.03.004","type":"journal-article"},{"key":"r96j-1lhdCc55R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01414863","type":"journal-article"},{"key":"r96j-1lhdCc56R1","doi-asserted-by":"crossref","DOI":"10.21236\/ADA087568","type":"book","volume-title":"The Effects of Nuclear Weapons","author":"S. Glasstone","year":"1977"},{"key":"r96j-1lhdCc57R1","doi-asserted-by":"publisher","DOI":"10.1002\/andp.18902770909","type":"journal-article"},{"key":"r96j-1lhdCc58R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjh\/e2011-10037-x","type":"journal-article"},{"key":"r96j-1lhdCc59R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511524578","type":"book","volume-title":"Principles of Plasma Spectroscopy","author":"H.\u00a0R. Griem","year":"1997"},{"key":"r96j-1lhdCc60R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1482156","type":"journal-article"},{"key":"r96j-1lhdCc61R1","doi-asserted-by":"publisher","DOI":"10.1071\/PH560198","type":"journal-article"},{"key":"r96j-1lhdCc62R1","doi-asserted-by":"publisher","DOI":"10.2514\/4.470677","type":"journal-article"},{"key":"r96j-1lhdCc63R1","doi-asserted-by":"publisher","DOI":"10.1515\/zna-1992-0906","type":"journal-article"},{"key":"r96j-1lhdCc64R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05016-9","type":"book","volume-title":"Vortex Rings","author":"D.\u00a0G. Akhmetov","year":"2009"},{"key":"r96j-1lhdCc65R1","doi-asserted-by":"publisher","DOI":"10.1016\/S1540-7489(02)80198-5","type":"journal-article"},{"key":"r96j-1lhdCc66R1","volume-title":"An Introduction to the Kinetic Theory of Gases","author":"J.\u00a0H. Jeans","year":"1940","type":"book"},{"key":"r96j-1lhdCc67R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4905190","type":"journal-article"},{"key":"r96j-1lhdCc68R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.128.219","type":"journal-article"},{"key":"r96j-1lhdCc69R1","doi-asserted-by":"crossref","DOI":"10.1201\/b17118","type":"book","volume-title":"CRC Handbook of Chemistry and Physics","author":"W.\u00a0M. Haynes","year":"2014"},{"key":"r96j-1lhdCc70R1","volume-title":"A Treatise on Hydrostatics and Hydrodynamics","author":"W.\u00a0H. Besant","year":"1859","type":"book"},{"key":"r96j-1lhdCc71R1","doi-asserted-by":"publisher","DOI":"10.1080\/14786440808635681","type":"journal-article"},{"key":"r96j-1lhdCc72R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5119794","type":"journal-article"},{"key":"r96j-1lhdCc73R1","volume-title":"Fluid Mechanics","author":"L.\u00a0D. Landau","year":"1987","type":"book"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/r96j-1lhd","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/r96j-1lhd\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T13:18:01Z","timestamp":1764076681000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/r96j-1lhd"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,25]]},"references-count":73,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,11]]}},"URL":"https:\/\/doi.org\/10.1103\/r96j-1lhd","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,25]]},"assertion":[{"value":"2025-03-25","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"055209"}}