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In this report, simple expressions to compute the angular frequencies of these rotations around a radial axis are given." property="og:description" />  <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="ru">  <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=ru&referer=https%3A//cds.cern.ch/record/2882363%3Fln%3Dru" 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=ru">Искать</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=ru">Внести</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=ru">Помощь</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=ru">Персонализовать</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=ru">Ваши оповещения</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=ru">Ваши книжные полки</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=ru">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=ru">Ваши поисковые запросы</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=ru" class="navtrail">Главная страница</a> > Systematic Errors of a ”frozen Spin” EDM measurement with electric and magnetic Fields due to imperfect Alignment of Fields </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <div class="detailedrecordbox"> <div class="detailedrecordtabs"> <div> <ul class="detailedrecordtabs"><li class="on first"><a href="/record/2882363/?ln=ru">Информация </a></li><li class=""><a href="/record/2882363/files?ln=ru">Файлы </a></li></ul> <div id="tabsSpacer" style="clear:both;height:0px"> </div></div> </div> <div class="detailedrecordboxcontent"> <div class="top-left-folded"></div> <div class="top-right-folded"></div> <div class="inside">  <abbr class="unapi-id" title="2882363"></abbr>  <link href="/img/download_and_embed_buttons.css" rel="stylesheet" type="text/css" /> <style type="text/css">  .video_talk_wrapper{ max-width: 640px; min-height: 360px; } </style> <table class="formatRecordTableFullWidth"> <tr> <td class="formatRecordHeader" style="background-image: url('/img/journals.jpg');" colspan="2">  </td> </tr> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;">CERN-PBC-Notes-2023-009</td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>Systematic Errors of a ”frozen Spin” EDM measurement with electric and magnetic Fields due to imperfect Alignment of Fields</b></td></tr> <style> .video_control_container, #video_controlbutton { display: none; }#video_detailbox_download {display: none;}#video_detailbox_embed {display: none;}</style> <div class="video_control_container"> <div style="box-sizing: inherit;position: relative;min-height: 1em;margin: 1em 0;background: #f8f8f9;padding: 1em 1.5em;line-height: 1.4285em;transition: opacity .1s ease,color .1s ease,background .1s ease,box-shadow .1s ease,-webkit-box-shadow .1s ease;border-radius: .28571429rem;font-size: 1.1em;margin-top: 0;margin-bottom: 6px;background-color: #f8ffff;color: #276f86;box-shadow: 0 0 0 1px #a9d5de inset,0 0 0 0 transparent;"> <i class="fa fa-info"></i><span style="padding-left: 9px;">If you experience any problem watching the video, click the download button below</span> </div> <a id="video_controlbutton_download" rel="download_button" class="video_controlbutton" href="#">Download</a> <a id="video_controlbutton_embed" class="video_controlbutton" href="#">Embed</a> </div> <div id="video_detailbox_download" style="margin:10px"> </div> <div id="video_detailbox_embed" style="margin:10px"> </div> <tr><td class="formatRecordLabel"> <span style="white-space:nowrap;">Author(s)</span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Cilento%2C%20Vera&ln=ru">Cilento, Vera</a> (CERN) ; <a href="https://cds.cern.ch/search?f=author&p=Carli%2C%20Christian&ln=ru">Carli, Christian</a> (CERN) ; <a href="https://cds.cern.ch/search?f=author&p=Haj%20Tahar%2C%20Malek&ln=ru">Haj Tahar, Malek</a> (CERN)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">28</td></tr>  <script type="text/javascript"> /* * Changes the Imprint title to Date - Duration as requested by RQF0820114 * This is a hack not to touch the general imprint format element */ $(document).ready(function() { var collections = 'NOTE'; if (collections.indexOf('E-LEARNING') > -1) { $('.cern-imprint-label').text('Date - Duration'); } }) </script> <tr><td class="formatRecordLabel cern-imprint-label"> Imprint </td><td style="padding-left:5px;">28-11-2023</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">15</td></tr>  <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">Accelerators and Storage Rings</td></tr> <tr><td class="formatRecordLabel"> Study </td><td style="padding-left:5px;"><a href='https://cds.cern.ch/search?p=693__s:"Physics Beyond Colliders"'>Physics Beyond Colliders</a></td></tr> <tr><td class="formatRecordLabel"> Project </td><td style="padding-left:5px;"><a href='https://cds.cern.ch/search?p=693__p:"Prototype EDM Storage Ring"'>Prototype EDM Storage Ring</a></td></tr> <tr><td class="formatRecordLabel"> Keywords </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=keyword&p=cpEDM&ln=ru">cpEDM</a> ; <a href="https://cds.cern.ch/search?f=keyword&p=frozen%20spin&ln=ru">frozen spin</a> ; <a href="https://cds.cern.ch/search?f=keyword&p=electric%20and%20magnetic%20fields&ln=ru">electric and magnetic fields</a> ; <a href="https://cds.cern.ch/search?f=keyword&p=spin%20transparent&ln=ru">spin transparent</a> ; <a href="https://cds.cern.ch/search?f=keyword&p=spin%20precession&ln=ru">spin precession</a></td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">Many of the rings proposed to measure the Electric Dipole Moment (EDM) of charged particles rely on a combination of magnetic and electric fields bending the beam to fulfil the ”frozen spin” condition. Imperfect alignment of the two fields bending the beam is known to rotate the spin from the longitudinal into the vertical direction. This effect is very similar to the signature of a finite EDM and, thus, a potential limitation for the sensitivity of the measurement. The concept of a ”spin transparent” quadrupole is to superimpose magnetic and electric contributions for focusing elements as well to increase the spin coherence time. A vertical offset between the two quadrupole contributions leads as well to rotations of the spin from the longitudinal to the vertical direction. In this report, simple expressions to compute the angular frequencies of these rotations around a radial axis are given.</td></tr> <tr><td class="formatRecordLabel"> Submitted by </td><td style="padding-left:5px;"><a href="mailto:christian.carli@cern.ch">christian.carli@cern.ch</a></td></tr> </table> <br/><div><div style="clear: both;"> </div></div> <script type="text/javascript"> // Initially hide: $(".longCaption").hide(); // Allow to toggle visibility: $(".toggleLongCaption").toggle(function(){ $(this).siblings(".longCaption").show('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "ещё" ? "меньше" : "ещё"); },function(){ $(this).siblings(".longCaption").hide('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "ещё" ? 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Imperfect alignment of the two fields bending the beam is known to rotate the spin from the longitudinal into the vertical direction. This effect is very similar to the signature of a finite EDM and, thus, a potential limitation for the sensitivity of the measurement. The concept of a \u201dspin transparent\u201d quadrupole is to superimpose magnetic and electric contributions for focusing elements as well to increase the spin coherence time. A vertical offset between the two quadrupole contributions leads as well to rotations of the spin from the longitudinal to the vertical direction. 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