CINXE.COM

<!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>Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses - 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/2318948/plots" /> <link rel="alternate" hreflang="el" href="https://cds.cern.ch/record/2318948/plots?ln=el" /> <link rel="alternate" hreflang="fr" href="https://cds.cern.ch/record/2318948/plots?ln=fr" /> <link rel="alternate" hreflang="bg" href="https://cds.cern.ch/record/2318948/plots?ln=bg" /> <link rel="alternate" hreflang="zh-TW" href="https://cds.cern.ch/record/2318948/plots?ln=zh_TW" /> <link rel="alternate" hreflang="pt" href="https://cds.cern.ch/record/2318948/plots?ln=pt" /> <link rel="alternate" hreflang="no" href="https://cds.cern.ch/record/2318948/plots?ln=no" /> <link rel="alternate" hreflang="hr" href="https://cds.cern.ch/record/2318948/plots?ln=hr" /> <link rel="alternate" hreflang="ca" href="https://cds.cern.ch/record/2318948/plots?ln=ca" /> <link rel="alternate" hreflang="de" href="https://cds.cern.ch/record/2318948/plots?ln=de" /> <link rel="alternate" hreflang="it" href="https://cds.cern.ch/record/2318948/plots?ln=it" /> <link rel="alternate" hreflang="zh-CN" href="https://cds.cern.ch/record/2318948/plots?ln=zh_CN" /> <link rel="alternate" hreflang="sv" href="https://cds.cern.ch/record/2318948/plots?ln=sv" /> <link rel="alternate" hreflang="sk" href="https://cds.cern.ch/record/2318948/plots?ln=sk" /> <link rel="alternate" hreflang="en" href="https://cds.cern.ch/record/2318948/plots?ln=en" /> <link rel="alternate" hreflang="pl" href="https://cds.cern.ch/record/2318948/plots?ln=pl" /> <link rel="alternate" hreflang="ru" href="https://cds.cern.ch/record/2318948/plots?ln=ru" /> <link rel="alternate" hreflang="ka" href="https://cds.cern.ch/record/2318948/plots?ln=ka" /> <link rel="alternate" hreflang="ja" href="https://cds.cern.ch/record/2318948/plots?ln=ja" /> <link rel="alternate" hreflang="es" href="https://cds.cern.ch/record/2318948/plots?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="We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies. We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses (HEL) for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies. Fitterer, Miriam; Stancari, Giulio; Valishev, Alexander; Redaelli, Stefano; Valuch, Daniel" /> <meta name="keywords" content="CERN Document Server, WebSearch, CERN Document Server" /> <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"/> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$']], processEscapes: true}, showProcessingMessages: false, messageStyle: "none" }); </script> <script src="/MathJax/MathJax.js?config=TeX-AMS_CHTML" type="text/javascript"> </script>  <meta content="arXiv : Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses" name="citation_title" /> <meta content="Fitterer, Miriam" name="citation_author" /> <meta content="Stancari, Giulio" name="citation_author" /> <meta content="Redaelli, Stefano" name="citation_author" /> <meta content="Valishev, Alexander" name="citation_author" /> <meta content="Valuch, Daniel" name="citation_author" /> <meta content="10.1103/PhysRevAccelBeams.24.021001" name="citation_doi" /> <meta content="Phys. Rev. Accel. Beams" name="citation_journal_title" /> <meta content="24" name="citation_volume" /> <meta content="021001" name="citation_firstpage" /> <meta content="2018/04/19" name="citation_publication_date" /> <meta name="citation_online_date" content="2018/05/19"> <meta content="arXiv:1804.07418" name="citation_technical_report_number" /> <meta content="FERMILAB-PUB-18-084-AD-APC" name="citation_technical_report_number" /> <meta content="FERMILAB-PUB-21-008-AD" name="citation_technical_report_number" /> <meta content="10.1103/PhysRevAccelBeams.24.021001" name="citation_doi" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2318948/files/PhysRevAccelBeams.24.pdf" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2318948/files/fermilab-pub-18-084-ad-apc.pdf" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2318948/files/1804.07418.pdf" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2318948/files/10.1103_PhysRevAccelBeams.24.021001.pdf" />  <meta content="Effects of Resonant and Random Excitations on the Proton Beam in the Large Hadron Collider, with Applications to the Design of Pulsed Hollow Electron Lenses for Active Halo Control" property="og:title" /> <meta content="arXiv" property="og:title" /> <meta content="Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses" property="og:title" /> <meta content="website" property="og:type" /> <meta content="https://cds.cern.ch/record/2318948" property="og:url" /> <meta name="twitter:image" content="https://cds.cern.ch/record/2318948/files/kick_hel_lhc_no_grid.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/kick_hel_lhc_no_grid.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/kick_hel_lhc_no_grid.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_h7th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_h7th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_with_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_with_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_50.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_50.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hvran_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hvran_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2696.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2696.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hv7th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hv7th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hvran_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hvran_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_804.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_804.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t7skhv_3_5um_hist_x.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t7skhv_3_5um_hist_x.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skh_dp0_ord10.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skh_dp0_ord10.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_2D.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_2D.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8hv_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8hv_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2862.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2862.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_v10th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_v10th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_j-vs-r_binned_nogrid_nolabel.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_j-vs-r_binned_nogrid_nolabel.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8v_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8v_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7hv_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7hv_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/hel_layout_epbeam.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/hel_layout_epbeam.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skv_dp0_ord7.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skv_dp0_ord7.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_3_5um_hist_y.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_3_5um_hist_y.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit1.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit1.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8h_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8h_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_intensity.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_intensity.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_ord14_annotate_7th.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_ord14_annotate_7th.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_no_damper_no_text.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_no_damper_no_text.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranv_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranv_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_v10th_no_damper_avg.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_v10th_no_damper_avg.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7th_ranhv_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7th_ranhv_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2_rel.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2_rel.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7h_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7h_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_amp.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_amp.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_vran_no_damper_avg.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_vran_no_damper_avg.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_ranhv_3_5um_hist_x.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_ranhv_3_5um_hist_x.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_h7th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_h7th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_intensity.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_intensity.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_with_damper_no_text.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_with_damper_no_text.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skv_dp0_ord7.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skv_dp0_ord7.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_sigm.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_sigm.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hvran_no_damper_avg.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hvran_no_damper_avg.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_1300.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_1300.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skv_dp0_ord10.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skv_dp0_ord10.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit1.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit1.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Emap.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Emap.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_vran_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_vran_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut8skhv_dp0_amp_annotate.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut8skhv_dp0_amp_annotate.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_intensity.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_intensity.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016+2017_scale_amp_7h_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016+2017_scale_amp_7h_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1698.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1698.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper_no_text.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper_no_text.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranhv_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranhv_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skh_dp0_ord7.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skh_dp0_ord7.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Eslice.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Eslice.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/bunchfilling_measured.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/bunchfilling_measured.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/passive_halo_control.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/passive_halo_control.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t10skhv_3_5um_hist_y.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t10skhv_3_5um_hist_y.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_rel_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_rel_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/bunchfilling_2016.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/bunchfilling_2016.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/bunchfilling_2017.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/bunchfilling_2017.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_scale_amp_10v_ran_lblshort_sim_prstab.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_scale_amp_10v_ran_lblshort_sim_prstab.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1532.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1532.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit1.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit1.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/diffusion_illustration.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/diffusion_illustration.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_632.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_632.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_sigm.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_sigm.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hv7th_no_damper_avg.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hv7th_no_damper_avg.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerru_dp0_ord10_annotate.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerru_dp0_ord10_annotate.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_intensity.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_intensity.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerruranadthv_1nrad_dp0_amp.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerruranadthv_1nrad_dp0_amp.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skhv_dp0_ord10.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skhv_dp0_ord10.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skhv_dp0_ord7.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skhv_dp0_ord7.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_sigm.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_sigm.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranh_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranh_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_intensity.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_intensity.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/active_halo_control.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/active_halo_control.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_h7th_no_damper_avg.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_h7th_no_damper_avg.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit1.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit1.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit1.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit1.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_with_damper_no_text.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_with_damper_no_text.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hv7th_no_damper.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hv7th_no_damper.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7v_lblshort.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7v_lblshort.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skh_dp0_ord7.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skh_dp0_ord7.png" /> <meta content="CERN Document Server" property="og:site_name" /> <meta content="APS" property="og:description" /> <meta content="arXiv" property="og:description" /> <meta content="We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies." property="og:description" /> <meta content="We present the results of numerical simulations and experimental studies about the effects of resonant and random excitations on proton losses, emittances, and beam distributions in the Large Hadron Collider (LHC). In addition to shedding light on complex nonlinear effects, these studies are applied to the design of hollow electron lenses (HEL) for active beam halo control. In the High-Luminosity Large Hadron Collider (HL-LHC), a considerable amount of energy will be stored in the beam tails. To control and clean the beam halo, the installation of two hollow electron lenses, one per beam, is being considered. In standard electron-lens operation, a proton bunch sees the same electron current at every revolution. Pulsed electron beam operation (i.e., different currents for different turns) is also considered, because it can widen the range of achievable halo removal rates. For an axially symmetric electron beam, only protons in the halo are excited. If a residual field is present at the location of the beam core, these particles are exposed to time-dependent transverse kicks and to noise. We discuss the numerical simulations and the experiments conducted in 2016 and 2017 at injection energy in the LHC. The excitation patterns were generated by the transverse feedback and damping system, which acted as a flexible source of dipole kicks. Proton beam losses, emittances, and transverse distributions were recorded as a function of excitation patterns and strengths. The resonant excitations induced rich dynamical effects and nontrivial changes of the beam distributions, which, to our knowledge, have not previously been observed and studied in this detail. We conclude with a discussion of the tolerable and achievable residual fields and proposals for further studies." property="og:description" />  <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/2318948/plots" 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/2318948">Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses</a> > Plots </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <div class="detailedrecordbox"> <div class="detailedrecordtabs"> <div> <ul class="detailedrecordtabs"><li class="first"><a href="/record/2318948/?ln=en">Information </a></li><li class=""><a href="/record/2318948/files?ln=en">Files </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">  <div id="detailedrecordshortreminder"> <div id="clip"> </div> <div id="HB"> <strong><a href="/record/2318948?ln=en">Resonant and random excitations on the proton beam in the Large Hadron Collider for active halo control with pulsed hollow electron lenses</a></strong> - <a href="/search?f=author&p=Fitterer%2C%20Miriam&ln=en">Fitterer, Miriam</a> <em>et al</em> - arXiv:1804.07418FERMILAB-PUB-18-084-AD-APCFERMILAB-PUB-21-008-AD </div> </div> <div style="clear:both;height:1px"> </div> <table width="95%" style="display: inline;"><tr><td width="66%"><a name="0" href="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_with_damper_no_text.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_with_damper_no_text.png" width="95%"/></a></td><td width="33%"> Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="1" href="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_vran_no_damper_avg.png"><img src="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_vran_no_damper_avg.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="2" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranhv_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranhv_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates as a function of amplitude for random excitations in H only (left), V only (center), and H+V (right). For each of the three excitation modes, three consecutive data sets were taken (black, red, and yellow), with increasing maximum amplitude. Data were taken simultaneously with no transverse damper on some bunches (filled circles and solid lines) and with the damper active on other bunches (empty circles and dashed lines). The lines represent empirical second-order polynomial fits.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="3" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7v_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7v_lblshort.png" width="95%"/></a></td><td width="33%"> Comparison of the measured loss rates as a function of excitation amplitude during the 2017 experiment for \seventhtp\ in H only (left), V only (center), and in H+V (right). The three excitations generate similar loss rates.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="4" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_no_damper_no_text.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_no_damper_no_text.png" width="95%"/></a></td><td width="33%"> Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="5" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skh_dp0_ord7.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skh_dp0_ord7.png" width="95%"/></a></td><td width="33%"> FMA in betatron tune space based on the 2017 injection optics with no machine errors and tunes (62.27, 60.295): without excitation (top left) and for \seventhtp\ in H+V (top right), H only (bottom left) and V only (bottom right). The excitation amplitude is 96~nrad. The $7 Q_x$, $7 Q_y$, and 14th-order $7 Q_x + 7 Q_y$ resonances are excited.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="6" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_intensity.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_intensity.png" width="95%"/></a></td><td width="33%"> Calculated relative intensities (top left), bunch lengths (top right), horizontal emittances (bottom left), and vertical emittances (bottom right) from distribution-tracking simulations based on the 2017 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (62.27, 60.295)$. The solid black line is the reference case, including only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines are the results for \eighthtp, including the same random dipole noise component.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="7" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranh_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranh_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates as a function of amplitude for random excitations in H only (left), V only (center), and H+V (right). For each of the three excitation modes, three consecutive data sets were taken (black, red, and yellow), with increasing maximum amplitude. Data were taken simultaneously with no transverse damper on some bunches (filled circles and solid lines) and with the damper active on other bunches (empty circles and dashed lines). The lines represent empirical second-order polynomial fits.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="8" href="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hvran_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hvran_no_damper.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="9" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_sigm.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_sigm.png" width="95%"/></a></td><td width="33%"> Calculated relative intensities (top left), bunch lengths (top right), horizontal emittances (bottom left), and vertical emittances (bottom right) from distribution-tracking simulations based on the 2017 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (62.27, 60.295)$. The solid black line is the reference case, including only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines are the results for \eighthtp, including the same random dipole noise component.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="10" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_sigm.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_sigm.png" width="95%"/></a></td><td width="33%"> Simulations (distribution tracking) based on the 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative bunch intensity (top left), bunch length (top right), horizontal emittance (bottom left), and vertical emittance (bottom right). The solid black line indicates the reference case with no excitation. The dashed and dotted lines are the results of random excitations (H, V, or H+V) with amplitudes 12~nrad and 24~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="11" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerruranadthv_1nrad_dp0_amp.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerruranadthv_1nrad_dp0_amp.png" width="95%"/></a></td><td width="33%"> FMA in transverse amplitude space without excitation (left) and with a random 1-nrad H+V excitation (right), based on the 2017 injection optics with no lattice errors and tunes (62.27, 60.295).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="12" href="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1698.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1698.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of the random excitation in V. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The distribution changes in the bunch experiencing the maximum excitation (right) were larger than those in the reference bunch (left). In both cases, distributions retained a Gaussian shape.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="13" href="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_v10th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_v10th_no_damper.png" width="95%"/></a></td><td width="33%"> Summary of the 2016 experiments on \tenthtp\ in the vertical plane: losses (left), horizontal emittances (middle) and vertical emittances (right), relative to their initial values. The transverse damping system was not active in this case. The 3 excitation periods are labeled in black according to the value of the maximum excitation amplitude $A_{\mathrm{max}} = 5 \, \Delta A$: no excitation, 48~nrad or 96~nrad. The 4~bunches experiencing the same excitation amplitude $n \, \Delta A$ ($n = 0, \ldots, 5$) are grouped by color. The data are averaged over the 4~bunches, with the envelope representing the standard deviation. The area with a blue background highlights qualitatively the fast adjustment period of the beam distribution, transitioning into a new equilibrium state (indicated by the gray background).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="14" href="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper_no_text.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper_no_text.png" width="95%"/></a></td><td width="33%"> Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="15" href="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_h7th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_h7th_no_damper.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="16" href="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_rel_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_rel_emit2.png" width="95%"/></a></td><td width="33%"> Calculated bunch intensities and emittances from distribution tracking based on the 2016 injection optics with standard lattice errors and $(Q_x, Q_y) = (64.28, 59.31)$ and 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative intensity (top left); horizontal emittance (bottom left); vertical emittance (bottom right); the relative vertical emittance is also shown (top right). The solid black line includes only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines correspond to \seventhtp\ with two different excitation amplitudes (24~nrad and 48~nrad), plus a random dipole noise component in H+V of 6~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="17" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skhv_dp0_ord7.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skhv_dp0_ord7.png" width="95%"/></a></td><td width="33%"> FMA in betatron tune space based on the 2017 injection optics with no machine errors and tunes (62.27, 60.295): without excitation (top left) and for \seventhtp\ in H+V (top right), H only (bottom left) and V only (bottom right). The excitation amplitude is 96~nrad. The $7 Q_x$, $7 Q_y$, and 14th-order $7 Q_x + 7 Q_y$ resonances are excited.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="18" href="https://cds.cern.ch/record/2318948/files/kick_hel_lhc_no_grid.png"><img src="https://cds.cern.ch/record/2318948/files/kick_hel_lhc_no_grid.png" width="95%"/></a></td><td width="33%"> Illustration of the hollow electron beam charge distribution (blue), of the magnitude of the transverse kick experienced by the proton beam (red), and of the position of the primary collimators (gray).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="19" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit2.png" width="95%"/></a></td><td width="33%"> Relative intensity (top left), bunch length (top right) and horizontal (bottom left) and vertical (bottom right) emittances for different pulsing patterns, calculated by distribution tracking based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors. The resonant and random excitations are applied in both planes, with an amplitude of 96~nrad. No random noise component is added. Because of its much larger effects, the random excitation is shown with separate vertical axes.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="20" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit1.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_emit1.png" width="95%"/></a></td><td width="33%"> Relative intensity (top left), bunch length (top right) and horizontal (bottom left) and vertical (bottom right) emittances for different pulsing patterns, calculated by distribution tracking based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors. The resonant and random excitations are applied in both planes, with an amplitude of 96~nrad. No random noise component is added. Because of its much larger effects, the random excitation is shown with separate vertical axes.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="21" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skv_dp0_ord7.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut7skv_dp0_ord7.png" width="95%"/></a></td><td width="33%"> FMA in betatron tune space based on the 2017 injection optics with no machine errors and tunes (62.27, 60.295): without excitation (top left) and for \seventhtp\ in H+V (top right), H only (bottom left) and V only (bottom right). The excitation amplitude is 96~nrad. The $7 Q_x$, $7 Q_y$, and 14th-order $7 Q_x + 7 Q_y$ resonances are excited.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="22" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t7skhv_3_5um_hist_x.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t7skhv_3_5um_hist_x.png" width="95%"/></a></td><td width="33%"> Calculated beam distributions as a function of vertical position from distribution-tracking simulations based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors: no excitation (top left), random excitation (top right), \seventhtp\ (bottom left), and \tenthtp\ (bottom right). The excitations are applied in both planes with an amplitude of 96~nrad. For each of the 4~cases, 3~plots are shown. The top plot shows the normalized transverse distributions: `initial' (after $10^2$~turns, in gray), `final' (after $10^4$~turns, in black), and their Gaussian fits (light and dark red, respectively). The middle plots show the relative residuals (i.e., differences, in percent of the peak value) between final and initial distributions (in black) and between each distribution and its Gaussian fit (in light and dark red). The ratios between final and initial distributions are drawn in black in the bottom plots. The residuals emphasize changes near the core of the distributions, whereas ratios (when statistically significant), reveal variations in the tails.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="23" href="https://cds.cern.ch/record/2318948/files/passive_halo_control.png"><img src="https://cds.cern.ch/record/2318948/files/passive_halo_control.png" width="95%"/></a></td><td width="33%"> Left: Sketch of passive halo control with a conventional collimation system (top) and active halo control, with the addition of a hollow electron lens (bottom). Right: Illustration of a simplified model of active diffusion enhancement in the transverse plane. The diffusion coefficient as a function of amplitude (orange) is enhanced in a specific amplitude region when the hollow beam is turned on (from solid to dashed line). A corresponding reduction in beam tail population (black) is created (from solid to dashed line).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="24" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skv_dp0_ord10.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skv_dp0_ord10.png" width="95%"/></a></td><td width="33%"> FMA for \tenthtp\ based on the 2016 injection optics with no lattice errors and tunes (64.28, 59.31). The excitation is 120~nrad in the corresponding plane. There is no significant difference between pulsing in H only, V only, or in H+V.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="25" href="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_j-vs-r_binned_nogrid_nolabel.png"><img src="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_j-vs-r_binned_nogrid_nolabel.png" width="95%"/></a></td><td width="33%"> Example of current-density distribution measurements for the hollow electron gun prototype CHG1b, taken at the Fermilab electron lens test stand in 2017~\cite{hel_res_field_stancari_2017}: 2-dimensional transverse profile measurement (left) and calculated 1-dimensional radial projection (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="26" href="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Emap.png"><img src="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Emap.png" width="95%"/></a></td><td width="33%"> Calculated relative electric field for the hollow electron gun CHG1b in the transverse $x$-$y$ plane (left) and as 1-dimensional cuts through the $x$ and $y$ axes (right). The field calculations are based on measurements at the Fermilab electron-lens test stand combined with \code{warp} calculations of the electric potentials and fields in a cylindrical beam pipe.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="27" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_ord14_annotate_7th.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_ord14_annotate_7th.png" width="95%"/></a></td><td width="33%"> FMA in betatron tune space based on the 2017 injection optics with no machine errors and tunes (62.27, 60.295): without excitation (top left) and for \seventhtp\ in H+V (top right), H only (bottom left) and V only (bottom right). The excitation amplitude is 96~nrad. The $7 Q_x$, $7 Q_y$, and 14th-order $7 Q_x + 7 Q_y$ resonances are excited.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="28" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_with_damper_no_text.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_v7th_with_damper_no_text.png" width="95%"/></a></td><td width="33%"> Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="29" href="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_v10th_no_damper_avg.png"><img src="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_v10th_no_damper_avg.png" width="95%"/></a></td><td width="33%"> Summary of the 2016 experiments on \tenthtp\ in the vertical plane: losses (left), horizontal emittances (middle) and vertical emittances (right), relative to their initial values. The transverse damping system was not active in this case. The 3 excitation periods are labeled in black according to the value of the maximum excitation amplitude $A_{\mathrm{max}} = 5 \, \Delta A$: no excitation, 48~nrad or 96~nrad. The 4~bunches experiencing the same excitation amplitude $n \, \Delta A$ ($n = 0, \ldots, 5$) are grouped by color. The data are averaged over the 4~bunches, with the envelope representing the standard deviation. The area with a blue background highlights qualitatively the fast adjustment period of the beam distribution, transitioning into a new equilibrium state (indicated by the gray background).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="30" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_intensity.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_intensity.png" width="95%"/></a></td><td width="33%"> Relative intensity (top left), bunch length (top right) and horizontal (bottom left) and vertical (bottom right) emittances for different pulsing patterns, calculated by distribution tracking based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors. The resonant and random excitations are applied in both planes, with an amplitude of 96~nrad. No random noise component is added. Because of its much larger effects, the random excitation is shown with separate vertical axes.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="31" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7h_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7h_lblshort.png" width="95%"/></a></td><td width="33%"> Comparison of the measured loss rates as a function of excitation amplitude during the 2017 experiment for \seventhtp\ in H only (left), V only (center), and in H+V (right). The three excitations generate similar loss rates.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="32" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7hv_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7hv_lblshort.png" width="95%"/></a></td><td width="33%"> Comparison of the measured loss rates as a function of excitation amplitude during the 2017 experiment for \seventhtp\ in H only (left), V only (center), and in H+V (right). The three excitations generate similar loss rates.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="33" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit1.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit1.png" width="95%"/></a></td><td width="33%"> Calculated relative intensities (top left), bunch lengths (top right), horizontal emittances (bottom left), and vertical emittances (bottom right) from distribution-tracking simulations based on the 2017 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (62.27, 60.295)$. The solid black line is the reference case, including only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines are the results for \eighthtp, including the same random dipole noise component.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="34" href="https://cds.cern.ch/record/2318948/files/bunchfilling_2016.png"><img src="https://cds.cern.ch/record/2318948/files/bunchfilling_2016.png" width="95%"/></a></td><td width="33%"> Bunch filling scheme and excitation patterns for the 2016~(top) and 2017~(bottom) LHC experiments. In 2016, a total of 48~bunches was used, whereas in 2017 there were 216~bunches. Each bunch is represented by a vertical cyan bar. The bunches were grouped in subsets of~4 in 2016 and in subsets of~6 in 2017. Each subset experienced the same excitation pattern and amplitude. The excitation amplitudes and relative phases are shown in blue or red. In 2016, the excitation was only applied in one plane. In 2017, more injected bunches were allowed without compromising machine protection, so it was possible to test all~3 excitation planes in the same fill. The transverse damper was active on half of the bunches, indicated by the black lines.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="35" href="https://cds.cern.ch/record/2318948/files/bunchfilling_2017.png"><img src="https://cds.cern.ch/record/2318948/files/bunchfilling_2017.png" width="95%"/></a></td><td width="33%"> Bunch filling scheme and excitation patterns for the 2016~(top) and 2017~(bottom) LHC experiments. In 2016, a total of 48~bunches was used, whereas in 2017 there were 216~bunches. Each bunch is represented by a vertical cyan bar. The bunches were grouped in subsets of~4 in 2016 and in subsets of~6 in 2017. Each subset experienced the same excitation pattern and amplitude. The excitation amplitudes and relative phases are shown in blue or red. In 2016, the excitation was only applied in one plane. In 2017, more injected bunches were allowed without compromising machine protection, so it was possible to test all~3 excitation planes in the same fill. The transverse damper was active on half of the bunches, indicated by the black lines.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="36" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit2.png" width="95%"/></a></td><td width="33%"> Simulations (distribution tracking) based on the 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative bunch intensity (top left), bunch length (top right), horizontal emittance (bottom left), and vertical emittance (bottom right). The solid black line indicates the reference case with no excitation. The dashed and dotted lines are the results of random excitations (H, V, or H+V) with amplitudes 12~nrad and 24~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="37" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_no_damper.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="38" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit1.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit1.png" width="95%"/></a></td><td width="33%"> Simulations (with the distribution-tracking method) based on the 2016 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (64.28, 59.31)$: relative beam intensity (top left); normalized horizontal (bottom left) and vertical (bottom right) emittances; vertical emittance relative to its initial value (top right). The solid lines indicate the effect of \tenthtp\ in the vertical plane. The dotted lines include both the resonant excitation and a random dipole noise component of 6~nrad (in both horizontal and vertical planes).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="39" href="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_h7th_no_damper_avg.png"><img src="https://cds.cern.ch/record/2318948/files/2016_bunch_intensity_h7th_no_damper_avg.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="40" href="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hv7th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_hv7th_no_damper.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="41" href="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_1300.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_1300.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2016 experiments on \tenthtp\ in the vertical plane. The transverse damping system was not active on these bunches. The beam distributions at the end of the excitation period are shown in black in the top plots, with a Gaussian fit in red. The bottom plots show the residuals: final profile minus initial profile (black); final profile minus its Gaussian fit (red). Residuals are expressed as a fraction of the peak profile amplitude. The black lines in the plots of the residuals are a measure of the overall change of the distribution shape. The red lines indicate how different the final distributions are from a Gaussian shape. Details of the analysis are given in Ref.~\cite{bsrtprofinj}. The distribution of the reference bunch (left) is almost unchanged, whereas the bunch experiencing the maximum excitation (right) shows a clear shift of particles from the axis towards approximately $\pm 2\sigma$.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="42" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skv_dp0_ord7.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skv_dp0_ord7.png" width="95%"/></a></td><td width="33%"> Frequency-map analysis in betatron tune space based on the 2016 injection optics with no machine errors and tunes (64.28, 59.31): without excitation (top left); \tenthtp\ in both horizontal and vertical planes (top right); \seventhtp\ in the horizontal (bottom left) and vertical (bottom right) planes. The excitation amplitude is 120~nrad in the corresponding plane. The colors (blue to red) represent the tune jitter of tracked particles starting at each given location in tune space~\cite{fmalaskar}. The absence of a strong excitation of any resonance in case of vertical \seventhtp\ and the strong excitation in case of horizontal pulsing confirms the excitation of the $7 Q_x$ resonance. For \tenthtp, there is in contrast no significant difference between H, V, or H+V (Fig.~\ref{fig:fma:10}).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="43" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hvran_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hvran_no_damper.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="44" href="https://cds.cern.ch/record/2318948/files/2016_scale_amp_10v_ran_lblshort_sim_prstab.png"><img src="https://cds.cern.ch/record/2318948/files/2016_scale_amp_10v_ran_lblshort_sim_prstab.png" width="95%"/></a></td><td width="33%"> Comparison between experiments and simulations of loss rates vs.\ resonant excitation amplitude for \tenthtp\ in the vertical plane. The relative average loss rate~$R$ is defined in Eq.~\ref{eqn:lossrate}. The experimental results for a maximum excitation amplitude of 48~nrad are shown in black and those for 96~nrad are plotted in green (see also Fig.~\ref{fig:10thexp}, left, for instance). The results with damper off are represented by solid dots, those with damper on are shown with open circles. The simulation results, including random dipole noise, are shown in red (see also Fig.~\ref{fig:10thsim}). Statistical and systematic uncertainties are discussed in the text. The curves represent empirical quadratic fits to the data with damper off (solid) and with damper on (dashed).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="45" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_with_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_vran_with_damper.png" width="95%"/></a></td><td width="33%"> Comparison of measured vertical emittances for bunches with transverse damper off (top row) and with transverse damper on (bottom row), during random V excitations (left), \seventhtp\ in V (center) and \tenthtp\ in V (right). (Because of a change in experimental setup, for the bunches represented by the yellow line in the bottom right plot, the excitation was zero instead of the maximum value.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="46" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_3_5um_hist_y.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_3_5um_hist_y.png" width="95%"/></a></td><td width="33%"> Calculated beam distributions as a function of vertical position from distribution-tracking simulations based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors: no excitation (top left), random excitation (top right), \seventhtp\ (bottom left), and \tenthtp\ (bottom right). The excitations are applied in both planes with an amplitude of 96~nrad. For each of the 4~cases, 3~plots are shown. The top plot shows the normalized transverse distributions: `initial' (after $10^2$~turns, in gray), `final' (after $10^4$~turns, in black), and their Gaussian fits (light and dark red, respectively). The middle plots show the relative residuals (i.e., differences, in percent of the peak value) between final and initial distributions (in black) and between each distribution and its Gaussian fit (in light and dark red). The ratios between final and initial distributions are drawn in black in the bottom plots. The residuals emphasize changes near the core of the distributions, whereas ratios (when statistically significant), reveal variations in the tails.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="47" href="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit2.png" width="95%"/></a></td><td width="33%"> Calculated bunch intensities and emittances from distribution tracking based on the 2016 injection optics with standard lattice errors and $(Q_x, Q_y) = (64.28, 59.31)$ and 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative intensity (top left); horizontal emittance (bottom left); vertical emittance (bottom right); the relative vertical emittance is also shown (top right). The solid black line includes only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines correspond to \seventhtp\ with two different excitation amplitudes (24~nrad and 48~nrad), plus a random dipole noise component in H+V of 6~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="48" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2_rel.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2_rel.png" width="95%"/></a></td><td width="33%"> Simulations (with the distribution-tracking method) based on the 2016 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (64.28, 59.31)$: relative beam intensity (top left); normalized horizontal (bottom left) and vertical (bottom right) emittances; vertical emittance relative to its initial value (top right). The solid lines indicate the effect of \tenthtp\ in the vertical plane. The dotted lines include both the resonant excitation and a random dipole noise component of 6~nrad (in both horizontal and vertical planes).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="49" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranv_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_ranv_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates as a function of amplitude for random excitations in H only (left), V only (center), and H+V (right). For each of the three excitation modes, three consecutive data sets were taken (black, red, and yellow), with increasing maximum amplitude. Data were taken simultaneously with no transverse damper on some bunches (filled circles and solid lines) and with the damper active on other bunches (empty circles and dashed lines). The lines represent empirical second-order polynomial fits.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="50" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_ranhv_3_5um_hist_x.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_ranhv_3_5um_hist_x.png" width="95%"/></a></td><td width="33%"> Calculated beam distributions as a function of vertical position from distribution-tracking simulations based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors: no excitation (top left), random excitation (top right), \seventhtp\ (bottom left), and \tenthtp\ (bottom right). The excitations are applied in both planes with an amplitude of 96~nrad. For each of the 4~cases, 3~plots are shown. The top plot shows the normalized transverse distributions: `initial' (after $10^2$~turns, in gray), `final' (after $10^4$~turns, in black), and their Gaussian fits (light and dark red, respectively). The middle plots show the relative residuals (i.e., differences, in percent of the peak value) between final and initial distributions (in black) and between each distribution and its Gaussian fit (in light and dark red). The ratios between final and initial distributions are drawn in black in the bottom plots. The residuals emphasize changes near the core of the distributions, whereas ratios (when statistically significant), reveal variations in the tails.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="51" href="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_vran_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emith_avg_rel_vran_no_damper.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="52" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8h_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8h_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates vs.\ excitation amplitude for \eighthtp\ in H only (left), in V only (center) and in H+V (right) during the 2017 experiment. Uncertainties are statistical. The differences between the three data sets within each excitation mode (black, red, and yellow curves) provide an estimate of the systematic errors.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="53" href="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit1.png"><img src="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_emit1.png" width="95%"/></a></td><td width="33%"> Calculated bunch intensities and emittances from distribution tracking based on the 2016 injection optics with standard lattice errors and $(Q_x, Q_y) = (64.28, 59.31)$ and 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative intensity (top left); horizontal emittance (bottom left); vertical emittance (bottom right); the relative vertical emittance is also shown (top right). The solid black line includes only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines correspond to \seventhtp\ with two different excitation amplitudes (24~nrad and 48~nrad), plus a random dipole noise component in H+V of 6~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="54" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7th_ranhv_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_7th_ranhv_lblshort.png" width="95%"/></a></td><td width="33%"> Comparison of measured loss rates vs.\ excitation amplitude between random and \seventhtp\ in H+V, obtained during the 2017 experiment.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="55" href="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_intensity.png"><img src="https://cds.cern.ch/record/2318948/files/2016+2017injerra2b2uran1_2e-3_7th_3_5um_intensity.png" width="95%"/></a></td><td width="33%"> Calculated bunch intensities and emittances from distribution tracking based on the 2016 injection optics with standard lattice errors and $(Q_x, Q_y) = (64.28, 59.31)$ and 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative intensity (top left); horizontal emittance (bottom left); vertical emittance (bottom right); the relative vertical emittance is also shown (top right). The solid black line includes only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines correspond to \seventhtp\ with two different excitation amplitudes (24~nrad and 48~nrad), plus a random dipole noise component in H+V of 6~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="56" href="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emitv_avg_rel_v10th_no_damper.png" width="95%"/></a></td><td width="33%"> Summary of the 2016 experiments on \tenthtp\ in the vertical plane: losses (left), horizontal emittances (middle) and vertical emittances (right), relative to their initial values. The transverse damping system was not active in this case. The 3 excitation periods are labeled in black according to the value of the maximum excitation amplitude $A_{\mathrm{max}} = 5 \, \Delta A$: no excitation, 48~nrad or 96~nrad. The 4~bunches experiencing the same excitation amplitude $n \, \Delta A$ ($n = 0, \ldots, 5$) are grouped by color. The data are averaged over the 4~bunches, with the envelope representing the standard deviation. The area with a blue background highlights qualitatively the fast adjustment period of the beam distribution, transitioning into a new equilibrium state (indicated by the gray background).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="57" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut8skhv_dp0_amp_annotate.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerrut8skhv_dp0_amp_annotate.png" width="95%"/></a></td><td width="33%"> FMA in transverse amplitude space without excitation (left) and for \eighthtp\ (right) based on the 2017 injection optics with no lattice errors and tunes (62.27, 60.295). The excitation amplitude is 96~nrad in both planes. The $16 Q_y$ and \mbox{$8 Q_x - 4 Q_y$} resonances are excited.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="58" href="https://cds.cern.ch/record/2318948/files/diffusion_illustration.png"><img src="https://cds.cern.ch/record/2318948/files/diffusion_illustration.png" width="95%"/></a></td><td width="33%"> Left: Sketch of passive halo control with a conventional collimation system (top) and active halo control, with the addition of a hollow electron lens (bottom). Right: Illustration of a simplified model of active diffusion enhancement in the transverse plane. The diffusion coefficient as a function of amplitude (orange) is enhanced in a specific amplitude region when the hollow beam is turned on (from solid to dashed line). A corresponding reduction in beam tail population (black) is created (from solid to dashed line).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="59" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t10skhv_3_5um_hist_y.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_t10skhv_3_5um_hist_y.png" width="95%"/></a></td><td width="33%"> Calculated beam distributions as a function of vertical position from distribution-tracking simulations based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors: no excitation (top left), random excitation (top right), \seventhtp\ (bottom left), and \tenthtp\ (bottom right). The excitations are applied in both planes with an amplitude of 96~nrad. For each of the 4~cases, 3~plots are shown. The top plot shows the normalized transverse distributions: `initial' (after $10^2$~turns, in gray), `final' (after $10^4$~turns, in black), and their Gaussian fits (light and dark red, respectively). The middle plots show the relative residuals (i.e., differences, in percent of the peak value) between final and initial distributions (in black) and between each distribution and its Gaussian fit (in light and dark red). The ratios between final and initial distributions are drawn in black in the bottom plots. The residuals emphasize changes near the core of the distributions, whereas ratios (when statistically significant), reveal variations in the tails.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="60" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8v_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8v_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates vs.\ excitation amplitude for \eighthtp\ in H only (left), in V only (center) and in H+V (right) during the 2017 experiment. Uncertainties are statistical. The differences between the three data sets within each excitation mode (black, red, and yellow curves) provide an estimate of the systematic errors.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="61" href="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_h7th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2016_emith_avg_rel_h7th_no_damper.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="62" href="https://cds.cern.ch/record/2318948/files/2016+2017_scale_amp_7h_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2016+2017_scale_amp_7h_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates vs.\ excitation amplitude for \seventhtp\ in the horizontal plane during the 2016 experiment (red and yellow) and the 2017 experiment (black and green). The uncertainties on the excitation amplitude are dominated by the calibration of the transverse feedback and damping system. The uncertainties on the loss rates are statistical. An estimate of the systematic uncertainties (due to changes in beam distribution, for instance) is given by the difference between the two data sets within each experiment. The lines indicate empirical second-order polynomial fits, with damper off (solid) and with damper on (dashed).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="63" href="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_50.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_10thv_slot_50.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2016 experiments on \tenthtp\ in the vertical plane. The transverse damping system was not active on these bunches. The beam distributions at the end of the excitation period are shown in black in the top plots, with a Gaussian fit in red. The bottom plots show the residuals: final profile minus initial profile (black); final profile minus its Gaussian fit (red). Residuals are expressed as a fraction of the peak profile amplitude. The black lines in the plots of the residuals are a measure of the overall change of the distribution shape. The red lines indicate how different the final distributions are from a Gaussian shape. Details of the analysis are given in Ref.~\cite{bsrtprofinj}. The distribution of the reference bunch (left) is almost unchanged, whereas the bunch experiencing the maximum excitation (right) shows a clear shift of particles from the axis towards approximately $\pm 2\sigma$.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="64" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_sigm.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2u_pattern_3_5um_sigm.png" width="95%"/></a></td><td width="33%"> Relative intensity (top left), bunch length (top right) and horizontal (bottom left) and vertical (bottom right) emittances for different pulsing patterns, calculated by distribution tracking based on the 2016 injection optics with $(Q_x, Q_y) = (64.28, 59.31)$ and standard lattice errors. The resonant and random excitations are applied in both planes, with an amplitude of 96~nrad. No random noise component is added. Because of its much larger effects, the random excitation is shown with separate vertical axes.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="65" href="https://cds.cern.ch/record/2318948/files/hel_layout_epbeam.png"><img src="https://cds.cern.ch/record/2318948/files/hel_layout_epbeam.png" width="95%"/></a></td><td width="33%"> Layout of the hollow electron lens for HL-LHC. (Courtesy of CERN EN-MME mechanical engineering group.)</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="66" href="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hvran_no_damper_avg.png"><img src="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hvran_no_damper_avg.png" width="95%"/></a></td><td width="33%"> Measured effects of the random excitation (in V, top row; and H+V, bottom row) during the 2017 experiment: relative intensity losses (left), relative horizontal emittance (center), and relative vertical emittance (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="67" href="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hv7th_no_damper_avg.png"><img src="https://cds.cern.ch/record/2318948/files/2017_bunch_intensity_hv7th_no_damper_avg.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="68" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_intensity.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_intensity.png" width="95%"/></a></td><td width="33%"> Simulations (distribution tracking) based on the 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative bunch intensity (top left), bunch length (top right), horizontal emittance (bottom left), and vertical emittance (bottom right). The solid black line indicates the reference case with no excitation. The dashed and dotted lines are the results of random excitations (H, V, or H+V) with amplitudes 12~nrad and 24~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="69" href="https://cds.cern.ch/record/2318948/files/active_halo_control.png"><img src="https://cds.cern.ch/record/2318948/files/active_halo_control.png" width="95%"/></a></td><td width="33%"> Left: Sketch of passive halo control with a conventional collimation system (top) and active halo control, with the addition of a hollow electron lens (bottom). Right: Illustration of a simplified model of active diffusion enhancement in the transverse plane. The diffusion coefficient as a function of amplitude (orange) is enhanced in a specific amplitude region when the hollow beam is turned on (from solid to dashed line). A corresponding reduction in beam tail population (black) is created (from solid to dashed line).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="70" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_intensity.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_intensity.png" width="95%"/></a></td><td width="33%"> Simulations (with the distribution-tracking method) based on the 2016 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (64.28, 59.31)$: relative beam intensity (top left); normalized horizontal (bottom left) and vertical (bottom right) emittances; vertical emittance relative to its initial value (top right). The solid lines indicate the effect of \tenthtp\ in the vertical plane. The dotted lines include both the resonant excitation and a random dipole noise component of 6~nrad (in both horizontal and vertical planes).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="71" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skh_dp0_ord7.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut7skh_dp0_ord7.png" width="95%"/></a></td><td width="33%"> Frequency-map analysis in betatron tune space based on the 2016 injection optics with no machine errors and tunes (64.28, 59.31): without excitation (top left); \tenthtp\ in both horizontal and vertical planes (top right); \seventhtp\ in the horizontal (bottom left) and vertical (bottom right) planes. The excitation amplitude is 120~nrad in the corresponding plane. The colors (blue to red) represent the tune jitter of tracked particles starting at each given location in tune space~\cite{fmalaskar}. The absence of a strong excitation of any resonance in case of vertical \seventhtp\ and the strong excitation in case of horizontal pulsing confirms the excitation of the $7 Q_x$ resonance. For \tenthtp, there is in contrast no significant difference between H, V, or H+V (Fig.~\ref{fig:fma:10}).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="72" href="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1532.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_ranv_slot_1532.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of the random excitation in V. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The distribution changes in the bunch experiencing the maximum excitation (right) were larger than those in the reference bunch (left). In both cases, distributions retained a Gaussian shape.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="73" href="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_2D.png"><img src="https://cds.cern.ch/record/2318948/files/CHG1b_170523_8p75A_2-4-2kG_500V_75mA_hires_2D.png" width="95%"/></a></td><td width="33%"> Example of current-density distribution measurements for the hollow electron gun prototype CHG1b, taken at the Fermilab electron lens test stand in 2017~\cite{hel_res_field_stancari_2017}: 2-dimensional transverse profile measurement (left) and calculated 1-dimensional radial projection (right).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="74" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skh_dp0_ord10.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skh_dp0_ord10.png" width="95%"/></a></td><td width="33%"> FMA for \tenthtp\ based on the 2016 injection optics with no lattice errors and tunes (64.28, 59.31). The excitation is 120~nrad in the corresponding plane. There is no significant difference between pulsing in H only, V only, or in H+V.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="75" href="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_804.png"><img src="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_804.png" width="95%"/></a></td><td width="33%"> Horizontal beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of the \eighthtp\ in H. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The profile changes in the bunch affected by the maximum excitation (right) are larger than those displayed by the control bunch (left).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="76" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerru_dp0_ord10_annotate.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerru_dp0_ord10_annotate.png" width="95%"/></a></td><td width="33%"> Frequency-map analysis in betatron tune space based on the 2016 injection optics with no machine errors and tunes (64.28, 59.31): without excitation (top left); \tenthtp\ in both horizontal and vertical planes (top right); \seventhtp\ in the horizontal (bottom left) and vertical (bottom right) planes. The excitation amplitude is 120~nrad in the corresponding plane. The colors (blue to red) represent the tune jitter of tracked particles starting at each given location in tune space~\cite{fmalaskar}. The absence of a strong excitation of any resonance in case of vertical \seventhtp\ and the strong excitation in case of horizontal pulsing confirms the excitation of the $7 Q_x$ resonance. For \tenthtp, there is in contrast no significant difference between H, V, or H+V (Fig.~\ref{fig:fma:10}).FMA for \tenthtp\ based on the 2016 injection optics with no lattice errors and tunes (64.28, 59.31). The excitation is 120~nrad in the corresponding plane. There is no significant difference between pulsing in H only, V only, or in H+V.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="77" href="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2016injerra2b2uran1_2e-3_10thV_3_5um_emit2.png" width="95%"/></a></td><td width="33%"> Simulations (with the distribution-tracking method) based on the 2016 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (64.28, 59.31)$: relative beam intensity (top left); normalized horizontal (bottom left) and vertical (bottom right) emittances; vertical emittance relative to its initial value (top right). The solid lines indicate the effect of \tenthtp\ in the vertical plane. The dotted lines include both the resonant excitation and a random dipole noise component of 6~nrad (in both horizontal and vertical planes).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="78" href="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skhv_dp0_ord10.png"><img src="https://cds.cern.ch/record/2318948/files/2016injnocolc15o+19_6noerrut10skhv_dp0_ord10.png" width="95%"/></a></td><td width="33%"> Frequency-map analysis in betatron tune space based on the 2016 injection optics with no machine errors and tunes (64.28, 59.31): without excitation (top left); \tenthtp\ in both horizontal and vertical planes (top right); \seventhtp\ in the horizontal (bottom left) and vertical (bottom right) planes. The excitation amplitude is 120~nrad in the corresponding plane. The colors (blue to red) represent the tune jitter of tracked particles starting at each given location in tune space~\cite{fmalaskar}. The absence of a strong excitation of any resonance in case of vertical \seventhtp\ and the strong excitation in case of horizontal pulsing confirms the excitation of the $7 Q_x$ resonance. For \tenthtp, there is in contrast no significant difference between H, V, or H+V (Fig.~\ref{fig:fma:10}).FMA for \tenthtp\ based on the 2016 injection optics with no lattice errors and tunes (64.28, 59.31). The excitation is 120~nrad in the corresponding plane. There is no significant difference between pulsing in H only, V only, or in H+V.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="79" href="https://cds.cern.ch/record/2318948/files/bunchfilling_measured.png"><img src="https://cds.cern.ch/record/2318948/files/bunchfilling_measured.png" width="95%"/></a></td><td width="33%"> Example of bunch-by-bunch beam centroid motion for Beam~1 in the horizontal (B1H, left) and vertical (B1V, right) planes, detected by the real-time transverse activity monitor during the 2017 experiment, when the beam was excited every 8th~turn.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="80" href="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8hv_lblshort.png"><img src="https://cds.cern.ch/record/2318948/files/2017_scale_amp_8hv_lblshort.png" width="95%"/></a></td><td width="33%"> Measured loss rates vs.\ excitation amplitude for \eighthtp\ in H only (left), in V only (center) and in H+V (right) during the 2017 experiment. Uncertainties are statistical. The differences between the three data sets within each excitation mode (black, red, and yellow curves) provide an estimate of the systematic errors.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="81" href="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2862.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2862.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of \seventhtp\ in H+V. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The profile changes in the bunch affected by the maximum excitation (right) are larger than those displayed by the reference bunch (left).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="82" href="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_amp.png"><img src="https://cds.cern.ch/record/2318948/files/2017injnocolc15o+19_6noerru_dp0_amp.png" width="95%"/></a></td><td width="33%"> FMA in transverse amplitude space without excitation (left) and for \eighthtp\ (right) based on the 2017 injection optics with no lattice errors and tunes (62.27, 60.295). The excitation amplitude is 96~nrad in both planes. The $16 Q_y$ and \mbox{$8 Q_x - 4 Q_y$} resonances are excited.FMA in transverse amplitude space without excitation (left) and with a random 1-nrad H+V excitation (right), based on the 2017 injection optics with no lattice errors and tunes (62.27, 60.295).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="83" href="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_632.png"><img src="https://cds.cern.ch/record/2318948/files/profile_h_8thh_slot_632.png" width="95%"/></a></td><td width="33%"> Horizontal beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of the \eighthtp\ in H. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The profile changes in the bunch affected by the maximum excitation (right) are larger than those displayed by the control bunch (left).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="84" href="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hv7th_no_damper.png"><img src="https://cds.cern.ch/record/2318948/files/2017_emitv_avg_rel_hv7th_no_damper.png" width="95%"/></a></td><td width="33%"> Measured losses and emittances during the 2016 and 2017 experiments: relative losses (left), relative horizontal emittances (middle), and relative vertical emittances (right). Measurements are averaged over the bunches experiencing the same excitation amplitude. The transverse damping system was not active in this set of measurements.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="85" href="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2696.png"><img src="https://cds.cern.ch/record/2318948/files/profile_v_7thhv_slot_2696.png" width="95%"/></a></td><td width="33%"> Vertical beam profiles measured with the Beam Synchrotron Radiation Telescope (BSRT) during the 2017 experiments. The profiles are taken at the end of \seventhtp\ in H+V. For these bunches, the transverse damper was not active. The data are presented in the same way as in Fig.~\ref{fig:10thexpprof}. The profile changes in the bunch affected by the maximum excitation (right) are larger than those displayed by the reference bunch (left).</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="86" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit1.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2u_ranadt_3_5um_emit1.png" width="95%"/></a></td><td width="33%"> Simulations (distribution tracking) based on the 2017 injection optics with standard lattice errors and $(Q_x, Q_y) = (62.27, 60.295)$: relative bunch intensity (top left), bunch length (top right), horizontal emittance (bottom left), and vertical emittance (bottom right). The solid black line indicates the reference case with no excitation. The dashed and dotted lines are the results of random excitations (H, V, or H+V) with amplitudes 12~nrad and 24~nrad.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="87" href="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit2.png"><img src="https://cds.cern.ch/record/2318948/files/2017injerra2b2uran1_2e-3_8th_3_5um_emit2.png" width="95%"/></a></td><td width="33%"> Calculated relative intensities (top left), bunch lengths (top right), horizontal emittances (bottom left), and vertical emittances (bottom right) from distribution-tracking simulations based on the 2017 injection optics with standard lattice errors and tunes $(Q_x, Q_y) = (62.27, 60.295)$. The solid black line is the reference case, including only a random dipole noise component in H+V of 6~nrad. The dotted and dashed lines are the results for \eighthtp, including the same random dipole noise component.</td></tr></table><table width="95%" style="display: inline;"><tr><td width="66%"><a name="88" href="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Eslice.png"><img src="https://cds.cern.ch/record/2318948/files/CHG1b_170512_8p75A_2-4-2p7kG_500V_76mA_hires_Eslice.png" width="95%"/></a></td><td width="33%"> Calculated relative electric field for the hollow electron gun CHG1b in the transverse $x$-$y$ plane (left) and as 1-dimensional cuts through the $x$ and $y$ axes (right). The field calculations are based on measurements at the Fermilab electron-lens test stand combined with \code{warp} calculations of the electric potentials and fields in a cylindrical beam pipe.</td></tr></table><br /><br /> <div class="bottom-left-folded"></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=en&p=recid%3A2318948&rm=wrd" class="moreinfo">Similar records</a></span></div> </div> </div> </div> <br/> </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? Contact <a href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Support</a>. <br /> </div> <div class="pagefooterstriperight"> <div class="cern-logo"> <a id="logo" href="http://cern.ch" title="CERN" rel="CERN" ><img src="https://cds.cern.ch/img/cern_theme/img/cern-logo-large.png" alt="CERN" /></a> </div> <div class="cern-languagebox"> This site is also available in the following languages:<br /><a href="/record/2318948/plots?ln=bg" class="langinfo">Български</a>  <a href="/record/2318948/plots?ln=ca" class="langinfo">Català</a>  <a href="/record/2318948/plots?ln=de" class="langinfo">Deutsch</a>  <a href="/record/2318948/plots?ln=el" class="langinfo">Ελληνικά</a>  <span class="langinfo">English</span>  <a href="/record/2318948/plots?ln=es" class="langinfo">Español</a>  <a href="/record/2318948/plots?ln=fr" class="langinfo">Français</a>  <a href="/record/2318948/plots?ln=hr" class="langinfo">Hrvatski</a>  <a href="/record/2318948/plots?ln=it" class="langinfo">Italiano</a>  <a href="/record/2318948/plots?ln=ja" class="langinfo">日本語</a>  <a href="/record/2318948/plots?ln=ka" class="langinfo">ქართული</a>  <a href="/record/2318948/plots?ln=no" class="langinfo">Norsk/Bokmål</a>  <a href="/record/2318948/plots?ln=pl" class="langinfo">Polski</a>  <a href="/record/2318948/plots?ln=pt" class="langinfo">Português</a>  <a href="/record/2318948/plots?ln=ru" class="langinfo">Русский</a>  <a href="/record/2318948/plots?ln=sk" class="langinfo">Slovensky</a>  <a href="/record/2318948/plots?ln=sv" class="langinfo">Svenska</a>  <a href="/record/2318948/plots?ln=zh_CN" class="langinfo">中文(简)</a>  <a href="/record/2318948/plots?ln=zh_TW" class="langinfo">中文(繁)</a> </div> </div>  </footer> <script type="text/javascript"> var SyndeticsBookCovers = (function() { var SMALL_SIZE = "sc.gif", MEDIUM_SIZE = "mc.gif", RAW_URL = "https://secure.syndetics.com/index.aspx?isbn=THEISBN/THESIZE&client=cernlibrary"; replaceCover = function(imgElement, isbns, hdFormat) { var img = new Image(), size = hdFormat ? MEDIUM_SIZE : SMALL_SIZE; var _isbns = isbns.sort(function(a, b) { // sort from shortest to longest ISBN (more modern) return a.length > b.length ? 1 : -1; }); function next() { var isbn = _isbns.pop(); if (isbn) { var url = RAW_URL.replace("THEISBN", isbn).replace("THESIZE", size); img.src = url; } } function done() { imgElement.src = img.src; } img.onload = function() { if (this.width > 1) { done(); } else { next(); } }; next(); }; return { replaceCover: replaceCover }; })(); $(document).ready(function() { // get book covers $("img.book-cover").each(function() { var $this = $(this), strIsbns = $this.data("isbns") || "", isbnsArray = String(strIsbns).split(","), hdFormat = $this.hasClass("hd"); SyndeticsBookCovers.replaceCover(this, isbnsArray, hdFormat); }); // WebNews tooltips $.ajax({ url: "/news/tooltips", success: function(data) { create_tooltips(data); }, dataType: "json", cache: false }); }); </script>  <script src="//cds.cern.ch/js/feedback.js"></script>   <script> var _paq = window._paq = window._paq || []; /* tracker methods like "setCustomDimension" should be called before "trackPageView" */ _paq.push(['trackPageView']); _paq.push(['enableLinkTracking']); (function() { var u="https://webanalytics.web.cern.ch/"; _paq.push(['setTrackerUrl', u+'matomo.php']); _paq.push(['setSiteId', '756']); var d=document, g=d.createElement('script'), s=d.getElementsByTagName('script')[0]; g.async=true; g.src=u+'matomo.js'; s.parentNode.insertBefore(g,s); })(); </script>  </body> </html>