Revising the Nottingham Inversion Instability as a discontinuous transition between two distinct steady states of thermo-field emission from micro-protrusions  

Revising the Nottingham Inversion Instability as a discontinuous transition between two distinct steady states of thermo-field emission from micro-protrusions | 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 Article Revising the Nottingham Inversion Instability as a discontinuous transition between two distinct steady states of thermo-field emission from micro-protrusions Darius Mofakhami, Benjamin Seznec, Philippe Teste, Romaric Landfried, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4705950/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract Since the publication of our article: Unveiling the Nottingham Inversion Instability during the thermo-field emission from refractory metal micro-protrusions [1], we have performed new simulations that have led us to a renewed interpretation of this phenomenon. In this follow-up article, we show that the initial instability is solely due to the postitive feedback loop between temperature and resistive heating that can diverge above a threshold electric field. The Nottingham inversion is not the trigger but brings the negative feedback loop with temperature that can balance the thermal runaway, eventually yielding the observed jump in current and temperature. From this new perspective, we therefore suggest replacing the original term "Instability" by the Nottingham Inversion "Jump". This jump represents an intermediate possibility between the two usual scenarios envisaged to date – a stable transition with increasing voltage from low to high temperature steady states up to the melting temperature versus the occurrence beforehand of a resistive instability. To formally compare this third path with the other two, a stability analysis of the micro-protrusion self heating during electron emission is proposed. For the system to exhibit a jump, it must reach a point where the retroaction of a temperature rise on the Joule heating exceeds the combined negative feedback on the Nottingham effect and the heat evacuation, before this situation reverses at higher temperature. Formal revisions of our original article are given accordingly. Physical sciences/Materials science/Condensed matter physics/Electronic properties and materials Physical sciences/Engineering/Electrical and electronic engineering Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 07 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 06 Aug, 2024 Reviews received at journal 02 Aug, 2024 Reviews received at journal 01 Aug, 2024 Reviews received at journal 31 Jul, 2024 Reviewers agreed at journal 31 Jul, 2024 Reviewers agreed at journal 30 Jul, 2024 Reviewers agreed at journal 30 Jul, 2024 Reviewers agreed at journal 25 Jul, 2024 Reviewers agreed at journal 25 Jul, 2024 Reviewers invited by journal 24 Jul, 2024 Editor assigned by journal 24 Jul, 2024 Editor invited by journal 09 Jul, 2024 Submission checks completed at journal 09 Jul, 2024 First submitted to journal 08 Jul, 2024 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. 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