{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T00:30:07Z","timestamp":1766449807469,"version":"3.38.0"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"unspecified","delay-in-days":39,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Plasma Phys."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p>Two-dimensional particle-in-cell (PIC) simulations explore the collisionless tearing instability developing in a Harris equilibrium configuration in a pair (electron\u2013positron) plasma, with no guide field, for a range of parameters from non-relativistic to relativistic temperatures and drift velocities. Growth rates match the predictions of Zelenyi &amp; Krasnosel'skikh (<jats:italic>Astron. Zh.<\/jats:italic>, vol. 56, 1979, pp. 819\u2013832) modified for relativistic drifts by Hoshino (<jats:italic>Astrophys. J.<\/jats:italic>, vol. 900, issue 1, 2020, p. 66) as long as the assumption holds that the thickness <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$a$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline1.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula> of the current sheet is larger than the Larmor radius <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$\\rho _L$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline2.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>, with the fastest growing mode at <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$ka \\approx 1\/\\sqrt {3}$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline3.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>. Aside from confirming these predictions, we explore the transitions from thick to thin current sheets and from classical to relativistic temperatures. We show that for thinner current sheets (<jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$a&lt; \\rho _L$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline4.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>), the growth rate matches the prediction for the case <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$a=\\rho _L$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline5.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>. We also explore the nonlinear evolution of the modes. While the wavenumber with the fastest growth rate initially matches the prediction of Zelenyi &amp; Krasnosel'skikh (1979), these modes saturate moving the dominant mode to lower wavenumbers (especially for thick current sheets with low growth rates). Furthermore, at a late, nonlinear stage, the growth rate (initially following the growth rate prediction proportional to <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$(\\rho _L\/a)^{3\/2} &lt; 1$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline6.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>) increases faster than exponentially, reaching a maximum growth rate equivalent to the linear growth rate prediction at <jats:inline-formula>\n\t      <jats:alternatives>\n\t\t<jats:tex-math>$\\rho _L\/a = 1$<\/jats:tex-math>\n\t\t<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377825000030_inline7.png\"\/>\n\t      <\/jats:alternatives>\n\t    <\/jats:inline-formula>, before eventually saturating.<\/jats:p>","DOI":"10.1017\/s0022377825000030","type":"journal-article","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T10:14:33Z","timestamp":1741774473000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Particle-in-cell simulations of the tearing instability for relativistic pair plasmas"],"prefix":"10.1017","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7644-7381","authenticated-orcid":false,"given":"K.M.","family":"Schoeffler","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3061-1118","authenticated-orcid":false,"given":"B.","family":"Eichmann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4161-8512","authenticated-orcid":false,"given":"F.","family":"Pucci","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5782-0013","authenticated-orcid":false,"given":"M.E.","family":"Innocenti","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2025,3,12]]},"reference":[{"key":"S0022377825000030_ref30","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2966.2006.11152.x"},{"key":"S0022377825000030_ref46","doi-asserted-by":"publisher","DOI":"10.1086\/522226"},{"key":"S0022377825000030_ref11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.16.1207"},{"key":"S0022377825000030_ref16","doi-asserted-by":"publisher","DOI":"10.1063\/1.862017"},{"key":"S0022377825000030_ref1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stw384"},{"key":"S0022377825000030_ref39","doi-asserted-by":"publisher","DOI":"10.1017\/S002237781600088X"},{"key":"S0022377825000030_ref28","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/ac1c77"},{"key":"S0022377825000030_ref42","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/ab29f6"},{"key":"S0022377825000030_ref27","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/ab7661"},{"key":"S0022377825000030_ref12","doi-asserted-by":"publisher","DOI":"10.1063\/1.873374"},{"key":"S0022377825000030_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377822001088"},{"key":"S0022377825000030_ref9","doi-asserted-by":"publisher","DOI":"10.1063\/1.865395"},{"key":"S0022377825000030_ref24","doi-asserted-by":"publisher","DOI":"10.1063\/5.0050389"},{"key":"S0022377825000030_ref40","doi-asserted-by":"publisher","DOI":"10.1063\/1.4973833"},{"key":"S0022377825000030_ref3","doi-asserted-by":"publisher","DOI":"10.1088\/0004-637X\/750\/2\/129"},{"key":"S0022377825000030_ref47","doi-asserted-by":"publisher","DOI":"10.1086\/528708"},{"key":"S0022377825000030_ref23","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/aba59d"},{"key":"S0022377825000030_ref34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.145101"},{"key":"S0022377825000030_ref35","doi-asserted-by":"publisher","DOI":"10.1088\/0741-3335\/49\/11\/009"},{"key":"S0022377825000030_ref25","doi-asserted-by":"publisher","DOI":"10.1126\/science.abg3395"},{"key":"S0022377825000030_ref26","doi-asserted-by":"publisher","DOI":"10.1088\/2041-8205\/810\/2\/L19"},{"key":"S0022377825000030_ref44","first-page":"819","article-title":"Relativistic modes of tearing instability in a background plasma","volume":"56","author":"Zelenyi","year":"1979","journal-title":"Astron. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}],"article-number":"E42"}}