Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr.

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Herr.</h1> <p class="uk-article-meta">Published by<a href="/user/11120384/" class="uk-margin-small-left uk-margin-small-right">Sophie Nicholson</a> <span id="timeago" class="uk-float-right">Modified over 8 years ago</span> </p> </div> <div id="social-share" class="uk-float-left uk-margin"> <div id="pluses"> <div class="addthis_toolbox addthis_default_style addthis_32x32_style"> <a class="addthis_button_facebook"></a> <a class="addthis_button_twitter"></a> <a class="addthis_button_linkedin"></a> <a class="addthis_button_google_plusone_share"></a> <a class="addthis_button_blogger"></a> <a class="addthis_button_flipboard"></a> <a class="addthis_button_google"></a> <a class="addthis_button_gmail"></a> <a class="addthis_button_vk"></a> <a class="addthis_button_email"></a> <a class="addthis_button_pinterest_share"></a> <a class="addthis_button_tumblr"></a> <a class="addthis_button_myspace"></a> <a class="addthis_button_wordpress"></a> <a class="addthis_button_ziczac"></a> <a class="addthis_button_print"></a> <a class="addthis_button_favorites"></a> <a class="addthis_button_whatsapp"></a> <a class="addthis_button_reddit"></a> <a class="addthis_counter addthis_bubble_style"></a> </div> </div> </div>  <div class="uk-float-right uk-margin" id="get-code-btn"> <div class="uk-button-group uk-margin-small-right"> <button type="button" class="uk-button uk-button uk-button-primary"><span class="uk-icon-code"></span></button> <button type="button" data-original-title="Embed this presentation" id="get_embed" class="uk-button uk-button">Embed</button> </div>  <div class="uk-button-group" id="download-btn"> <button class="uk-button uk-button uk-button-success" data-toggle="modal" data-target="#download-modal"><span class="uk-icon-cloud-download"></span></button> <button class="uk-button uk-button" data-toggle="modal" data-target="#download-modal">Download presentation</button> </div>  </div>   </div> </div> <div class="uk-panel uk-panel-box uk-panel-box-secondary uk-margin" id="embed" style="display: none"> <div class="uk-margin uk-text-right"> <div class="uk-form-row"> <textarea rows="3" cols="" id="embed_input"></textarea> </div> <div class="uk-button-group"> <button class="uk-button uk-button uk-button-success"><span class="uk-icon-copy"></span></button> <button title="Customize embed code" id="copyembed" class="uk-button uk-button"> Copy to clipboard</button> </div> </div> </div> <div class="top_comment_banners uk-text-center uk-nbfc"> </div> <div class="uk-panel uk-panel-box uk-panel-box-secondary uk-margin" id="fb_wrapper"> <div class="fb-comments" data-href="http://slideplayer.com/slide/9655442/" data-numposts="5" data-width="100%""></div> </div> <div class="bottom_comment_banners uk-text-center uk-nbfc"> <style>#place_137 > ins[data-ad-slot="4312680294"]{display:none;} @media (min-width: 0px) and (max-width: 5000px) { #place_137 > ins[data-ad-slot="4312680294"]{display:inline-block;} } </style><div id="place_137" class="ads uk-text-center uk-margin-small-bottom uk-margin-small-right uk-display-inline-block uk-margin-small-top"> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" style="min-width:234px; max-width:728px; width:100%; height:60px" data-ad-client="ca-pub-6133583279631137" data-ad-slot="4312680294" ></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script></div> </div> <div id="after_comment_similars" class="uk-margin-bottom uk-margin-top uk-panel uk-panel-box uk-panel-box-secondary uk-margin"> <h3 class="tm-text-dark"> <span class="uk-icon-list uk-margin-small-right"></span>Similar presentations </h3> <hr class="uk-article-divider"> <div></div> <button class="uk-button uk-margin-top uk-button-primary uk-width-1-1" id="load_more_btn"><span class="uk-icon-arrow-circle-down uk-margin-small-right"></span>More</button> </div> <div class="uk-panel uk-panel-box uk-panel-box-secondary uk-margin"> <div class="uk-article"> <h2 class="transkript-title">Presentation on theme: "Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr."— Presentation transcript:</h2> <style> @media(min-width:801px){#place_14>ins[data-ad-slot="4502451947"]{display:none !important;}} @media(max-width:800px){#place_14>ins:not([data-ad-slot="4502451947"]){display:none !important;}} @media(max-width:800px){#place_14 { width: 250px;}} @media(max-width:500px) {#place_14 { width: 120px;}} </style><div id="place_14" class="ads "> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6133583279631137" data-ad-slot="4502451947" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" data-ad-client="ca-pub-6133583279631137" style="display:inline-block;width:320px;height:100px" data-ad-slot="2030221560"></ins> <script>(adsbygoogle = window.adsbygoogle || []).push({});</script></div> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_1.jpg" target="_blank" title="Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr" > 1 </a> </span> Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_1.jpg", "name": "Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr", "description": "Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_1.jpg" width="800" align="left" alt="Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr" title="Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. Herr"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_2.jpg" target="_blank" title="Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency" > 2 </a> </span> Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_2.jpg", "name": "Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency", "description": "Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_2.jpg" width="800" align="left" alt="Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency" title="Hadron Circular Colliders Bunch intensity: Transverse Beam size : Number of bunches Revolution frequency"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_3.jpg" target="_blank" title="When do we have beam-beam effects." > 3 </a> </span> When do we have beam-beam effects?  They occur when two beams get closer and collide  Two types  High energy collisions between two particles (wanted)  Distortions of beam by electromagnetic forces (unwanted)  Unfortunately: usually both go together…  0.001% (or less) of particles collide  99.999% (or more) of particles are distorted <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_3.jpg", "name": "When do we have beam-beam effects.", "description": "\uf0d8 They occur when two beams get closer and collide \uf0d8 Two types \uf0d8 High energy collisions between two particles (wanted) \uf0d8 Distortions of beam by electromagnetic forces (unwanted) \uf0d8 Unfortunately: usually both go together\u2026 \uf0d8 0.001% (or less) of particles collide \uf0d8 % (or more) of particles are distorted.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_3.jpg" width="800" align="left" alt="When do we have beam-beam effects." title=" They occur when two beams get closer and collide  Two types  High energy collisions between two particles (wanted)  Distortions of beam by electromagnetic forces (unwanted)  Unfortunately: usually both go together…  0.001% (or less) of particles collide  % (or more) of particles are distorted."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_4.jpg" target="_blank" title="Beam-beam effects: overview  Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage And CAS Proceedings" > 4 </a> </span> Beam-beam effects: overview  Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage http://lhc-beam-beam.web.cern.ch/lhc-beam-beam/http://lhc-beam-beam.web.cern.ch/lhc-beam-beam/ And CAS Proceedings <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_4.jpg", "name": "Beam-beam effects: overview \uf0d8 Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage And CAS Proceedings", "description": "Beam-beam effects: overview \uf0d8 Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage And CAS Proceedings", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_4.jpg" width="800" align="left" alt="Beam-beam effects: overview  Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage And CAS Proceedings" title="Beam-beam effects: overview  Circular Colliders: interaction occurs at every turn Many effects and problems Try to understand some of them Overview of effects (single particle and multi-particle effects) Qualitative and physical picture of effects Observations from the LHC Mathematical derivations and more info in References or at Beam-beam webpage And CAS Proceedings"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_5.jpg" target="_blank" title="References: [1] [2] V." > 5 </a> </span> References: [1] http://cern.ch/Werner.Herr/CAS2009/proceedings/bb_proc.pdfhttp://cern.ch/Werner.Herr/CAS2009/proceedings/bb_proc.pdf [2] V. Shiltsev et al, “Beam beam effects in the Tevatron”, Phys. Rev. ST Accel. Beams 8, 101001 (2005) [3] Lyn Evans “The beam-beam interaction”, CERN 84-15 (1984) [4] Alex Chao “Lie Algebra Techniques for Nonlinear Dynamics” SLAC-PUB-9574 (2002) [5] J. D. Jackson, “Classical Electrodynamics”, John Wiley & Sons, NY, 1962. [6] H. Grote, F. Schmidt, L. H. A. Leunissen,”LHC Dynamic Aperture at Collision”, LHC-Project-Note 197, (1999). [7] W. Herr,”Features and implications of different LHC crossing schemes”, LHC-Project-Note 628, (2003). [8] A. Hofmann,”Beam-beam modes for two beams with unequal tunes”, CERN-SL-99-039 (AP) (1999) p. 56. [9] Y. Alexahin, ”On the Landau damping and decoherence of transverse dipole oscillations in colliding beams ”, Part. Acc. 59, 43 (1996). …much more on the LHC Beam-beam webpage: http://lhc-beam-beam.web.cern.ch/lhc-beam-beam/ <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_5.jpg", "name": "References: [1] [2] V.", "description": "Shiltsev et al, Beam beam effects in the Tevatron , Phys. Rev. ST Accel. Beams 8, (2005) [3] Lyn Evans The beam-beam interaction , CERN (1984) [4] Alex Chao Lie Algebra Techniques for Nonlinear Dynamics SLAC-PUB-9574 (2002) [5] J. D. Jackson, Classical Electrodynamics , John Wiley & Sons, NY, [6] H. Grote, F. Schmidt, L. H. A. Leunissen, LHC Dynamic Aperture at Collision , LHC-Project-Note 197, (1999). [7] W. Herr, Features and implications of different LHC crossing schemes , LHC-Project-Note 628, (2003). [8] A. Hofmann, Beam-beam modes for two beams with unequal tunes , CERN-SL (AP) (1999) p. 56. [9] Y. Alexahin, On the Landau damping and decoherence of transverse dipole oscillations in colliding beams , Part. Acc. 59, 43 (1996). \u2026much more on the LHC Beam-beam webpage:", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_5.jpg" width="800" align="left" alt="References: [1] [2] V." title="Shiltsev et al, Beam beam effects in the Tevatron , Phys. Rev. ST Accel. Beams 8, (2005) [3] Lyn Evans The beam-beam interaction , CERN (1984) [4] Alex Chao Lie Algebra Techniques for Nonlinear Dynamics SLAC-PUB-9574 (2002) [5] J. D. Jackson, Classical Electrodynamics , John Wiley & Sons, NY, [6] H. Grote, F. Schmidt, L. H. A. Leunissen, LHC Dynamic Aperture at Collision , LHC-Project-Note 197, (1999). [7] W. Herr, Features and implications of different LHC crossing schemes , LHC-Project-Note 628, (2003). [8] A. Hofmann, Beam-beam modes for two beams with unequal tunes , CERN-SL (AP) (1999) p. 56. [9] Y. Alexahin, On the Landau damping and decoherence of transverse dipole oscillations in colliding beams , Part. Acc. 59, 43 (1996). …much more on the LHC Beam-beam webpage:"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_6.jpg" target="_blank" title="Beams EM potential  Beam is a collection of charges  Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but… Single particle motion and whole bunch motion distorted" > 6 </a> </span> Beams EM potential  Beam is a collection of charges  Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but… Single particle motion and whole bunch motion distorted <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_6.jpg", "name": "Beams EM potential \uf0d8 Beam is a collection of charges \uf0d8 Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but\u2026 Single particle motion and whole bunch motion distorted", "description": "Beams EM potential \uf0d8 Beam is a collection of charges \uf0d8 Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but\u2026 Single particle motion and whole bunch motion distorted", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_6.jpg" width="800" align="left" alt="Beams EM potential  Beam is a collection of charges  Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but… Single particle motion and whole bunch motion distorted" title="Beams EM potential  Beam is a collection of charges  Beam is an electromagnetic potential for other charges Force on itself (space charge) and opposing beam (beam-beam effects) Focusing quadrupoleOpposite Beam A beam acts on particles like an electromagnetic lens, but… Single particle motion and whole bunch motion distorted"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_7.jpg" target="_blank" title="Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution  Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force…" > 7 </a> </span> Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution  Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force… <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_7.jpg", "name": "Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution \uf072 Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force\u2026", "description": "Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution \uf072 Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force\u2026", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_7.jpg" width="800" align="left" alt="Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution  Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force…" title="Beam-beam Mathematics General approach in electromagnetic problems Reference[5] already applied to beam-beam interactions in Reference[1,3, 4] Derive potential from Poisson equation for charges with distribution  Then compute the fields Solution of Poisson equation From Lorentz force one calculates the force acting on test particle with charge q Making some assumptions we can simplify the problem and derive analytical formula for the force…"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_8.jpg" target="_blank" title="Round Gaussian distributions: Gaussian distribution for charges: Round beams: Very relativistic, Force has only radial component : Beam-beam kick obtained integrating the force over the collision (i.e." > 8 </a> </span> Round Gaussian distributions: Gaussian distribution for charges: Round beams: Very relativistic, Force has only radial component : Beam-beam kick obtained integrating the force over the collision (i.e. time of passage) Only radial component in relativistic case Beam-beam Force How does this force looks like? <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_8.jpg", "name": "Round Gaussian distributions: Gaussian distribution for charges: Round beams: Very relativistic, Force has only radial component : Beam-beam kick obtained integrating the force over the collision (i.e.", "description": "time of passage) Only radial component in relativistic case Beam-beam Force How does this force looks like .", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_8.jpg" width="800" align="left" alt="Round Gaussian distributions: Gaussian distribution for charges: Round beams: Very relativistic, Force has only radial component : Beam-beam kick obtained integrating the force over the collision (i.e." title="time of passage) Only radial component in relativistic case Beam-beam Force How does this force looks like ."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_9.jpg" target="_blank" title="Beam-beam Force" > 9 </a> </span> Beam-beam Force <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_9.jpg", "name": "Beam-beam Force", "description": "Beam-beam Force", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_9.jpg" width="800" align="left" alt="Beam-beam Force" title="Beam-beam Force"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_10.jpg" target="_blank" title="Why do we care. Strongest non-linearity in a collider YOU CANNOT AVOID." > 10 </a> </span> Why do we care? Strongest non-linearity in a collider YOU CANNOT AVOID! Pushing for luminosity means stronger beam-beam effects Physics fill lasts for many hours 10h – 24h Two main questions: What happens to a single particle? What happens to the whole beam? <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_10.jpg", "name": "Why do we care. Strongest non-linearity in a collider YOU CANNOT AVOID.", "description": "Pushing for luminosity means stronger beam-beam effects Physics fill lasts for many hours 10h \u2013 24h Two main questions: What happens to a single particle. What happens to the whole beam .", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_10.jpg" width="800" align="left" alt="Why do we care. Strongest non-linearity in a collider YOU CANNOT AVOID." title="Pushing for luminosity means stronger beam-beam effects Physics fill lasts for many hours 10h – 24h Two main questions: What happens to a single particle. What happens to the whole beam ."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_11.jpg" target="_blank" title="Beam-Beam Force: single particle… For small amplitudes: linear force For large amplitude: very non-linear The beam will act as a strong non-linear electromagnetic lens." > 11 </a> </span> Beam-Beam Force: single particle… For small amplitudes: linear force For large amplitude: very non-linear The beam will act as a strong non-linear electromagnetic lens! Lattice defocusing quadrupole Beam-beam force Linear force <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_11.jpg", "name": "Beam-Beam Force: single particle\u2026 For small amplitudes: linear force For large amplitude: very non-linear The beam will act as a strong non-linear electromagnetic lens.", "description": "Lattice defocusing quadrupole Beam-beam force Linear force.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_11.jpg" width="800" align="left" alt="Beam-Beam Force: single particle… For small amplitudes: linear force For large amplitude: very non-linear The beam will act as a strong non-linear electromagnetic lens." title="Lattice defocusing quadrupole Beam-beam force Linear force."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_12.jpg" target="_blank" title="Can we quantify the beam-beam strenght." > 12 </a> </span> Can we quantify the beam-beam strenght? Beam-beam force For small amplitudes: linear force The slope of the force gives you the beam-beam parameter Quantifies the strength of the force but does NOT reflect the nonlinear nature of the force <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_12.jpg", "name": "Can we quantify the beam-beam strenght.", "description": "Beam-beam force For small amplitudes: linear force The slope of the force gives you the beam-beam parameter Quantifies the strength of the force but does NOT reflect the nonlinear nature of the force.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_12.jpg" width="800" align="left" alt="Can we quantify the beam-beam strenght." title="Beam-beam force For small amplitudes: linear force The slope of the force gives you the beam-beam parameter Quantifies the strength of the force but does NOT reflect the nonlinear nature of the force."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_13.jpg" target="_blank" title="Colliders: For round beams: For non-round beams: Examples:" > 13 </a> </span> Colliders: For round beams: For non-round beams: Examples: <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_13.jpg", "name": "Colliders: For round beams: For non-round beams: Examples:", "description": "Colliders: For round beams: For non-round beams: Examples:", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_13.jpg" width="800" align="left" alt="Colliders: For round beams: For non-round beams: Examples:" title="Colliders: For round beams: For non-round beams: Examples:"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_14.jpg" target="_blank" title="Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune  Q and beta function at the IP  *:" > 14 </a> </span> Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune  Q and beta function at the IP  *: <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_14.jpg", "name": "Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune \uf044 Q and beta function at the IP \uf062 *:", "description": "Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune \uf044 Q and beta function at the IP \uf062 *:", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_14.jpg" width="800" align="left" alt="Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune  Q and beta function at the IP  *:" title="Linear Tune shift For small amplitudes beam-beam can be approximated as linear force as a quadrupole Focal length: Beam-beam matrix: Perturbed one turn matrix with perturbed tune  Q and beta function at the IP  *:"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_15.jpg" target="_blank" title="Linear tune Solving the one turn matrix one can derive the tune shift  Q and the perturbed beta function at the IP  *: Tune is changed  -function is changed: …how do they change" > 15 </a> </span> Linear tune Solving the one turn matrix one can derive the tune shift  Q and the perturbed beta function at the IP  *: Tune is changed  -function is changed: …how do they change? <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_15.jpg", "name": "Linear tune Solving the one turn matrix one can derive the tune shift \uf044 Q and the perturbed beta function at the IP \uf062 *: Tune is changed \uf062 -function is changed: \u2026how do they change", "description": "Linear tune Solving the one turn matrix one can derive the tune shift \uf044 Q and the perturbed beta function at the IP \uf062 *: Tune is changed \uf062 -function is changed: \u2026how do they change", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_15.jpg" width="800" align="left" alt="Linear tune Solving the one turn matrix one can derive the tune shift  Q and the perturbed beta function at the IP  *: Tune is changed  -function is changed: …how do they change" title="Linear tune Solving the one turn matrix one can derive the tune shift  Q and the perturbed beta function at the IP  *: Tune is changed  -function is changed: …how do they change"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_16.jpg" target="_blank" title="Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger  Strongest variation with Q" > 16 </a> </span> Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger  Strongest variation with Q <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_16.jpg", "name": "Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger \uf078 Strongest variation with Q", "description": "Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger \uf078 Strongest variation with Q", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_16.jpg" width="800" align="left" alt="Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger  Strongest variation with Q" title="Tune dependence of tune shift and dynamic beta Tune shift as a function of tune Larger  Strongest variation with Q"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_17.jpg" target="_blank" title="Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction" > 17 </a> </span> Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_17.jpg", "name": "Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction", "description": "Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_17.jpg" width="800" align="left" alt="Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction" title="Head-on and Long-range interactions Beam-beam force Head-on Long-range Other beam passing in the center force: HEAD-ON beam-beam interaction Other beam passing at an offset of the force: LONG-RANGE beam-beam interaction"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_18.jpg" target="_blank" title="Multiple bunch Complications For 25ns case 124 BBIs per turn: 4 HO and 120 LR Num." > 18 </a> </span> Multiple bunch Complications For 25ns case 124 BBIs per turn: 4 HO and 120 LR Num. of bunches: MANY INTERACTIONS Head-On Long range 3.7 m <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_18.jpg", "name": "Multiple bunch Complications For 25ns case 124 BBIs per turn: 4 HO and 120 LR Num.", "description": "of bunches: MANY INTERACTIONS Head-On Long range 3.7 m.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_18.jpg" width="800" align="left" alt="Multiple bunch Complications For 25ns case 124 BBIs per turn: 4 HO and 120 LR Num." title="of bunches: MANY INTERACTIONS Head-On Long range 3.7 m."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_19.jpg" target="_blank" title="Crossing angle operation High number of bunches in train structures Head-On Long Range LHC, KEKB… colliders 72 bunches …." > 19 </a> </span> Crossing angle operation High number of bunches in train structures Head-On Long Range LHC, KEKB… colliders 72 bunches …. SppSTevatronRHICLHC Number Bunches6361092808 LR interactions9700120/40 Head-on interactions3224 <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_19.jpg", "name": "Crossing angle operation High number of bunches in train structures Head-On Long Range LHC, KEKB\u2026 colliders 72 bunches \u2026.", "description": "SppSTevatronRHICLHC Number Bunches LR interactions \/40 Head-on interactions3224.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_19.jpg" width="800" align="left" alt="Crossing angle operation High number of bunches in train structures Head-On Long Range LHC, KEKB… colliders 72 bunches …." title="SppSTevatronRHICLHC Number Bunches LR interactions /40 Head-on interactions3224."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_20.jpg" target="_blank" title="A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces" > 20 </a> </span> A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_20.jpg", "name": "A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces", "description": "A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_20.jpg" width="800" align="left" alt="A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces" title="A beam is a collection of particles Beam-beam force Tune shift as a function of amplitude (detuning with amplitude or tune spread) Beam 2 passing in the center of force produce by Beam 1 Particles of Beam 2 will experience different ranges of the beam-beam forces"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_21.jpg" target="_blank" title="A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction" > 21 </a> </span> A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_21.jpg", "name": "A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction", "description": "A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_21.jpg" width="800" align="left" alt="A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction" title="A beam will experience all the force range Beam-beam force Different particles will see different force Beam-beam force Second beam passing in the center HEAD-ON beam-beam interaction Second beam displaced offset LONG-RANGE beam-beam interaction"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_22.jpg" target="_blank" title="Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift" > 22 </a> </span> Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_22.jpg", "name": "Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift", "description": "Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_22.jpg" width="800" align="left" alt="Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift" title="Detuning with Amplitude for head-on Instantaneous tune shift of test particle when it crosses the other beam is related to the derivative of the force with respect to the amplitude For small amplitude test particle linear tune shift"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_23.jpg" target="_blank" title="Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on" > 23 </a> </span> Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_23.jpg", "name": "Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on", "description": "Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_23.jpg" width="800" align="left" alt="Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on" title="Beam with many particles this results in a tune spread Mathematical derivation in Ref [3] using Hamiltonian formalism and in Ref [4] using Lie Algebra Detuning with Amplitude for head-on"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_24.jpg" target="_blank" title="Head-on detuning with amplitude and footprints 1-D plot of detuning with amplitude And in the other plane." > 24 </a> </span> Head-on detuning with amplitude and footprints 1-D plot of detuning with amplitude And in the other plane? THE SAME DERIVATION same tune spread FOOTPRINT 2-D mapping of the detuning with amplitude of particles <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_24.jpg", "name": "Head-on detuning with amplitude and footprints 1-D plot of detuning with amplitude And in the other plane.", "description": "THE SAME DERIVATION same tune spread FOOTPRINT 2-D mapping of the detuning with amplitude of particles.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_24.jpg" width="800" align="left" alt="Head-on detuning with amplitude and footprints 1-D plot of detuning with amplitude And in the other plane." title="THE SAME DERIVATION same tune spread FOOTPRINT 2-D mapping of the detuning with amplitude of particles."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_25.jpg" target="_blank" title="And for long-range interactions. Second beam centered at d (i.e." > 25 </a> </span> And for long-range interactions? Second beam centered at d (i.e. 6  Small amplitude particles positive tune shifts Large amplitude can go to negative tune shifts Long range tune shift scaling for distances <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_25.jpg", "name": "And for long-range interactions. Second beam centered at d (i.e.", "description": "6 \uf073\uf029 Small amplitude particles positive tune shifts Large amplitude can go to negative tune shifts Long range tune shift scaling for distances.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_25.jpg" width="800" align="left" alt="And for long-range interactions. Second beam centered at d (i.e." title="6  Small amplitude particles positive tune shifts Large amplitude can go to negative tune shifts Long range tune shift scaling for distances."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_26.jpg" target="_blank" title="Long-range footprints Separation in vertical plane." > 26 </a> </span> Long-range footprints Separation in vertical plane! And in horizontal plane? The test particle is centered with the opposite beam tune spread more like for head-on at large amplitudes The picture is more complicated now the LARGE amplitude particles see the second beam and have larger tune shift <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_26.jpg", "name": "Long-range footprints Separation in vertical plane.", "description": "And in horizontal plane. The test particle is centered with the opposite beam tune spread more like for head-on at large amplitudes The picture is more complicated now the LARGE amplitude particles see the second beam and have larger tune shift.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_26.jpg" width="800" align="left" alt="Long-range footprints Separation in vertical plane." title="And in horizontal plane. The test particle is centered with the opposite beam tune spread more like for head-on at large amplitudes The picture is more complicated now the LARGE amplitude particles see the second beam and have larger tune shift."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_27.jpg" target="_blank" title="Beam-beam tune shift and spread Footprints depend on: number of interactions Type (Head-on and long-range) Plane of interaction When long-range effects become important footprint wings appear and alternating crossing important Aim to reduce the area as much as possible." > 27 </a> </span> Beam-beam tune shift and spread Footprints depend on: number of interactions Type (Head-on and long-range) Plane of interaction When long-range effects become important footprint wings appear and alternating crossing important Aim to reduce the area as much as possible! Passive compensation of tune shift Ref[7] QxQx QyQy (0,6) (0,0) (0,6) <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_27.jpg", "name": "Beam-beam tune shift and spread Footprints depend on: number of interactions Type (Head-on and long-range) Plane of interaction When long-range effects become important footprint wings appear and alternating crossing important Aim to reduce the area as much as possible.", "description": "Passive compensation of tune shift Ref[7] QxQx QyQy (0,6) (0,0) (0,6).", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_27.jpg" width="800" align="left" alt="Beam-beam tune shift and spread Footprints depend on: number of interactions Type (Head-on and long-range) Plane of interaction When long-range effects become important footprint wings appear and alternating crossing important Aim to reduce the area as much as possible." title="Passive compensation of tune shift Ref[7] QxQx QyQy (0,6) (0,0) (0,6)."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_28.jpg" target="_blank" title="Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches …." > 28 </a> </span> Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches …. <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_28.jpg", "name": "Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches \u2026.", "description": "Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches \u2026.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_28.jpg" width="800" align="left" alt="Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches …." title="Complications Different bunch families: Pacman and Super Pacman Super Pacman: miss head-on BBI IP2 and IP8 depending on filling scheme Pacman: miss long range BBI PACMAN and SUPER PACMAN bunches 72 bunches …."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_29.jpg" target="_blank" title="LHC Complications: filling schemes Pacman Bunche: different number of long-range interactions 72 bunches …." > 29 </a> </span> LHC Complications: filling schemes Pacman Bunche: different number of long-range interactions 72 bunches …. Nominal Bunches PACMAN PS extraction kicker SPS extraction kicker Abort Gap <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_29.jpg", "name": "LHC Complications: filling schemes Pacman Bunche: different number of long-range interactions 72 bunches \u2026.", "description": "Nominal Bunches PACMAN PS extraction kicker SPS extraction kicker Abort Gap.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_29.jpg" width="800" align="left" alt="LHC Complications: filling schemes Pacman Bunche: different number of long-range interactions 72 bunches …." title="Nominal Bunches PACMAN PS extraction kicker SPS extraction kicker Abort Gap."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_30.jpg" target="_blank" title="Pacman and Super-pacman LHC ATLAS+CMS+LHCb ATLAS+CMS+LHCb+ALICE(LR) ATLAS+CMS LHCb LHCb+ALICE(LR) …operationally it is even more complicated." > 30 </a> </span> Pacman and Super-pacman LHC ATLAS+CMS+LHCb ATLAS+CMS+LHCb+ALICE(LR) ATLAS+CMS LHCb LHCb+ALICE(LR) …operationally it is even more complicated! …intensities, emittances… <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_30.jpg", "name": "Pacman and Super-pacman LHC ATLAS+CMS+LHCb ATLAS+CMS+LHCb+ALICE(LR) ATLAS+CMS LHCb LHCb+ALICE(LR) \u2026operationally it is even more complicated.", "description": "\u2026intensities, emittances\u2026.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_30.jpg" width="800" align="left" alt="Pacman and Super-pacman LHC ATLAS+CMS+LHCb ATLAS+CMS+LHCb+ALICE(LR) ATLAS+CMS LHCb LHCb+ALICE(LR) …operationally it is even more complicated." title="…intensities, emittances…."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_31.jpg" target="_blank" title="Particle Losses Dynamic Aperture: area in amplitude space with stable motion Stable area of particles depends on beam intensity and crossing angle Stable area depends on beam-beam interactions therefore the choice of running parameters (crossing angles,  *, intensity) is the result of careful study of different effects." > 31 </a> </span> Particle Losses Dynamic Aperture: area in amplitude space with stable motion Stable area of particles depends on beam intensity and crossing angle Stable area depends on beam-beam interactions therefore the choice of running parameters (crossing angles,  *, intensity) is the result of careful study of different effects! Ref [6] Stable Area (  ) 10-12  separation <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_31.jpg", "name": "Particle Losses Dynamic Aperture: area in amplitude space with stable motion Stable area of particles depends on beam intensity and crossing angle Stable area depends on beam-beam interactions therefore the choice of running parameters (crossing angles, \uf062 *, intensity) is the result of careful study of different effects.", "description": "Ref [6] Stable Area ( \uf073 ) \uf073 separation.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_31.jpg" width="800" align="left" alt="Particle Losses Dynamic Aperture: area in amplitude space with stable motion Stable area of particles depends on beam intensity and crossing angle Stable area depends on beam-beam interactions therefore the choice of running parameters (crossing angles,  *, intensity) is the result of careful study of different effects." title="Ref [6] Stable Area (  )  separation."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_32.jpg" target="_blank" title="DO we see the effects of LR in the LHC." > 32 </a> </span> DO we see the effects of LR in the LHC? Particle losses follow number of Long range interactions Nominal LHC will have twice the number of interactions Small crossing angle = small separation If separation of long range too small particles become unstable and get lost Courtesy G. Papotti Courtesy X. Buffat 6  separation <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_32.jpg", "name": "DO we see the effects of LR in the LHC.", "description": "Particle losses follow number of Long range interactions Nominal LHC will have twice the number of interactions Small crossing angle = small separation If separation of long range too small particles become unstable and get lost Courtesy G. Papotti Courtesy X. Buffat 6 \uf073 separation.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_32.jpg" width="800" align="left" alt="DO we see the effects of LR in the LHC." title="Particle losses follow number of Long range interactions Nominal LHC will have twice the number of interactions Small crossing angle = small separation If separation of long range too small particles become unstable and get lost Courtesy G. Papotti Courtesy X. Buffat 6  separation."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_33.jpg" target="_blank" title="Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK" > 33 </a> </span> Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_33.jpg", "name": "Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK", "description": "Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_33.jpg" width="800" align="left" alt="Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK" title="Long-range BB and Orbit Effects Long Range Beam-beam interactions lead to orbit effects Orbit can be corrected but we should remember PACMAN effects Long range kick For well separated beams The force has an amplitude independent contribution: ORBIT KICK"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_34.jpg" target="_blank" title="LHC orbit effects d = units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7]" > 34 </a> </span> LHC orbit effects d = 0 - 0.4 units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7] <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_34.jpg", "name": "LHC orbit effects d = units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7]", "description": "LHC orbit effects d = units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7]", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_34.jpg" width="800" align="left" alt="LHC orbit effects d = units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7]" title="LHC orbit effects d = units of beam size Orbit effects different due to Pacman effects and the many long-range add up giving a non negligible effect Ref [7]"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_35.jpg" target="_blank" title="Long range orbit effect Long range interactions leads to orbit offsets at the experiment a direct consequence is deterioration of the luminosity Measurement of the vertex centroid by ATLAS Ref [7] Effect is already visible with reduced number of interactions Courtesy W." > 35 </a> </span> Long range orbit effect Long range interactions leads to orbit offsets at the experiment a direct consequence is deterioration of the luminosity Measurement of the vertex centroid by ATLAS Ref [7] Effect is already visible with reduced number of interactions Courtesy W. Kozanecki Calculations for nominal LHC <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_35.jpg", "name": "Long range orbit effect Long range interactions leads to orbit offsets at the experiment a direct consequence is deterioration of the luminosity Measurement of the vertex centroid by ATLAS Ref [7] Effect is already visible with reduced number of interactions Courtesy W.", "description": "Kozanecki Calculations for nominal LHC.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_35.jpg" width="800" align="left" alt="Long range orbit effect Long range interactions leads to orbit offsets at the experiment a direct consequence is deterioration of the luminosity Measurement of the vertex centroid by ATLAS Ref [7] Effect is already visible with reduced number of interactions Courtesy W." title="Kozanecki Calculations for nominal LHC."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_36.jpg" target="_blank" title="IP8IP1IP2IP5IP5 Courtesy T." > 36 </a> </span> IP8IP1IP2IP5IP5 Courtesy T. Baer Vertical oscillation starts when one beam is ejected and dumped Long range orbit effect observations: <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_36.jpg", "name": "IP8IP1IP2IP5IP5 Courtesy T.", "description": "Baer Vertical oscillation starts when one beam is ejected and dumped Long range orbit effect observations:.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_36.jpg" width="800" align="left" alt="IP8IP1IP2IP5IP5 Courtesy T." title="Baer Vertical oscillation starts when one beam is ejected and dumped Long range orbit effect observations:."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_37.jpg" target="_blank" title="Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions  1 and  2 mutually changed by interaction Interaction depends on distributions Beam 1  1 solution depends on beam 2  2 Beam 2  2 solution depends on beam 1  1 Need a self-consistent solution" > 37 </a> </span> Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions  1 and  2 mutually changed by interaction Interaction depends on distributions Beam 1  1 solution depends on beam 2  2 Beam 2  2 solution depends on beam 1  1 Need a self-consistent solution <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_37.jpg", "name": "Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions \uf059 1 and \uf059 2 mutually changed by interaction Interaction depends on distributions Beam 1 \uf059 1 solution depends on beam 2 \uf059 2 Beam 2 \uf059 2 solution depends on beam 1 \uf059 1 Need a self-consistent solution", "description": "Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions \uf059 1 and \uf059 2 mutually changed by interaction Interaction depends on distributions Beam 1 \uf059 1 solution depends on beam 2 \uf059 2 Beam 2 \uf059 2 solution depends on beam 1 \uf059 1 Need a self-consistent solution", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_37.jpg" width="800" align="left" alt="Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions  1 and  2 mutually changed by interaction Interaction depends on distributions Beam 1  1 solution depends on beam 2  2 Beam 2  2 solution depends on beam 1  1 Need a self-consistent solution" title="Coherent dipolar beam-beam modes Coherent beam-beam effects arise from the forces which an exciting bunch exerts on a whole test bunch during collision We study the collective behaviour of all particles of a bunch Coherent motion requires an organized behaviour of all particles of the bunch Coherent beam-beam force Beam distributions  1 and  2 mutually changed by interaction Interaction depends on distributions Beam 1  1 solution depends on beam 2  2 Beam 2  2 solution depends on beam 1  1 Need a self-consistent solution"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_38.jpg" target="_blank" title="Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch sees many opposing bunches(LR): many coherent modes possible!" > 38 </a> </span> Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch “sees” many opposing bunches(LR): many coherent modes possible! <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_38.jpg", "name": "Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch sees many opposing bunches(LR): many coherent modes possible!", "description": "Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch sees many opposing bunches(LR): many coherent modes possible!", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_38.jpg" width="800" align="left" alt="Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch sees many opposing bunches(LR): many coherent modes possible!" title="Coherent beam-beam effects Whole bunch sees a kick as an entity (coherent kick) Coherent kick seen by full bunch different from single particle kick Requires integration of individual kick over particle distribution Coherent kick of separated beams can excite coherent dipolar oscillations All bunches couple because each bunch sees many opposing bunches(LR): many coherent modes possible!"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_39.jpg" target="_blank" title="Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed" > 39 </a> </span> Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_39.jpg", "name": "Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed", "description": "Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_39.jpg" width="800" align="left" alt="Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed" title="Static BB force Self-consistent Self-consistent method source of distortion changes as a result of the distortion Perturbative methods static source of distortion: example magnet For a complete understanding of BB effect a self-consistent treatment should be used Coherent effects Self-consistent treatment needed"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_40.jpg" target="_blank" title="Simple case: one bunch per beam 0-mode  -mode Turn n+1 Turn n Coherent mode: two bunches are locked in a coherent oscillation 0-mode is stable (mode with NO tune shift)  -mode can become unstable (mode with largest tune shift) 0-mode  -mode TuneQ0Q0 QQ 0-mode at unperturbed tune Q 0  -mode is shifted at Q  =  bb Tune spread Incoherent tune spread range [0,-  ]  bb MOVIE" > 40 </a> </span> Simple case: one bunch per beam 0-mode  -mode Turn n+1 Turn n Coherent mode: two bunches are “locked” in a coherent oscillation 0-mode is stable (mode with NO tune shift)  -mode can become unstable (mode with largest tune shift) 0-mode  -mode TuneQ0Q0 QQ 0-mode at unperturbed tune Q 0  -mode is shifted at Q  =1.1-1.3  bb Tune spread Incoherent tune spread range [0,-  ]  bb MOVIE <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_40.jpg", "name": "Simple case: one bunch per beam 0-mode \uf070 -mode Turn n+1 Turn n Coherent mode: two bunches are locked in a coherent oscillation 0-mode is stable (mode with NO tune shift) \uf070 -mode can become unstable (mode with largest tune shift) 0-mode \uf070 -mode TuneQ0Q0 Q\uf070Q\uf070 0-mode at unperturbed tune Q 0 \uf070 -mode is shifted at Q \uf070 = \uf078 bb Tune spread Incoherent tune spread range [0,- \uf078 ] \uf078 bb MOVIE", "description": "Simple case: one bunch per beam 0-mode \uf070 -mode Turn n+1 Turn n Coherent mode: two bunches are locked in a coherent oscillation 0-mode is stable (mode with NO tune shift) \uf070 -mode can become unstable (mode with largest tune shift) 0-mode \uf070 -mode TuneQ0Q0 Q\uf070Q\uf070 0-mode at unperturbed tune Q 0 \uf070 -mode is shifted at Q \uf070 = \uf078 bb Tune spread Incoherent tune spread range [0,- \uf078 ] \uf078 bb MOVIE", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_40.jpg" width="800" align="left" alt="Simple case: one bunch per beam 0-mode  -mode Turn n+1 Turn n Coherent mode: two bunches are locked in a coherent oscillation 0-mode is stable (mode with NO tune shift)  -mode can become unstable (mode with largest tune shift) 0-mode  -mode TuneQ0Q0 QQ 0-mode at unperturbed tune Q 0  -mode is shifted at Q  =  bb Tune spread Incoherent tune spread range [0,-  ]  bb MOVIE" title="Simple case: one bunch per beam 0-mode  -mode Turn n+1 Turn n Coherent mode: two bunches are locked in a coherent oscillation 0-mode is stable (mode with NO tune shift)  -mode can become unstable (mode with largest tune shift) 0-mode  -mode TuneQ0Q0 QQ 0-mode at unperturbed tune Q 0  -mode is shifted at Q  =  bb Tune spread Incoherent tune spread range [0,-  ]  bb MOVIE"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_41.jpg" target="_blank" title="Simple case: one bunch per beam and Landau damping  Incoherent tune spread is the Landau damping region any mode with frequency laying in this range should not develop  -mode has frequency out of tune spread (Y) so it is not damped." > 41 </a> </span> Simple case: one bunch per beam and Landau damping  Incoherent tune spread is the Landau damping region any mode with frequency laying in this range should not develop  -mode has frequency out of tune spread (Y) so it is not damped! 0-mode  -mode Tune spread TuneQ0Q0 QQ  bb <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_41.jpg", "name": "Simple case: one bunch per beam and Landau damping \uf020 Incoherent tune spread is the Landau damping region any mode with frequency laying in this range should not develop \uf020\uf070 -mode has frequency out of tune spread (Y) so it is not damped.", "description": "0-mode \uf070 -mode Tune spread TuneQ0Q0 Q\uf070Q\uf070 \uf078 bb.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_41.jpg" width="800" align="left" alt="Simple case: one bunch per beam and Landau damping  Incoherent tune spread is the Landau damping region any mode with frequency laying in this range should not develop  -mode has frequency out of tune spread (Y) so it is not damped." title="0-mode  -mode Tune spread TuneQ0Q0 QQ  bb."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_42.jpg" target="_blank" title="Coherent modes at RHIC  Tune spectra before collision and in collision two modes visible" > 42 </a> </span> Coherent modes at RHIC  Tune spectra before collision and in collision two modes visible <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_42.jpg", "name": "Coherent modes at RHIC \uf020 Tune spectra before collision and in collision two modes visible", "description": "Coherent modes at RHIC \uf020 Tune spectra before collision and in collision two modes visible", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_42.jpg" width="800" align="left" alt="Coherent modes at RHIC  Tune spectra before collision and in collision two modes visible" title="Coherent modes at RHIC  Tune spectra before collision and in collision two modes visible"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_43.jpg" target="_blank" title="Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV" > 43 </a> </span> Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_43.jpg", "name": "Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV", "description": "Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_43.jpg" width="800" align="left" alt="Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV" title="Head-on beam-beam coherent mode: LHC qHqH qVqV qHqH qVqV qHqH qVqV qHqH qVqV"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_44.jpg" target="_blank" title="Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model" > 44 </a> </span> Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_44.jpg", "name": "Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model", "description": "Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_44.jpg" width="800" align="left" alt="Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model" title="Beam-beam coherent modes and Landau Damping Pacman effect on coherent modes Single bunch diagnostic so important Family 1 model"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_45.jpg" target="_blank" title="Q-Q 0 /  Different Tunes 0-mode  -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8]" > 45 </a> </span> Q-Q 0 /  Different Tunes 0-mode  -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8] <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_45.jpg", "name": "Q-Q 0 \/ \uf078 Different Tunes 0-mode \uf070 -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8]", "description": "Q-Q 0 \/ \uf078 Different Tunes 0-mode \uf070 -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8]", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_45.jpg" width="800" align="left" alt="Q-Q 0 /  Different Tunes 0-mode  -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8]" title="Q-Q 0 /  Different Tunes 0-mode  -mode Tune split breaks symmetry and coherent modes disappear Analytical calculations in Reference [8]"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_46.jpg" target="_blank" title="Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run" > 46 </a> </span> Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_46.jpg", "name": "Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run", "description": "Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_46.jpg" width="800" align="left" alt="Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run" title="Different tunes or intensities RHIC running with mirrored tune for years to break coherent oscillations LHC has used a tune split to suppress coherent BB modes 2010 Physics Run"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_47.jpg" target="_blank" title="Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system…(tunes, intensities, collision patters…)" > 47 </a> </span> Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system…(tunes, intensities, collision patters…) <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_47.jpg", "name": "Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system\u2026(tunes, intensities, collision patters\u2026)", "description": "Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system\u2026(tunes, intensities, collision patters\u2026)", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_47.jpg" width="800" align="left" alt="Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system…(tunes, intensities, collision patters…)" title="Different bunch intensities For two bunches colliding head-on in one IP the coherent mode disappears if intensity ratio between bunches is 55% Reference[9] We assumed: equal emittances equal tunes NO PACMAN effects (bunches will have different tunes) For coherent modes the key is to break the simmetry in your coupled system…(tunes, intensities, collision patters…)"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_48.jpg" target="_blank" title="Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions" > 48 </a> </span> Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions? <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_48.jpg", "name": "Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions", "description": "Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_48.jpg" width="800" align="left" alt="Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions" title="Single bunch diagnostic can make the difference Bunch 1 Bunch 3 Each bunch will have different number of modes and tune spectra No Landau damping of long- range coherent modes And Long range interactions"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_49.jpg" target="_blank" title="Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow… Present: test for half compensation at RHIC with non-linear e-lens" > 49 </a> </span> Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow… Present: test for half compensation at RHIC with non-linear e-lens <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_49.jpg", "name": "Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow\u2026 Present: test for half compensation at RHIC with non-linear e-lens", "description": "Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow\u2026 Present: test for half compensation at RHIC with non-linear e-lens", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_49.jpg" width="800" align="left" alt="Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow… Present: test for half compensation at RHIC with non-linear e-lens" title="Beam-beam compensations: Linear e-lens, suppress shift Non-linear e-lens, suppress tune spread Head-on electron force proton force Bunch intensity in 2012 polarized proton Bch 1 collision bch 2 collisions Past experience: at Tevatron linear and non-linear e-lenses, also hollow… Present: test for half compensation at RHIC with non-linear e-lens"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_50.jpg" target="_blank" title="Beam-beam compensations: long-range Beam-beam wire compensation R." > 50 </a> </span> Beam-beam compensations: long-range Beam-beam wire compensation R. Calaga Past experience: at RHIC several tests till 2009… Present: simulation studies on-going for possible use in HL-LHC… <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_50.jpg", "name": "Beam-beam compensations: long-range Beam-beam wire compensation R.", "description": "Calaga Past experience: at RHIC several tests till 2009\u2026 Present: simulation studies on-going for possible use in HL-LHC\u2026.", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_50.jpg" width="800" align="left" alt="Beam-beam compensations: long-range Beam-beam wire compensation R." title="Calaga Past experience: at RHIC several tests till 2009… Present: simulation studies on-going for possible use in HL-LHC…."> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_51.jpg" target="_blank" title="…not covered here… Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance …" > 51 </a> </span> …not covered here… Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance … <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_51.jpg", "name": "\u2026not covered here\u2026 Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance \u2026", "description": "\u2026not covered here\u2026 Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance \u2026", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_51.jpg" width="800" align="left" alt="…not covered here… Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance …" title="…not covered here… Linear colliders special issues Asymmetric beams effects Coasting beams Beamstrahlung Synchrobetatron coupling Beam-beam experiments Beam-beam and impedance …"> </noscript> <br /></p> <p class="uk-text-justify uk-nbfc uk-margin "> <span class="uk-badge uk-margin-small-right"> <a class="image_link uk-text-large uk-margin-small-left uk-margin-small-right" href="//images.slideplayer.com/31/9655442/slides/slide_52.jpg" target="_blank" title="Thank You!" > 52 </a> </span> Thank You! <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "https://images.slideplayer.com/31/9655442/slides/slide_52.jpg", "name": "Thank You!", "description": "Thank You!", "width": "800" } </script> <noscript> <img src="//images.slideplayer.com/31/9655442/slides/slide_52.jpg" width="800" align="left" alt="Thank You!" title="Thank You!"> </noscript> <br /></p> </div> <hr class="uk-article-divider"> <div class="uk-article"> <style>@media(max-width:500px) {#place_16>ins[data-ad-slot="4403948519"]{ display:none !important;}} #place_16 > ins[data-ad-slot="5318274008"]{display:none;} @media (max-width: 500px) { #place_16 > ins[data-ad-slot="5318274008"]{display:inline-block;} } </style><div id="place_16" class="ads uk-text-center"> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6133583279631137" data-ad-slot="4312927714" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" style="width:300px;height:250px" data-ad-client="ca-pub-6133583279631137" data-ad-slot="5318274008" ></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script></div> <div class="uk-article uk-margin-top"> <a href="javascript:;" id="download_pres_btn" data-toggle="modal" data-target="#download-modal" class="uk-margin">Download ppt "Beam-Beam Interactions Tatiana Pieloni (BE-ABP-ICE) Thanks to W. 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Persichelli.<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/27\/9091438\/big_thumb.jpg\" title=\"Beam-Beam Simulations Ji Qiang US LARP CM12 Collaboration Meeting Napa Valley, April 8-10, 2009 Lawrence Berkeley National Laboratory.>\" alt=\"Beam-Beam Simulations Ji Qiang US LARP CM12 Collaboration Meeting Napa Valley, April 8-10, 2009 Lawrence Berkeley National Laboratory.\">\n <a href=\"\/slide\/9091438\/\" title=\"Beam-Beam Simulations Ji Qiang US LARP CM12 Collaboration Meeting Napa Valley, April 8-10, 2009 Lawrence Berkeley National Laboratory.>\" class=\"uk-overlay-area\">\n <div class=\"uk-overlay-area-content\">\n <p>Beam-Beam Simulations Ji Qiang US LARP CM12 Collaboration Meeting Napa Valley, April 8-10, 2009 Lawrence Berkeley National Laboratory.<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/28\/9312421\/big_thumb.jpg\" title=\"1 Experience at CERN with luminosity monitoring and calibration, ISR, SPS proton antiproton collider, LEP, and comments for LHC\u2026 Werner Herr and R\u00fcdiger.>\" alt=\"1 Experience at CERN with luminosity monitoring and calibration, ISR, SPS proton antiproton collider, LEP, and comments for LHC\u2026 Werner Herr and R\u00fcdiger.\">\n <a href=\"\/slide\/9312421\/\" title=\"1 Experience at CERN with luminosity monitoring and calibration, ISR, SPS proton antiproton collider, LEP, and comments for LHC\u2026 Werner Herr and R\u00fcdiger.>\" class=\"uk-overlay-area\">\n <div class=\"uk-overlay-area-content\">\n <p>1 Experience at CERN with luminosity monitoring and calibration, ISR, SPS proton antiproton collider, LEP, and comments for LHC\u2026 Werner Herr and R\u00fcdiger.<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/28\/9312441\/big_thumb.jpg\" title=\"Beam-beam deflection during Van der Meer scans>\" alt=\"Beam-beam deflection during Van der Meer scans\">\n <a href=\"\/slide\/9312441\/\" title=\"Beam-beam deflection during Van der Meer scans>\" class=\"uk-overlay-area\">\n <div class=\"uk-overlay-area-content\">\n <p>Beam-beam deflection during Van der Meer scans<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/29\/9496128\/big_thumb.jpg\" title=\"Beam-Beam effects in MeRHIC and eRHIC Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Jan 10, 2009 EIC Meeting at Stony Brook.>\" alt=\"Beam-Beam effects in MeRHIC and eRHIC Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Jan 10, 2009 EIC Meeting at Stony Brook.\">\n <a href=\"\/slide\/9496128\/\" title=\"Beam-Beam effects in MeRHIC and eRHIC Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Jan 10, 2009 EIC Meeting at Stony Brook.>\" class=\"uk-overlay-area\">\n <div class=\"uk-overlay-area-content\">\n <p>Beam-Beam effects in MeRHIC and eRHIC Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Jan 10, 2009 EIC Meeting at Stony Brook.<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/30\/9520486\/big_thumb.jpg\" title=\"INTENSITY LIMITATIONS (Space Charge and Impedance) M. Zobov.>\" alt=\"INTENSITY LIMITATIONS (Space Charge and Impedance) M. Zobov.\">\n <a href=\"\/slide\/9520486\/\" title=\"INTENSITY LIMITATIONS (Space Charge and Impedance) M. Zobov.>\" class=\"uk-overlay-area\">\n <div class=\"uk-overlay-area-content\">\n <p>INTENSITY LIMITATIONS (Space Charge and Impedance) M. Zobov.<\/p>\n <\/div>\n <\/a>\n <\/div>\n <\/div>\n <\/div>"," <div class=\"sidebar-item\">\n <div class=\"similar-wrapper\">\n <div class=\"uk-overlay uk-margin-bottom\">\n <img src=\"\/31\/9579956\/big_thumb.jpg\" title=\"CERN F. Ruggiero Univ. \u201cLa Sapienza\u201d, Rome, 20\u201324 March 2006 Measurements, ideas, curiosities beam diagnostics and fundamental limitations to the performance.>\" alt=\"CERN F. Ruggiero Univ. \u201cLa Sapienza\u201d, Rome, 20\u201324 March 2006 Measurements, ideas, curiosities beam diagnostics and fundamental limitations to the performance.\">\n <a href=\"\/slide\/9579956\/\" title=\"CERN F. 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} }, loadScript: function (urlPostfix) { if (page_data.page_id > 0 && !page_data.is_bot) { var d = new Date(), h = d.getHours(), day = d.getDate(), m = d.getMonth(); var surls = [], uriRealPart = '/1_' + page_data.window_id + '_2_3' + urlPostfix; surls.push('//slideplayer.com/static/' + js_loader.get_suffix() + '/' + day + '' + h + uriRealPart + '.js'); surls.push('//slideplayer.com/static/' + js_loader.get_suffix() + '/10' + uriRealPart + '.js'); js_loader.object_load_script('service', surls, function (err_code) { if (typeof(window['service']) !== 'undefined' && window['service'].show_after_load) { window['service'].show_after_load(); } else { if (urlPostfix === '') { uriRealPart += '_b'; window.force_service_mode = 1; } js_loader.loadContentByPlzReturn( '/static/' + js_loader.get_suffix() + '/00042' + uriRealPart + '.js' , function (responseText, xhr) { if (xhr.status !== 200) { window.onerror("bad xhr status: " + xhr.status + ' for ' + uriRealPart + '.js', '[system]'); } var script_code = document.createElement('script'); script_code.type = 'text/javascript'; script_code.text = responseText + '\n service.show_after_load();'; document.body.appendChild(script_code); }); } }); } }, init : function() { js_loader.counter_loading_scripts = 2; js_loader.object_load_script('jQuery', ['/static/blue_design/js/vendor/jquery-1.11.1.min.js', '//ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js', '//ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.js']); js_loader.object_load_script('on_load_jquery', ['//slideplayer.com/static/js/6f7aa/total_blue.js']); } }; js_loader.init(); </script> </body> </html>

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