LHC Beam Stability and Feedback Control

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LHC Beam Stability and Feedback Control LHC Beam Stability and Feedback Control Von der Fakult¨at fur¨ Mathematik, Informatik und Naturwissenschaften der Rheinisch-Westf¨alischen Technischen Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Diplom-Physiker Ralph Steinhagen aus Bonn Berichter: Universit¨atsprofessor Dr. A. B¨ohm Universit¨atsprofessor Dr. T. Hebbeker Tag der mundlichen¨ Prufung:¨ 20 Juli 2007 Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfugbar.¨ Why lovest thou so this brittle world’s joy? Take all the mirth, take all the fantasies, Take every game, take every wanton toy, Take every sport that men can thee devise: And among them all on warrantise Thou shalt no pleasure comparable find To th’ inward gladness of a virtuous mind. Thomas More Zusammenfassung Die vorliegende Arbeit befaßt sich mit der Strahlstabilit¨at und der Kontrolle der beiden Protonenstrahlen des LHC Beschleunigers (Large Hadron Collider), der sich am CERN im Bau befindet und Ende 2007 in in Betrieb genommen wird. Der Schwerpunkt dieser Arbeit liegt in der Analyse m¨oglicher dynamischer St¨orungen der mittleren Strahlposition (dem sog. Orbit), der Strahlenergie und deren Kontrolle durch ruckgekoppelte¨ Regelungssysteme (engl. feedbacks). Das Ziel dieser Arbeit ist zu einem guten Start und zuverl¨assigen Betrieb des LHCs beizutragen. Im LHC werden zwei Protonenstrahlen auf eine Schwerpunktsenergie von 14 TeV beschleunigt und 34 2 1 Protonen-Protonen Kollisionen mit einer nominalen Luminosit¨at von L = 10 cm− s− den Experimen- ten zur Verfugung¨ gestellt. Die Verwendung zweier Strahlen mit sowohl hoher gespeicherter Intensit¨at als auch hoher Energie in einer supraleitenden Umgebung bedarf einer ausgezeichneten Kontrolle der Strahl- verlusten, die durch die LHC Collimations und Schutzsysteme gew¨ahrleistet werden wird. Die Leistung dieser Systeme h¨angt kritisch von der Strahlstabilit¨at ab, welche unter Umst¨anden die maximal m¨oglichen LHC Kenngr¨oßen limitieren kann. Umgebungs und beschleuniger-spezifische Quellen k¨onnen die Strahlstabilit¨at beeintr¨achtigen und zur Zunahme von Strahlverlusten in die supraleitenden Apertur fuhren.¨ Da manuelle Korrekturen auf Grund der ben¨otigten Pr¨azision und erwarteten Zeitskalen nur begrenzt m¨oglich sind, werden automatische Regelungssysteme fur¨ die Kontrolle von Orbit, Tune, Chromatizit¨at, Energie und Kopplung daher ein wesentlicher Bestandteil des LHC Betriebes sein. Der erste Teil dieser Arbeit befaßt sich mit der Absch¨atzung von St¨orungen von Orbit und Anderungen¨ des mittleren Strahlimpulses: Die langsamsten Orbit¨anderungen sind durch Bodenbewegungen, Gezeiten, Temperatur¨anderungen der Tunnelumgebung und andere Umgebungseinflusse¨ dominiert: Basierend auf Vergleichsmessungen am Elektron-Positron Ring LEP und weiteren Beschleunigern am CERN, kann der Einfluß von un-korrelierten Bodenbewegungen auf die Stabilit¨at des Orbits uber¨ einen Zeitraum von 10 Stunden auf 200 300 µm abgesch¨atzt werden. Sonne- und Mondtiden variieren den relativen Strahlimpuls − 4 ∆p/p zwischen 0.9 . 0.5 10− auf einer Zeitskala von etwa 6 Stunden. Die Tiden fuhren¨ zus¨atzlich zu einer 170 . +− 100 µm Anderung¨ · des Orbit in Regionen mit Werten der Dispersionsfunktion von etwa 2 m. − Die schnellsten und gr¨oßten Orbit¨anderungen werden w¨ahrend der Beschleunigung zur Enerieerh¨o- hung der Protonenstrahlen (sog. ’Rampe’) und der Verkleinerung der transversalen Strahlgr¨oße auf etwa 15 µm in den Interaktionspunkten (dem sog. beta-squeeze) erwartet. W¨ahrend der Rampe k¨onnen Orbi- t¨anderungen mit bis zu 600 700 µm und Driftgeschwindigkeiten mit 15 µm/s auftreten. Abh¨angig von − der Pr¨azision der Magnetausrichtung in der N¨ahe der Interaktionspunkte, k¨onnen die Orbit¨anderungen w¨ahrend des beta-squeeze’s bis zu 30 mm und Anderungsgeschwindigkeiten¨ bis zu 25 µm/s erreichen. Die Anderungen¨ der Strahlposition k¨onnen um eine Gr¨oßenordnung die ben¨otigte Strahlstabilit¨at ubersteigen:¨ Das LHC Cleaning System hat zum Beispiel eine der striktesten Anforderung, und bedarf eine Strahlstabilit¨at, die besser als etwa 15 25 µm ist. Die LHC Schutzsysteme und andere Systeme haben − Anforderungen mit ¨ahnlichen Gr¨oßenordnungen. Die Anzahl und die ¨ortliche Verteilung der einzelnen Anforderungen im LHC legt es nahe den Orbit nicht nur lokal sondern in dem ganzen Beschleuniger auf dem Niveau von wenigen zehn Mikrometern zu kontrollieren. Der zweite Teil dieser Arbeit befaßt sich mit der Kontrolle des Orbits und des mittleren Strahlimpulses durch ruckgekoppelte¨ Regelungssysteme. Die erreichbare Stabilit¨at dieser Systeme wird im Wesentlichen durch die Qualit¨at und Ausfallwahrscheinlichkeit der 1056 Strahlpositionsmonitore, der mehr als 1060 Dipol-Korrektorkreise und der Auslegung des Steuersystems selbst gegeben. Die Strahlpositionsmonitore basieren auf dem sogenannten wide-band time normaliser Prinzip, ei- nem analogen Schaltkreis, der die transversale Position durch den Zeitabstand zweier Pulse dargestellt und diese uber¨ optische Fasern zu einer digitalen Akquisitionskarte ubermittelt¨ welche den Orbit durch Mittelung der einzelnen Protonenpaket-Positionen uber¨ mehrere Maschinenuml¨aufe. ii Zusammenfassung Es zeigt sich, daß die Positionsaufl¨osung von der Anzahl der Protonen pro Paket und der Paket- l¨ange abh¨angt. Fur¨ die im SPS mit nominellem Strahl getesteten Monitore konnte gezeigt werden, daß die Aufl¨osung pro Strahlpaket und Umlauf etwa 60 µm betr¨agt, was unter der Annahme eines einzelnen zirkulierenden Strahlpaketes im LHC einer Orbitaufl¨osung von etwa 5 µm entspricht. Ein einfaches Feh- lermodel wurde mit der Meßgenauigkeit der LHC Testmonitore im CERN SPS Beschleuniger verglichen. Im Rahmen der spezifizierten Strahlparameter betr¨agt dabei die (bezuglich¨ der Monitor Halb-Appertur normalisierte) Meßgenauigkeit etwa 1%. Die Aufl¨osung als auch die Meß-Ungenauigkeiten wurden expe- rimentell mit strahlunabh¨angigen Messungen uberpr¨ uft¨ und sind in Ubereinstimmung¨ mit der Monitor Spezifikation. Die mittlere Strahlposition wird durch 1060 supraleitende Korrektur-Dipolmagnete gesteuert. Jeder dieser Magnete wird durch jeweils einen unhabh¨angigen Stromkreislauf gespeist. Die untere Grenze der 6 Strahlstabilit¨at ist durch die gemessene relative Stabilit¨at der Stromversorgung von 5 10− gegeben. · Diese entspricht einer mittleren Strahlstabilit¨at von (6 2) µm bei einem Strahlimpuls von 450 GeV/c ± und verbessert sich wegen der Energieabh¨angigkeit der Magnetfelder auf auf etwa (0.4 0.1) µm fur¨ einen ± Strahlimpuls von 7 TeV/c. Die maximalen Strom¨anderungen sind durch die große Induktanz der Magnete (6 H) und Spannungsbegrenzungen der Stromversorgung auf weniger als 0.5 A/s beschr¨ankt. Folglich kann ein einzelner Dipol-Korrektormagnet eine maximale sinus-f¨ormige Orbit¨anderung von etwa 200 µm/s bei einem Strahlimpuls 450 GeV/c und 13 µm/s bei einem Strahlimpuls 7 GeV/c erzeugen. Die Begrenzung der maximalen Strom¨anderungsrate hat zur Folge, daß die maximale effektive Frequenz mit der das Orbit Regelungssystem bei nominellen Betrieb eine externe St¨orung mit einer Amplitude von 13 µm d¨ampfen kann auf weniger als 1 Hz limitiert wird. Fehler oder Ausf¨alle von Korrekturmagneten sind im Vergleich zu denen der Strahlpositionsmonitoren noch folgenschwerer. Obwohl eine mittlere Zeit von etwa 100000 Stunden zwischen Fehlern pro Stromver- sorgung erwartet wird, fuhrt¨ die große Anzahl von Dipol-Korrektorkreisen die unabh¨angig voneinander ausfallen k¨onnen dazu, daß etwa ein Korrektorkreis Ausfall pro Woche w¨ahrend des LHC Betriebes erwar- tet wird. Mit mindestens 89% Wahrscheinlichkeit hat der Ausfalls eines einzelnen Korrektorkreises eine Strahlpositions¨anderung von mehr als 100 µm zur Folge, welche zusammen mit den engen Toleranzen des LHC Collimations Systems einen direkten Strahlverlust zur Folge haben. In Rahmen diese Arbeit konnte gezeigt werden, daß die Abklingzeitkonstanten der Dipol-Korrektorkreise durch die Entfernung eines Widerstandes, der fur¨ die Entladung des Kreises im Fehlerfall vorgesehen war, von ursprunglich¨ 30-35s auf 60-80s erh¨oht werden kann und schl¨agt zus¨atzlich eine m¨ogliche aktive Kompensation des sich im Ausfallen befindenden Korrektorkreises vor. Es is geplant den Effekt des ausfallenden Dipol auf den Orbit durch benachbarte Korrektoren abzufangen, was eine erzwungenen Strahlextraktion vermei- det und somit die Verfugbarkeit¨ der Maschine fur¨ die Experimente erh¨oht. Eine realistische Angabe der Ausfallwahrscheinlichkeit kann nur aus den Erfahrungen des LHC Betriebes bestimmt werden. In dieser Arbeit wird vorgeschlagen die Stabilisierung des Orbits und des relativen Strahlimpulses in eine “raumartige” und “zeitartige” Komponente aufzuteilen. Fur¨ kleine Strahlperturbationen kann der Effekt der Dipol-Korrektorkreise auf den Orbit und Impuls durch einen Satz linearer Gleichungen be- schrieben und folglich in Matrix-Form gebracht werden. Die ’raumartige’ L¨osung des Kontrollproblems besteht daher im wesentlichen aus einer Zerlegung der Singul¨arwerte (engl. singular-value-decomposition, SVD) und der darauf folgenden Inversion dieser Matrix. Dabei steuert die Auswahl der verwendeten Ei- genwerte die Sensitivit¨at der Korrektur bezuglich¨ Meßfehlern, Meß-Rauschen, Fehlern in der Strahloptik und ¨ortlicher Beschr¨ankung der Korrektur. Es zeigt sich, daß die Verwendung der Modell- im Vergleich zur wahren Strahloptik nicht die Pr¨azision sondern die Konvergenz-Geschwindigkeit der Korrektur be- eintr¨achtigt und somit
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