{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T16:57:03Z","timestamp":1767373023951,"version":"3.34.0"},"reference-count":82,"publisher":"American Astronomical Society","issue":"2","license":[{"start":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T00:00:00Z","timestamp":1738108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T00:00:00Z","timestamp":1738108800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100006132","name":"DOE \u2223 Office of Science","doi-asserted-by":"publisher","award":["DE-SC002436"],"award-info":[{"award-number":["DE-SC002436"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["ApJ"],"published-print":{"date-parts":[[2025,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In astrophysical relativistic plasmas, Alfv\u00e9nic turbulence exists across a wide range of scales. Similar to a nonrelativistic case, this turbulence can be influenced by the tearing instability. We argue that in an ultrarelativistic pair plasma the tearing effects become significant at the critical scale given by <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mi>a<\/mml:mi>\n                           <mml:mi>t<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>\u223c<\/mml:mo>\n                        <mml:msub>\n                           <mml:mi>d<\/mml:mi>\n                           <mml:mi>rel<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:msup>\n                           <mml:mfenced close=\")\" open=\"(\">\n                              <mml:mrow>\n                                 <mml:msub>\n                                    <mml:mi>L<\/mml:mi>\n                                    <mml:mo>\u22a5<\/mml:mo>\n                                 <\/mml:msub>\n                                 <mml:mo>\/<\/mml:mo>\n                                 <mml:msub>\n                                    <mml:mi>d<\/mml:mi>\n                                    <mml:mi>rel<\/mml:mi>\n                                 <\/mml:msub>\n                              <\/mml:mrow>\n                           <\/mml:mfenced>\n                           <mml:mrow>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mo>\/<\/mml:mo>\n                              <mml:mo stretchy=\"false\">(<\/mml:mo>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mn>5<\/mml:mn>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                           <\/mml:mrow>\n                        <\/mml:msup>\n                     <\/mml:math>\n                  <\/jats:inline-formula>, where <jats:italic>L<\/jats:italic>\n                  <jats:sub>\u22a5<\/jats:sub> represents the outer scale of the turbulence and <jats:italic>d<\/jats:italic>\n                  <jats:sub>rel<\/jats:sub> the relativistic electron inertial scale. Here <jats:italic>n<\/jats:italic> = 1 corresponds to the Harris magnetic configurations, while <jats:italic>n<\/jats:italic> = 2 applies to localized (non-Harris) magnetic profiles of turbulence-generated current sheets. Below the critical scale, the energy spectrum of magnetic fluctuations steepens to <jats:italic>W<\/jats:italic>(<jats:italic>k<\/jats:italic>)<jats:italic>dk<\/jats:italic> \u221d <jats:italic>k<\/jats:italic>\n                  <jats:sup>\u2212(7<jats:italic>n<\/jats:italic>+2)\/3<jats:italic>n<\/jats:italic>\n                  <\/jats:sup>\n                  <jats:italic>dk<\/jats:italic>. However, this happens only when <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mover accent=\"true\">\n                           <mml:mi>\u03c3<\/mml:mi>\n                           <mml:mo>\u02dc<\/mml:mo>\n                        <\/mml:mover>\n                        <mml:mo>\u226a<\/mml:mo>\n                        <mml:msup>\n                           <mml:mfenced close=\")\" open=\"(\">\n                              <mml:mrow>\n                                 <mml:msub>\n                                    <mml:mi>L<\/mml:mi>\n                                    <mml:mo>\u22a5<\/mml:mo>\n                                 <\/mml:msub>\n                                 <mml:mo>\/<\/mml:mo>\n                                 <mml:msub>\n                                    <mml:mi>d<\/mml:mi>\n                                    <mml:mi>rel<\/mml:mi>\n                                 <\/mml:msub>\n                              <\/mml:mrow>\n                           <\/mml:mfenced>\n                           <mml:mrow>\n                              <mml:mo stretchy=\"false\">(<\/mml:mo>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mo>\/<\/mml:mo>\n                              <mml:mo stretchy=\"false\">(<\/mml:mo>\n                              <mml:mn>4<\/mml:mn>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mn>5<\/mml:mn>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                           <\/mml:mrow>\n                        <\/mml:msup>\n                     <\/mml:math>\n                  <\/jats:inline-formula>, where <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mover accent=\"true\">\n                           <mml:mrow>\n                              <mml:mi>\u03c3<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:mo>\u02dc<\/mml:mo>\n                           <\/mml:mrow>\n                        <\/mml:mover>\n                     <\/mml:math>\n                  <\/jats:inline-formula> is the magnetization parameter based on the magnetic fluctuations. If the opposite inequality holds, the Alfv\u00e9nic cascade is instead affected by charge starvation at scales below <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mi>a<\/mml:mi>\n                           <mml:mi>ch<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:mo>\u223c<\/mml:mo>\n                        <mml:msub>\n                           <mml:mi>d<\/mml:mi>\n                           <mml:mi>rel<\/mml:mi>\n                        <\/mml:msub>\n                        <mml:msup>\n                           <mml:mfenced close=\")\" open=\"(\">\n                              <mml:mrow>\n                                 <mml:msub>\n                                    <mml:mi>d<\/mml:mi>\n                                    <mml:mi>rel<\/mml:mi>\n                                 <\/mml:msub>\n                                 <mml:mo>\/<\/mml:mo>\n                                 <mml:msub>\n                                    <mml:mi>L<\/mml:mi>\n                                    <mml:mo>\u22a5<\/mml:mo>\n                                 <\/mml:msub>\n                              <\/mml:mrow>\n                           <\/mml:mfenced>\n                           <mml:mrow>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>\/<\/mml:mo>\n                              <mml:mn>3<\/mml:mn>\n                           <\/mml:mrow>\n                        <\/mml:msup>\n                        <mml:msup>\n                           <mml:mover accent=\"true\">\n                              <mml:mi>\u03c3<\/mml:mi>\n                              <mml:mo>\u02dc<\/mml:mo>\n                           <\/mml:mover>\n                           <mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mo>\/<\/mml:mo>\n                              <mml:mn>3<\/mml:mn>\n                           <\/mml:mrow>\n                        <\/mml:msup>\n                     <\/mml:math>\n                  <\/jats:inline-formula>, and the energy spectrum becomes steeper than <jats:italic>W<\/jats:italic>(<jats:italic>k<\/jats:italic>)<jats:italic>dk<\/jats:italic> \u221d <jats:italic>k<\/jats:italic>\n                  <jats:sup>\u22123<\/jats:sup>\n                  <jats:italic>dk<\/jats:italic>. When <jats:italic>d<\/jats:italic>\n                  <jats:sub>rel<\/jats:sub> is replaced by its nonrelativistic equivalent, our results agree with the nonrelativistic analysis of N. F. Loureiro &amp; S. Boldyrev (2018). In the Harris case <jats:italic>n<\/jats:italic> = 1, they agree with the recent relativistic studies by I. Demidov &amp; Y. Lyubarsky.<\/jats:p>","DOI":"10.3847\/1538-4357\/ada28a","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T10:00:57Z","timestamp":1738144857000},"page":"232","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Tearing-mediated Alfv\u00e9nic Turbulence in a Relativistic Plasma"],"prefix":"10.3847","volume":"979","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6252-5169","authenticated-orcid":true,"given":"Stanislav","family":"Boldyrev","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9755-6563","authenticated-orcid":true,"given":"Nuno 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