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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">     <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en" xmlns:og="http://ogp.me/ns#" xmlns:fb="http://ogp.me/ns/fb#"> <head> <title>Statistical Properties of Schottky Spectra - CERN Document Server</title> <link href='https://framework.web.cern.ch/framework/2.0/fonts/PTSansWeb/PTSansWeb.css' rel='stylesheet' type='text/css' /> <link rel="stylesheet" href="https://cds.cern.ch/img/invenio.css?v=20141127" type="text/css" /> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_theme/css/cern_theme.css?v=20141127" type="text/css" /> <link rel="stylesheet"href="/css/font-awesome.min.css"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"/> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_toolbar/css/toolbar.css" type="text/css" />    <link rel="canonical" href="https://cds.cern.ch/record/2901223/export/hm" /> <link rel="alternate" hreflang="el" href="https://cds.cern.ch/record/2901223/export/hm?ln=el" /> <link rel="alternate" hreflang="fr" href="https://cds.cern.ch/record/2901223/export/hm?ln=fr" /> <link rel="alternate" hreflang="bg" href="https://cds.cern.ch/record/2901223/export/hm?ln=bg" /> <link rel="alternate" hreflang="zh-TW" href="https://cds.cern.ch/record/2901223/export/hm?ln=zh_TW" /> <link rel="alternate" hreflang="pt" href="https://cds.cern.ch/record/2901223/export/hm?ln=pt" /> <link rel="alternate" hreflang="no" href="https://cds.cern.ch/record/2901223/export/hm?ln=no" /> <link rel="alternate" hreflang="hr" href="https://cds.cern.ch/record/2901223/export/hm?ln=hr" /> <link rel="alternate" hreflang="ca" href="https://cds.cern.ch/record/2901223/export/hm?ln=ca" /> <link rel="alternate" hreflang="de" href="https://cds.cern.ch/record/2901223/export/hm?ln=de" /> <link rel="alternate" hreflang="it" href="https://cds.cern.ch/record/2901223/export/hm?ln=it" /> <link rel="alternate" hreflang="zh-CN" href="https://cds.cern.ch/record/2901223/export/hm?ln=zh_CN" /> <link rel="alternate" hreflang="sv" href="https://cds.cern.ch/record/2901223/export/hm?ln=sv" /> <link rel="alternate" hreflang="sk" href="https://cds.cern.ch/record/2901223/export/hm?ln=sk" /> <link rel="alternate" hreflang="en" href="https://cds.cern.ch/record/2901223/export/hm?ln=en" /> <link rel="alternate" hreflang="pl" href="https://cds.cern.ch/record/2901223/export/hm?ln=pl" /> <link rel="alternate" hreflang="ru" href="https://cds.cern.ch/record/2901223/export/hm?ln=ru" /> <link rel="alternate" hreflang="ka" href="https://cds.cern.ch/record/2901223/export/hm?ln=ka" /> <link rel="alternate" hreflang="ja" href="https://cds.cern.ch/record/2901223/export/hm?ln=ja" /> <link rel="alternate" hreflang="es" href="https://cds.cern.ch/record/2901223/export/hm?ln=es" /> <link rel="alternate" type="application/rss+xml" title="CERN Document Server RSS" href="/rss?ln=en" /> <link rel="search" type="application/opensearchdescription+xml" href="https://cds.cern.ch/opensearchdescription" title="CERN Document Server" /> <link rel="unapi-server" type="application/xml" title="unAPI" href="https://cds.cern.ch/unapi" /> <link rel="apple-touch-icon" href="/apple-touch-icon.png"/> <link rel="apple-touch-icon-precomposed" href="/apple-touch-icon-precomposed.png"/> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta http-equiv="Content-Language" content="en" /> <meta name="description" content="Schottky signals are used for non-invasive beam diagnostics as they contain information on various beam and machine parameters. The instantaneous Schottky signal is, however, only a single realisation of a random process, implicitly depending on the discrete distribution of synchrotron and betatron amplitudes and phases among the particles. To estimate the expected value of the Schottky power spectrum, and reveal the inner structure of the Bessel satellites described by the theory, the averaging of instantaneous Schottky spectra is required. This study describes this procedure quantitatively by analysing the statistical properties of the Schottky signals, including the expected value and variance of Schottky power spectra. Furthermore, we investigate how these quantities evolve with the number of particles in the bunch, the observed harmonic of the revolution frequency, the distribution of synchrotron oscillation amplitudes, and the bunch profile. The theoretical findings are compared against macro-particle simulations as well as Monte Carlo computations. Lannoy, Christophe; Alves, Diogo; Łasocha, Kacper; Mounet, Nicolas; Pieloni, Tatiana" /> <meta name="keywords" content="simulation, synchrotron, betatron, dipole, diagnostics" /> <script type="text/javascript" src="https://cds.cern.ch/js/jquery.min.js"></script>  <link rel="stylesheet" href="https://cds.cern.ch/img/webnews.css" type="text/css" />  <script type="text/javascript" src="https://cds.cern.ch/js/webnews.js?v=20131009"></script> <meta property="fb:app_id" content="137353533001720"/>  <meta content="JACOW : Statistical Properties of Schottky Spectra" name="citation_title" /> <meta content="Lannoy, Christophe" name="citation_author" /> <meta content="Łasocha, Kacper" name="citation_author" /> <meta content="Mounet, Nicolas" name="citation_author" /> <meta content="Alves, Diogo" name="citation_author" /> <meta content="Pieloni, Tatiana" name="citation_author" /> <meta content="10.18429/JACoW-IBIC2023-WEP035" name="citation_doi" /> <meta content="JACoW IBIC" name="citation_journal_title" /> <meta content="2023" name="citation_volume" /> <meta content="WEP035" name="citation_firstpage" /> <meta content="2023" name="citation_publication_date" /> <meta name="citation_online_date" content="2024/06/18"> <meta content="10.18429/JACoW-IBIC2023-WEP035" name="citation_doi" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2901223/files/document.pdf" />  <meta content="JACOW" property="og:title" /> <meta content="Statistical Properties of Schottky Spectra" property="og:title" /> <meta content="website" property="og:type" /> <meta content="website" property="og:type" /> <meta content="https://cds.cern.ch/record/2901223" property="og:url" /> <meta content="CERN Document Server" property="og:site_name" /> <meta content="JACOW" property="og:description" /> <meta content="Schottky signals are used for non-invasive beam diagnostics as they contain information on various beam and machine parameters. The instantaneous Schottky signal is, however, only a single realisation of a random process, implicitly depending on the discrete distribution of synchrotron and betatron amplitudes and phases among the particles. To estimate the expected value of the Schottky power spectrum, and reveal the inner structure of the Bessel satellites described by the theory, the averaging of instantaneous Schottky spectra is required. This study describes this procedure quantitatively by analysing the statistical properties of the Schottky signals, including the expected value and variance of Schottky power spectra. Furthermore, we investigate how these quantities evolve with the number of particles in the bunch, the observed harmonic of the revolution frequency, the distribution of synchrotron oscillation amplitudes, and the bunch profile. The theoretical findings are compared against macro-particle simulations as well as Monte Carlo computations." property="og:description" />  <meta content="summary" name="twitter:card" /> <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="en">  <div id="cern-toolbar"> <h1><a href="http://cern.ch" title="CERN">CERN <span>Accelerating science</span></a></h1> <ul> <li class="cern-accountlinks"><a class="cern-account" href="https://cds.cern.ch/youraccount/login?ln=en&referer=https%3A//cds.cern.ch/record/2901223/export/hm%3Fln%3Den" title="Sign in to your CERN account">Sign in</a></li> <li><a class="cern-directory" href="http://cern.ch/directory" title="Search CERN resources and browse the directory">Directory</a></li> </ul> </div>   <div role="banner" class="clearfix" id="header"> <div class="header-inner inner"> <hgroup class="clearfix"> <h2 id="site-name"> <a rel="home" title="Home" href="/"><span>CERN Document Server</span></a> </h2> <h3 id="site-slogan">Access articles, reports and multimedia content in HEP</h3> </hgroup> <div role="navigation" id="main-navigation" class="cdsmenu"> <h2 class="element-invisible">Main menu</h2><ul class="links inline clearfix"> <li class="menu-386 first active-trail"><a class="active-trail" href="https://cds.cern.ch/?ln=en">Search</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=en">Submit</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=en">Help</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=en">Personalize</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=en">Your alerts</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=en">Your baskets</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=en">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=en">Your searches</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=en" class="navtrail">Home</a> > <a class="navtrail" href="/record/2901223">Statistical Properties of Schottky Spectra</a> > HTML MARC </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <pre style="margin: 1em 0px;">002901223 001__ 2901223 002901223 003__ SzGeCERN 002901223 005__ 20240618222933.0 002901223 0247_ $$2DOI$$9JACOW$$a10.18429/JACoW-IBIC2023-WEP035 002901223 0248_ $$aoai:cds.cern.ch:2901223$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN 002901223 035__ $$9https://inspirehep.net/api/oai2d$$aoai:inspirehep.net:2754669$$d2024-06-17T11:33:34Z$$h2024-06-18T05:22:06Z$$mmarcxml 002901223 035__ $$9Inspire$$a2754669 002901223 041__ $$aeng 002901223 100__ $$aLannoy, Christophe$$jJACoW-00138205$$mchristophe.lannoy@epfl.ch$$uCERN$$uEPFL, Lausanne, FSL$$vEPFL, Lausanne, Switzerland 002901223 245__ $$9JACOW$$aStatistical Properties of Schottky Spectra 002901223 260__ $$c2023 002901223 300__ $$a5 p 002901223 520__ $$9JACOW$$aSchottky signals are used for non-invasive beam diagnostics as they contain information on various beam and machine parameters. The instantaneous Schottky signal is, however, only a single realisation of a random process, implicitly depending on the discrete distribution of synchrotron and betatron amplitudes and phases among the particles. To estimate the expected value of the Schottky power spectrum, and reveal the inner structure of the Bessel satellites described by the theory, the averaging of instantaneous Schottky spectra is required. This study describes this procedure quantitatively by analysing the statistical properties of the Schottky signals, including the expected value and variance of Schottky power spectra. Furthermore, we investigate how these quantities evolve with the number of particles in the bunch, the observed harmonic of the revolution frequency, the distribution of synchrotron oscillation amplitudes, and the bunch profile. The theoretical findings are compared against macro-particle simulations as well as Monte Carlo computations. 002901223 540__ $$aCC-BY-4.0$$bJACOW$$uhttps://creativecommons.org/licenses/by/4.0 002901223 542__ $$dthe author(s)$$g2024 002901223 65017 $$2SzGeCERN$$aAccelerators and Storage Rings 002901223 6531_ $$9author$$asimulation 002901223 6531_ $$9author$$asynchrotron 002901223 6531_ $$9author$$abetatron 002901223 6531_ $$9author$$adipole 002901223 6531_ $$9author$$adiagnostics 002901223 690C_ $$aARTICLE 002901223 690C_ $$aCERN 002901223 700__ $$aAlves, Diogo$$jJACoW-00051020$$mdiogo.alves@cern.ch$$uCERN 002901223 700__ $$aŁasocha, Kacper$$jJACoW-00091829$$mkacper.lasocha@cern.ch$$uCERN 002901223 700__ $$aMounet, Nicolas$$jJACoW-00042877$$mnicolas.mounet@cern.ch$$uCERN 002901223 700__ $$aPieloni, Tatiana$$jJACoW-00004675$$mtatiana.pieloni@epfl.ch$$uEPFL, Lausanne, FSL 002901223 773__ $$cWEP035$$pJACoW IBIC$$qIBIC2023$$v2023$$wC23-09-10.2$$y2023 002901223 8564_ $$82537991$$s456235$$uhttps://cds.cern.ch/record/2901223/files/document.pdf$$yFulltext 002901223 960__ $$a13 002901223 962__ $$b2900961$$kWEP035$$nsaskatoon20230910 002901223 980__ $$aARTICLE 002901223 980__ $$aConferencePaper</pre></div></div> <footer id="footer" class="pagefooter clearfix">  <div class="pagefooterstripeleft"> CERN Document Server :: <a class="footer" href="https://cds.cern.ch/?ln=en">Search</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=en">Submit</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=en">Personalize</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=en">Help</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> :: <a class="footer" href="https://repository.cern/content-policy" target="_blank">Content Policy</a> :: <a class="footer" href="https://repository.cern/terms" target="_blank">Terms and Conditions</a> <br /> Powered by <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Maintained by <a class="footer" href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Service</a> - Need help? 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