{"paper_id":"307ca4cc-1251-4224-8205-e024c2c50bec","body_text":"Similarities and Differences between Non-Linear Force Free Fields Produced by Evolution and Extrapolation Techniques | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Similarities and Differences between Non-Linear Force Free Fields Produced by Evolution and Extrapolation Techniques Duncan H Mackay This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7601367/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Jan, 2026 Read the published version in Solar Physics → Version 1 posted 7 You are reading this latest preprint version Abstract Non-Linear Force-Free Fields (NLFFF) play a key role in our understanding of the nature and evolution of coronal magnetic fields.Two of the most common methods for the construction of them are the ''extrapolation\" and ''evolution\" approaches.The aim of the present paper is to compare results from these two approaches when applied to the same boundary data to determine their similarities and differences. To begin with a NLFFF evolution simulation of AR10977 is carried out to produce a time series of the vector field at the lower boundary covering the full life-span of theactive region. Next at eight unique times in this time series, NLFFF extrapolations are constructed using the simulated vector boundary data. The resulting 3D coronal magnetic fields are then compared. During the the early stages in the lifetime of AR10977, when the coronal magnetic field is composed of simply connected field lines, both NLFFFapproaches produce a high level of agreement as long as the full vector field is injected into the extrapolation. When injectionis limited to only strong field locations, a poorer agreement is found. In contrast, once a flux rope has formed during the later stages in the lifetime of the active region poor agreement is found between the two approaches. This indicates that once a flux rope has formed and risen into the corona the information held within the boundary vector field is insufficient to capture the complexity of the 3D coronal magnetic field. This result is also supported by the poor agreement that arises when comparing the relative magnetic helicity between the two modelling approaches. While the present study considers one extrapolationapproach, it is important to repeat the study using alternative extrapolation methods that exist in the published literature. Flares Dynamics Helicity Magnetic Magnetic fields Corona Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 12 Jan, 2026 Read the published version in Solar Physics → Version 1 posted Editorial decision: Revision requested 27 Oct, 2025 Reviews received at journal 24 Oct, 2025 Reviewers agreed at journal 25 Sep, 2025 Reviewers invited by journal 16 Sep, 2025 Editor assigned by journal 12 Sep, 2025 Submission checks completed at journal 12 Sep, 2025 First submitted to journal 12 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-7601367\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":519241640,\"identity\":\"427bbb81-4ace-4f01-98c9-f8deebd7d054\",\"order_by\":0,\"name\":\"Duncan H Mackay\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYDCCGwyMDyCsBLgYMyEtzAYQ1SRoYZMgTQvf7e60yp8/GOTN2XMfPub5wyDP38BjbIBPi+Sds9tu8yQwGO7seW5szNvGYDjjAI9xAj4tBjdyt91mSPjPuOFGGpt0bgMD4wYGHuMDhLQU/khgsAdqYf+d8wfIIEYLA9BhiSBbmHPYgAwGAg6TvJG7WZonjSF5w5lnzNJ/2ySSZxxmK8brfb4buRs//rBhsN1wPI3x44w/Nrb97c2bJfBpQQcSBCNyFIyCUTAKRgERAAAYP0e4NyQ76QAAAABJRU5ErkJggg==\",\"orcid\":\"\",\"institution\":\"University of St Andrews\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Duncan\",\"middleName\":\"H\",\"lastName\":\"Mackay\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-09-12 14:08:22\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-7601367/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-7601367/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s11207-025-02599-6\",\"type\":\"published\",\"date\":\"2026-01-12T16:31:01+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":92111487,\"identity\":\"ee3f1de0-6851-4ba6-9069-c57628118c0e\",\"added_by\":\"auto\",\"created_at\":\"2025-09-24 18:30:18\",\"extension\":\"json\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"acdc-reference\",\"size\":4241,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"7c0872c9faa04042839bd30a2aeac6d0.json\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7601367/v1/ceed13598c8e9c778211d183.json\"},{\"id\":100616689,\"identity\":\"8faddadc-79a7-478e-99f8-33ba0358d6b3\",\"added_by\":\"auto\",\"created_at\":\"2026-01-19 17:45:06\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":4162122,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"NLFFFcomparisonsub1.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7601367/v1_covered_e6350f16-302e-4895-818d-1f13b9549613.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Similarities and Differences between Non-Linear Force Free Fields Produced by Evolution and Extrapolation Techniques\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"solar-physics\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"sola\",\"sideBox\":\"Learn more about [Solar Physics](http://link.springer.com/journal/11207)\",\"snPcode\":\"11207\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11207/3\",\"title\":\"Solar Physics\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"Flares, Dynamics; Helicity, Magnetic; Magnetic fields, Corona\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7601367/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7601367/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"Non-Linear Force-Free Fields (NLFFF) play a key role in our understanding of the nature and evolution of coronal magnetic fields.Two of the most common methods for the construction of them are the ''extrapolation\\\" and ''evolution\\\" approaches.The aim of the present paper is to compare results from these two approaches when applied to the same boundary data to determine their similarities and differences. To begin with a NLFFF evolution simulation of AR10977 is carried out to produce a time series of the vector field at the lower boundary covering the full life-span of theactive region. Next at eight unique times in this time series, NLFFF extrapolations are constructed using the simulated vector boundary data. The resulting 3D coronal magnetic fields are then compared. During the the early stages in the lifetime of AR10977, when the coronal magnetic field is composed of simply connected field lines, both NLFFFapproaches produce a high level of agreement as long as the full vector field is injected into the extrapolation. When injectionis limited to only strong field locations, a poorer agreement is found. In contrast, once a flux rope has formed during the later stages in the lifetime of the active region poor agreement is found between the two approaches. This indicates that once a flux rope has formed and risen into the corona the information held within the boundary vector field is insufficient to capture the complexity of the 3D coronal magnetic field. This result is also supported by the poor agreement that arises when comparing the relative magnetic helicity between the two modelling approaches. While the present study considers one extrapolationapproach, it is important to repeat the study using alternative extrapolation methods that exist in the published literature.\",\"manuscriptTitle\":\"Similarities and Differences between Non-Linear Force Free Fields Produced by Evolution and Extrapolation Techniques\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-09-24 18:30:14\",\"doi\":\"10.21203/rs.3.rs-7601367/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2025-10-27T13:11:02+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2025-10-24T15:32:24+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"52035862483647691134074478489048685902\",\"date\":\"2025-09-25T14:53:25+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2025-09-16T11:33:34+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2025-09-12T14:34:22+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2025-09-12T14:34:19+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Solar Physics\",\"date\":\"2025-09-12T14:01:37+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"solar-physics\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"sola\",\"sideBox\":\"Learn more about [Solar Physics](http://link.springer.com/journal/11207)\",\"snPcode\":\"11207\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11207/3\",\"title\":\"Solar Physics\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"85342ef2-b1e2-45c2-b496-8505bc99440a\",\"owner\":[],\"postedDate\":\"September 24th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-01-19T17:08:42+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-7601367\",\"link\":\"https://doi.org/10.1007/s11207-025-02599-6\",\"journal\":{\"identity\":\"solar-physics\",\"isVorOnly\":false,\"title\":\"Solar Physics\"},\"publishedOn\":\"2026-01-12 16:31:01\",\"publishedOnDateReadable\":\"January 12th, 2026\"},\"versionCreatedAt\":\"2025-09-24 18:30:14\",\"video\":\"\",\"vorDoi\":\"10.1007/s11207-025-02599-6\",\"vorDoiUrl\":\"https://doi.org/10.1007/s11207-025-02599-6\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-7601367\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-7601367\",\"identity\":\"rs-7601367\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}