The Physics of the Stable Phase-Locked Attractor in Spheromak Plasma

The Physics of the Stable Phase-Locked Attractor in Spheromak Plasma | 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Article The Physics of the Stable Phase-Locked Attractor in Spheromak Plasma Oleg Agamalov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9449730/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The generation and sustainment of stable, high-field Spheromak configurations remain critically limited by global tearing and tilt instabilities during helicity injection. This paper presents a novel theoretical and mathematical framework, which resolves this limitation by treating forced magnetic reconnection as an actively controlled Hamiltonian chaos system. We demonstrate that by applying High-Frequency Adaptive Stochastic Resonance ( HFASR ) - specifically, launching localized shear Alfvén waves tuned to the macroscopic magnetic shear length ( L ) - we can surgically induce micro-scale stochasticity at targeted rational q -surfaces. Using a phenomenological systems-dynamic framework coupling macroscopic scaling laws with the Klein-Kramers formalism, we theoretically demonstrate that this localized tearing acts as a 'stochastic pump.' The resulting energy released from destroyed Kolmogorov-Arnold-Moser ( KAM ) surfaces initiates a robust inverse turbulence cascade. Most crucially, we establish the existence of a "Phase-Locked Attractor" in the system's phase space. Provided the external radio-frequency ( RF ) modulation is phase-locked to the plasma's local Kramers transition rate ( r k ), the chaotic eddies self-organize, continuously transferring magnetic helicity to the global Taylor state ( ψ 0 ). Dynamic Grad-Shafranov simulations demonstrate that this mechanism successfully amplifies a 3 T Coaxial Helicity Injection ( CHI ) seed to a stable > 12 T core field without exceeding the Chirikov threshold for global stochasticity ( S < 1.0 ). This validates the proposed framework as a viable pathway for maintaining impenetrable, nested KAM surfaces during rapid, non-equilibrium field amplification, opening the door for compact, high-field aneutronic fusion topologies. Spheromak Adaptive Stochastic Resonance Inverse Magnetic Cascade Hamiltonian Topology Magnetic Reconnection Aneutronic Fusion (p-11B) Hot-Ion Mode Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-9449730","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626067071,"identity":"4a27abf8-6f9b-4ad5-a598-6754e2b6f9d9","order_by":0,"name":"Oleg Agamalov","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYDACdmTGByBmY8etGAKYkRiMM0BamPGoxtDCzIMiggPwMzMffvHjl100fzPzMWmbX9vk+ZgZGD98zMGtRbKZLc2yty85d8ZhtjTp3L7bhm3MDMySM7fh1mJwmMfMgLeHObfhMI+xcW7PbUagFjZmXrxa+L8Z/u2pz50P0mLZc9ueCC08zI95fhzO3XCYx/Axw4/biQS1AP1ixizbcDx342G2xIe9DbeT25gZm/H6hZ+9+fHHN3+qc+cdbz5w4Mef27bz25sPfviIRwsQsEkwtkGZEAZjA171QMD8geEPjP0Hn8JRMApGwSgYqQAAPRFPmhb8MkYAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Oleg","middleName":"","lastName":"Agamalov","suffix":""}],"badges":[],"createdAt":"2026-04-17 13:26:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9449730/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9449730/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108976412,"identity":"b9cca5f2-bb74-424a-8e0f-3eacacbb0034","added_by":"auto","created_at":"2026-05-11 11:17:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":560374,"visible":true,"origin":"","legend":"","description":"","filename":"SASRPH.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9449730/v1_covered_18be467a-f1d5-4496-8fce-628bf722114b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Physics of the Stable Phase-Locked Attractor in Spheromak Plasma","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Spheromak, Adaptive Stochastic Resonance, Inverse Magnetic Cascade, Hamiltonian Topology, Magnetic Reconnection, Aneutronic Fusion (p-11B), Hot-Ion Mode","lastPublishedDoi":"10.21203/rs.3.rs-9449730/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9449730/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe generation and sustainment of stable, high-field Spheromak configurations remain critically limited by global tearing and tilt instabilities during helicity injection. This paper presents a novel theoretical and mathematical framework, which resolves this limitation by treating forced magnetic reconnection as an actively controlled Hamiltonian chaos system. We demonstrate that by applying High-Frequency Adaptive Stochastic Resonance (\u003cem\u003eHFASR\u003c/em\u003e) - specifically, launching localized shear Alfv\u0026eacute;n waves tuned to the macroscopic magnetic shear length (\u003cem\u003eL\u003c/em\u003e) - we can surgically induce micro-scale stochasticity at targeted rational \u003cem\u003eq\u003c/em\u003e-surfaces. Using a phenomenological systems-dynamic framework coupling macroscopic scaling laws with the Klein-Kramers formalism, we theoretically demonstrate that this localized tearing acts as a 'stochastic pump.' The resulting energy released from destroyed Kolmogorov-Arnold-Moser (\u003cem\u003eKAM\u003c/em\u003e) surfaces initiates a robust inverse turbulence cascade. Most crucially, we establish the existence of a \"Phase-Locked Attractor\" in the system's phase space. Provided the external radio-frequency (\u003cem\u003eRF\u003c/em\u003e) modulation is phase-locked to the plasma's local Kramers transition rate (\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e), the chaotic eddies self-organize, continuously transferring magnetic helicity to the global Taylor state (\u003cem\u003eψ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e). Dynamic Grad-Shafranov simulations demonstrate that this mechanism successfully amplifies a \u003cem\u003e3 T\u003c/em\u003e Coaxial Helicity Injection (\u003cem\u003eCHI\u003c/em\u003e) seed to a stable\u0026thinsp;\u003cem\u003e\u0026gt;\u0026thinsp;12 T\u003c/em\u003e core field without exceeding the Chirikov threshold for global stochasticity (\u003cem\u003eS\u0026thinsp;\u0026lt;\u0026thinsp;1.0\u003c/em\u003e). This validates the proposed framework as a viable pathway for maintaining impenetrable, nested \u003cem\u003eKAM\u003c/em\u003e surfaces during rapid, non-equilibrium field amplification, opening the door for compact, high-field aneutronic fusion topologies.\u003c/p\u003e","manuscriptTitle":"The Physics of the Stable Phase-Locked Attractor in Spheromak Plasma","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-22 04:02:13","doi":"10.21203/rs.3.rs-9449730/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e98d74ad-0ff8-477b-98a4-a48e787ada3b","owner":[],"postedDate":"April 22nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-22T04:02:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-22 04:02:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9449730","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9449730","identity":"rs-9449730","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}