{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:56:44Z","timestamp":1791205004132,"version":"4.1.0"},"reference-count":53,"publisher":"AIP Publishing","issue":"10","license":[{"start":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T00:00:00Z","timestamp":1790985600000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>We present a generalized theoretical framework for Second-Harmonic Orthogonally Polarized Dispersion Interferometry (SHOP-DI) and the diagnostic\u2019s implementation for time-resolved electron areal-density measurements of pulsed-power Magnetically Insulated Transmission Line (MITL) electrode plasmas. The theoretical treatment extends standard SHOP-DI analysis by deriving the detected intensity response for arbitrary second-harmonic polarization angles, establishing a detector-bandwidth-limited criterion for the maximum trackable rate of change in electron areal density, modeling a counter-rotating phase-control-window system that enables reproducible phase-offset calibration, and introducing a power-normalized analysis method which separates refractive-index-induced phase shifts from static channel imbalance and common-mode optical-power fluctuations. Guided by these developments, the diagnostic was redesigned for operation on Sandia National Laboratories\u2019 (SNL\u2019s) 1 MA Mykonos accelerator, where MITL plasmas evolve on nanosecond time scales within sub-mm Anode\u2013Cathode (A\u2013K) gaps. The implemented system combines a 2\u00a0GHz bandwidth, corresponding to a maximum measurable areal-density rate of change of 4.8 \u00d7 1016 1\/cm2\/ns, with an overlapping 1\/e2 probing beam waist diameter of \u223c100\u03bcm. Improved optical throughput and optomechanical stiffness enabled the experiments at Mykonos to achieve a noise-limited 1\u03c3 areal-density uncertainty of 1.6 \u00d7 1014 1\/cm2. These results provide design criteria for future SHOP-DI systems and demonstrate a high-bandwidth, high-sensitivity design useful for pulsed-power electrode plasma measurements.<\/jats:p>","DOI":"10.1063\/5.0350688","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:41:37Z","timestamp":1791204097000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Generalized theory of second-harmonic orthogonally polarized dispersion interferometry and implementation for pulsed power electrode plasma measurements"],"prefix":"10.1063","volume":"97","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1531-6465","authenticated-orcid":false,"given":"Nathan R.","family":"Hines","sequence":"first","affiliation":[{"name":"Sandia National Laboratories 1 , Albuquerque, New Mexico 87185,","place":["USA"]},{"name":"Electrical and Computer Engineering Department, University of New Mexico 2 , Albuquerque, New Mexico 87106,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0459-0119","authenticated-orcid":false,"given":"Jens","family":"Schwarz","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories 1 , Albuquerque, New Mexico 87185,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1499-7986","authenticated-orcid":false,"given":"Thomas J.","family":"Awe","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories 1 , Albuquerque, New Mexico 87185,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3750-0885","authenticated-orcid":false,"given":"Mark A.","family":"Gilmore","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, University of New Mexico 2 , Albuquerque, New Mexico 87106,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,5]]},"reference":[{"key":"2026100508413275700_c1","doi-asserted-by":"publisher","first-page":"070501","DOI":"10.1063\/5.0007476","article-title":"Review of pulsed power-driven high energy density physics research on Z at Sandia","volume":"27","year":"2020","journal-title":"Phys. Plasmas"},{"key":"2026100508413275700_c2","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1109\/PPC.1997.679375","article-title":"PBFA-Z vacuum section design using TLCODE simulations","volume-title":"Digest of Technical Papers. 11th IEEE International Pulsed Power Conference (Cat. No.97CH36127)","year":"1997"},{"key":"2026100508413275700_c3","doi-asserted-by":"publisher","first-page":"120401","DOI":"10.1103\/physrevstab.12.120401","article-title":"55-TW magnetically insulated transmission-line system: Design, simulations, and performance","volume":"12","year":"2009","journal-title":"Phys. Rev. Spec. Top.-Accel. Beams"},{"key":"2026100508413275700_c4","doi-asserted-by":"publisher","first-page":"030401","DOI":"10.1103\/physrevstab.18.030401","article-title":"Requirements for self-magnetically insulated transmission lines","volume":"18","year":"2015","journal-title":"Phys. Rev. ST Accel. Beams"},{"key":"2026100508413275700_c5","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1098\/rspa.1928.0091","article-title":"Electron emission in intense electric fields","volume":"119","year":"1928","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026100508413275700_c6","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1098\/rspa.1928.0222","article-title":"The effect of the image force on the emission and reflexion of electrons by metals","volume":"121","year":"1928","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026100508413275700_c7","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1116\/1.2827505","article-title":"Physics of generalized Fowler\u2013Nordheim-type equations","volume":"26","year":"2008","journal-title":"J.\u00a0Vac. Sci. Technol., B"},{"key":"2026100508413275700_c8","doi-asserted-by":"publisher","first-page":"5248","DOI":"10.1063\/1.322600","article-title":"Physical properties of thin-film field emission cathodes with molybdenum cones","volume":"47","year":"1976","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026100508413275700_c9","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1103\/physrev.2.450","article-title":"The effect of space charge and residual gases on thermionic currents in high vacuum","volume":"2","year":"1913","journal-title":"Phys. Rev."},{"key":"2026100508413275700_c10","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1103\/physrev.102.1464","article-title":"Thermionic emission, field emission, and the transition region","volume":"102","year":"1956","journal-title":"Phys. Rev."},{"key":"2026100508413275700_c11","doi-asserted-by":"publisher","first-page":"2855","DOI":"10.1063\/1.1713118","article-title":"Vacuum voltage breakdown as a thermal instability of the emitting protrusion","volume":"35","year":"1964","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026100508413275700_c12","doi-asserted-by":"crossref","unstructured":"F.\n            Rohrbach\n          , \u201cIsolation sous vide,\u201d Technical Report No. CERN-71-05, European Organization for Nuclear Research, 1971.","DOI":"10.51257\/a-v1-d222"},{"key":"2026100508413275700_c13","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1070\/pu1975v018n01abeh004693","article-title":"Explosive emission of electrons","volume":"18","year":"1975","journal-title":"Sov. Phys. Usp."},{"key":"2026100508413275700_c14","unstructured":"D.\n            Hinshelwood\n          , \u201cExplosive emission cathode plasmas in intense relativistic electron beam diodes,\u201d Ph.D. dissertation (Massachusetts Institute of Technology, 1985)."},{"key":"2026100508413275700_c15","doi-asserted-by":"publisher","first-page":"2241","DOI":"10.1109\/tps.2015.2431317","article-title":"Hydrodynamics of the molten metal during the crater formation on the cathode surface in a vacuum arc","volume":"43","year":"2015","journal-title":"IEEE Trans. Plasma Sci."},{"key":"2026100508413275700_c16","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.1109\/tps.2017.2713484","article-title":"Semiempirical model of the microcrater formation in the cathode spot of a vacuum arc","volume":"45","year":"2017","journal-title":"IEEE Trans. Plasma Sci."},{"key":"2026100508413275700_c17","doi-asserted-by":"publisher","first-page":"015021","DOI":"10.1088\/1361-6595\/ab62da","article-title":"Cathode and plasma phenomena in vacuum-arc sources of hydrogen isotope ions: I. Desorption of hydrogen isotopes during the operation of vacuum arc cathode spots","volume":"29","year":"2020","journal-title":"Plasma Sources Sci. Technol."},{"key":"2026100508413275700_c18","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1063\/1.1702243","article-title":"The initiation of electrical breakdown in vacuum","volume":"23","year":"1952","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026100508413275700_c19","article-title":"Electrical breakdown and discharge in a vacuum"},{"key":"2026100508413275700_c20","doi-asserted-by":"publisher","first-page":"4536","DOI":"10.1063\/1.1660959","article-title":"Processes involved in the triggering of vacuum breakdown by low-velocity microparticles","volume":"43","year":"1972","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026100508413275700_c21","doi-asserted-by":"publisher","first-page":"3832","DOI":"10.1063\/1.1663870","article-title":"Microparticle-initiated vacuum breakdown\u2013some possible mechanisms","volume":"45","year":"1974","journal-title":"J.\u00a0Appl. Phys."},{"key":"2026100508413275700_c22","volume-title":"High Voltage Vacuum Insulation: Basic Concepts and Technological Practice","year":"1995"},{"key":"2026100508413275700_c23","volume-title":"The Emission of Electricity from Hot Bodies","year":"1921","edition":"2"},{"issue":"11","key":"2026100508413275700_c24","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1007\/BF01391020","article-title":"Zur Theorie der thermischen Emission und der Reflexion von Elektronen an Metallen","volume":"46","year":"1928","journal-title":"Z. Phys."},{"issue":"6","key":"2026100508413275700_c25","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1103\/PhysRev.21.623","article-title":"Electron emission from metals as a function of temperature","volume":"21","year":"1923","journal-title":"Phys. Rev."},{"key":"2026100508413275700_c26","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1515\/zpch-1889-0108","article-title":"\u00dcber die dissociationsw\u00e4rme und den einfluss der temperatur auf den dissociationsgrad der elektrolyte","volume":"4U","year":"1889","journal-title":"Z. Phys. Chem."},{"key":"2026100508413275700_c27","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/0042-207x(62)90978-8","article-title":"Thermal desorption of gases","volume":"12","year":"1962","journal-title":"Vacuum"},{"key":"2026100508413275700_c28","first-page":"49","volume-title":"\u00dcber die Interferenz von Eigenschwingungen als Ursache von Energieschwankungen und Chemischer Umsetzungen","year":"1997"},{"key":"2026100508413275700_c29","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1109\/94.788747","article-title":"The effect of electrode contamination, cleaning and conditioning on high-energy pulsed-power device performance","volume":"6","year":"1999","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"2026100508413275700_c30","doi-asserted-by":"publisher","first-page":"465002","DOI":"10.1088\/1361-648x\/aae4af","article-title":"Water desorption from rapidly-heated metal oxide surfaces\u2013first principles, molecular dynamics, and the Temkin isotherm","volume":"30","year":"2018","journal-title":"J.\u00a0Phys.: Condens. Matter"},{"key":"2026100508413275700_c31","unstructured":"N. R.\n            Hines\n          , \u201cDeveloping a dispersion interferometer for characterizing power flow plasma formation and transport studies,\u201d Ph.D. thesis, University of New Mexico, Albuquerque, New Mexico, 2026."},{"key":"2026100508413275700_c32","doi-asserted-by":"publisher","first-page":"030402","DOI":"10.1103\/physrevstab.18.030402","article-title":"Computational analysis of current-loss mechanisms in a post-hole convolute driven by magnetically insulated transmission lines","volume":"18","year":"2015","journal-title":"Phys. Rev. Spec. Top.-Accel. Beams"},{"key":"2026100508413275700_c33","doi-asserted-by":"publisher","first-page":"070401","DOI":"10.1103\/physrevaccelbeams.22.070401","article-title":"Electrode contaminant plasma effects in 107-A Z pinch accelerators","volume":"22","year":"2019","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c34","doi-asserted-by":"publisher","first-page":"120401","DOI":"10.1103\/physrevaccelbeams.22.120401","article-title":"Current transport and loss mechanisms in the Z accelerator","volume":"22","year":"2019","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c35","doi-asserted-by":"publisher","first-page":"080401","DOI":"10.1103\/physrevaccelbeams.23.080401","article-title":"Numerical simulations of enhanced ion current losses in the inner magnetically insulated transmission line of the Z accelerator","volume":"23","year":"2020","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c36","doi-asserted-by":"publisher","first-page":"060401","DOI":"10.1103\/physrevaccelbeams.24.060401","article-title":"Magnetized particle transport in multi-MA accelerators","volume":"24","year":"2021","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c37","doi-asserted-by":"publisher","first-page":"040401","DOI":"10.1103\/physrevaccelbeams.26.040401","article-title":"Electrode plasma formation and melt in Z-pinch accelerators","volume":"26","year":"2023","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c38","doi-asserted-by":"publisher","first-page":"062702","DOI":"10.1063\/5.0276238","article-title":"Modeled sensitivity of multi-MA accelerator performance to electrode contaminant inventory","volume":"32","year":"2025","journal-title":"Phys. Plasmas"},{"key":"2026100508413275700_c39","doi-asserted-by":"publisher","first-page":"040401","DOI":"10.1103\/physrevstab.13.040401","article-title":"107-A load-current B-dot monitor: Simulations, design, and performance","volume":"13","year":"2010","journal-title":"Phys. Rev. Spec. Top.-Accel. Beams"},{"key":"2026100508413275700_c40","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1109\/tps.2010.2042971","article-title":"Circuit model for driving three-dimensional resistive MHD wire array Z-pinch calculations","volume":"38","year":"2010","journal-title":"IEEE Trans. Plasma Sci."},{"key":"2026100508413275700_c41","doi-asserted-by":"publisher","first-page":"010401","DOI":"10.1103\/physrevaccelbeams.20.010401","article-title":"Experimental study of current loss and plasma formation in the Z machine post-hole convolute","volume":"20","year":"2017","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c42","doi-asserted-by":"publisher","first-page":"090401","DOI":"10.1103\/physrevaccelbeams.22.090401","article-title":"Large time-varying inductance load for studying power flow on the Z machine","volume":"22","year":"2019","journal-title":"Phys. Rev. Accel. Beams"},{"key":"2026100508413275700_c43","doi-asserted-by":"publisher","first-page":"1010","DOI":"10.1063\/1.1144170","article-title":"Dispersion interferometer for controlled fusion devices","volume":"64","year":"1993","journal-title":"Rev. Sci. Instrum."},{"key":"2026100508413275700_c44","doi-asserted-by":"publisher","first-page":"113501","DOI":"10.1063\/1.3258199","article-title":"Electron density measurements of a field-reversed configuration plasma using a novel compact ultrastable second-harmonic interferometer","volume":"80","year":"2009","journal-title":"Rev. Sci. Instrum."},{"key":"2026100508413275700_c45","doi-asserted-by":"publisher","first-page":"113505","DOI":"10.1063\/5.0101687","article-title":"A fiber-coupled dispersion interferometer for density measurements of pulsed power transmission line electron sheaths on Sandia\u2019s Z machine","volume":"93","year":"2022","journal-title":"Rev. Sci. Instrum."},{"key":"2026100508413275700_c46","unstructured":"N. R.\n            Hines\n          \n          , \u201cDevelopment of a colinear second-harmonic orthogonal polarization (SHOP) interferometer for electron areal density measurements in magnetically insulated transmission lines (MITLs),\u201d Technical Report No. SAND2023-10581, Sandia National Laboratory (SNL-NM) Albuquerque, NM, 2023."},{"key":"2026100508413275700_c47","unstructured":"D. C.\n            Lamppa\n          , S. C.Simpson, B. T.Hutsel, G. R.Laity, M. E.Cuneo, and D. V.Rose, \u201cAssessment of electrode contamination mitigation at 0.5 MA scale,\u201d Technical Report No. SAND2021-12691, Sandia National Laboratories (SNL-NM), Albuquerque, NM, 2021."},{"key":"2026100508413275700_c48","doi-asserted-by":"publisher","first-page":"101144","DOI":"10.1016\/j.hedp.2024.101144","article-title":"Mykonos: A pulsed power driver for science and innovation","volume":"53","year":"2024","journal-title":"High Energy Density Phys."},{"key":"2026100508413275700_c49","first-page":"XII, 490","volume-title":"Introduction to Plasma Physics and Controlled Fusion","year":"2016","edition":"3"},{"key":"2026100508413275700_c50","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1109\/t-aiee.1928.5055024","article-title":"Certain topics in telegraph transmission theory","volume":"47","year":"1928","journal-title":"Trans. Am. Inst. Electr. Eng."},{"key":"2026100508413275700_c51","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1109\/jrproc.1949.232969","article-title":"Communication in the presence of noise","volume":"37","year":"1949","journal-title":"Proc. IRE"},{"key":"2026100508413275700_c52","article-title":"DIP, a high-power IR dispersion interferometer using OpGaAs crystal for electron density measurement"},{"key":"2026100508413275700_c53","year":"2024"}],"container-title":["Review of Scientific Instruments"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/rsi\/article-pdf\/doi\/10.1063\/5.0350688\/21160963\/103511_1_5.0350688.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/rsi\/article-pdf\/doi\/10.1063\/5.0350688\/21160963\/103511_1_5.0350688.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T12:41:40Z","timestamp":1791204100000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/rsi\/article\/97\/10\/103511\/3405907\/Generalized-theory-of-second-harmonic-orthogonally"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":53,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0350688","relation":{},"ISSN":["0034-6748","1089-7623"],"issn-type":[{"value":"0034-6748","type":"print"},{"value":"1089-7623","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10]]},"published":{"date-parts":[[2026,10,1]]},"article-number":"103511"}}