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ORSAY N° D'ordre: JLAL92-20 UNIVERSITE PARIS-SUD CENTRE

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ORSAY N° D'ordre: JLAL92-20 UNIVERSITE PARIS-SUD CENTRE Gflftfon JLAL92-20 ORSAY Doe. enrag, Io : M* T0M • /^ f 4. n° d'ordre: n inn • hii'->J-tr Destination : 1,1+D1D UNIVERSITE PARIS-SUD CENTRE D'ORSAY THESE présentée pour obtenir le TITRE de DOCTEUR EN SCIENCES PHYSIQUES par Ghislain ROY le 29 Avril 1992 devant la Comission d'Examen soutenue Président MM. M. DAVIER j BUON J.-E. AUGUSTIN J. IRWIN O. NAPOLY ABSTRACT The Final Focus Test Beam being built at SLAC is a test bed for future linear collider final focus systems. The parameters and the optics of the FFTB are presented in chapter one. The mathematical tools for this thesis which are based on Lie algebras are then reviewed in chapter two. One relies particularly on the Lie transformations together with the similarity transformation and the Campbell- Baler-Haussdorff theorem for the manipulation of Hamiltonians. Chapter three presents the application of these methods to magnetic optics in accelerators; the separation of linear and non-linear effects and the building of the total Hamiltonian of the line from the thin-lens formulation. Chapter four analytically establishes a catalog of aberrations, up to order five in the Hamiltonians, at the FFTB. The emphasis is put on the methods of analysis. It is shown that the system has a significant fifth-order aberration and that no higher-order aberration appears. Finally chapter six presents some stability tolerances —alignement strength and multipole content —for the FFTB. In the conclusion the present situation of these methods, as well as possible computer codes using them, are reviewed. KEY-WORDS Optics Final focus Chromaticity Lie Algebra Hamiltonians Aberrations Tolerances Synchrotron radiation ORSAY LAL 92-20 n° d'ordre: Avril 1992 UNIVERSITE PARIS-SUD CENTRE D'ORSAY THESE présentée pour obtenir le TITRE de DOCTEUR EN SCIENCES PHYSIQUES par Ghislain ROY Analyse de l'optique du Final Focus Test Beam à l'aide de méthodes basées sur les algèbres de Lie. soutenue le 29 Avril 1992 devant la Comission d'Examen MM. M. DAVIER Président J. BUON J.-E. AUGUSTIN J. IRWIN O. NAPOLY A mes parents. Acknowledgments I first want to thank Professor Jean Buon. He initiated my steps on the way to accelerator physics. His teaching and friendship are very precious. My thoughts also go to John Irwin. He also taught me a great deal. For the numerous discussions, your great patience and disponibility, thank you John. To Michel Davier who accepted to chair the jury and to Jean-Eudes Augustin for being part of it, my sincere thanks. Olivier Napoly also accepted the position of "rapporteur" for this thesis and I thank him for this; his comments are always important to me. I want to express my very sincere thanks to J.M. Paterson and Ron Ruth for hosting me in their Accelerator Theory and Special Projects group at SLAC for these three years. It has been a great priviledge to learn among some of the greatest. Special thanks go to Matt Sands. I am indebted to the FFTB Optics group. Thanks to K. Oide, K. Brown, R. Helm, N. Yamamoto, F. Bulos. Special thanks to Peter Tenenbaum and Rick Iverson for your questions and the discussions they triggered. Of course I want to express my gratitude to the entire FFTB collaboration. A special mention goes to Bcrnie Denton, Gerry Fischer, Finn Halbo and Dieter WaIz; Their great experience and very high professionalism were remarkable. They have been true models for me. Thank you also Dave Burke for leading the FFTB with such enthusiasm. For their help with the codes and machines, let me acknowledge the help and advice of M. Berz, A. Dragt, R. Servranckx and T. Knight. A special thought goes to those at SLAC who have always encouraged me and have become true friends. Nick Walker, Paul Emma, Tanya Boysen, Bill Gabella and the happy group. Let them be thanked here. A special word must go to Lia Merminga; For these discussions and advices late at night, thank you so much. And to all who have shown their support; the friends from Stanford but also the members of the St Ann's choir, their families and friends. To all of you, I dedicate this work. Remerciements Je voudrais d'abord remercier vivement le Professeur Jean Buon. Le premier il a su me présenter la physique des accélérateurs. Son enseignement et son amitié me sont très précieux. Mes pensées vont ensuite à John Irwin. Je me suis enrichi à son contact pendant près de trois ans. Pour les nombreuses discussions, sa très grande patience et sa disponibilité qu'il soit ici remercié. Je tiens a exprimer ma gratitude à Michel Davier pour avoir bien voulu présider cette thèse, ainsi qu'à Jean-Eudes Augustin qui a accepté de faire partie du jury. Olivier Napoly a accepté d'être rapporteur et je l'en remercie; ses commentaires me sont toujours précieux. Pour m'avoir accueilli durant ces trois années à SLAC dans le groupe de Théorie des Accélérateurs et Projets Spéciaux, je veux sincèrement remercier J.M. Paterson et Ron Ruth. Ce fut pour moi l'occasion d'apprendre mon metier parmi les plus grands. Merci à tous et spécialement à Matt Sands. Le petit groupe qui a étudié l'optique du FFTB a droit à toute ma gratitude. Merci à K. Oide, K. Brown, R. Helm, N. Yamamoto, F. Bulos. Merci aussi Peter Tenenbaum et Rick Iverson pour vos questions et les discussions qui s'ensuivirent. Dans la collaboration du FFTB que je veux collectivement remercier, ma grati- tude va particulièrement h Bernie Denton, Gerry Fischer, Finn Halbo et Dieter WaIz; leur expérience sans pareille et leur très grande conscience professionelle sont remarquables. Ils furent de véritables modèles. Ma gratitude va également à Dave Burke; son dynamisme et son entrain dans la direction du projet furent communicatifs. Pour leur aide avec les codes et les machines, je veux remercier particulièrement M. Berz, A. Dragt, R. Servranckx et T. Knight. Une pensée va à ceux qui à SLAC sont devenus de véritables amis et ont su m'encourager. Nick Walker, Paul Emma, Tanya Boysen, Bill Gabella et tout le joyeux groupe; ils ont droit à ma reconnaissance. Une mention spéciale est de rigueur pour Lia Merminga. Merci pour ces conseils et discussions à des heures tardives. Et à tous ceux qui m'ont supporté pendant ce temps; les amis de Stanford mais aussi les membres du St Ann's Choir, leurs familles et leurs amis. A tous ceux là cette thèse est dédiée... Introduction Les collisionneurs e+e~ de haute énergie sont actuellement limités dans la course aux énergies de plus de 100 GeV par le rayonnement synchrotronique. Lorsque leur trajec- toire est courbée sous l'effet d'un champ magnétique les particules chargées émettent un rayonnement électromagnétique. La puissance rayonnée est proportionelle à la puissance quatre de l'énergie des particules et inversement proportionelle au carré du rayon de cour- bure de la trajectoire. Afin de garder cette puissance rayonnée à un niveau acceptable, le plus grand anneau collisionneur à e+e~ à l'heure actuelle, le LEP au CERN, a une circonférence de 27 kilomètres pour une énergie maximale de 100 GeF par faisceau. L'un des buts pour les collisionneurs dans les vingt années à venir est l'augmentation de l'énergie par un ordre de grandeur pour atteindre une énergie de collision de 1 TeVdans le centre de masse. L'extrapolation du LEP à de telles énergies, en gardant une puissance rayonnée par unité de longueur constante, serait une machine vingt cinq fois plus grande avec une circonférence de près de 700 kilomètres. Clairement ceci n'est économiquement pas un choix possible. L'autre voie pour la construction de machines de haute énergie et qui ne demande pas une taille gigantesque est le collisionneur linéaire. Deux accélérateurs linéaires se faisant face, les deux faisceaux sont amenés en collision au point d'interaction (IP) puis éliminés. Le concept d'une telle machine a été testé à SLAC avec le Stanford Linear Collider (SLC ' ) qui a été un succès dans ce rôle de machine test; de nombreux problèmes spécifiques ont pu être étudiés, certains même y ont été découvert (blindage contre les muons, collimation) et pour beaucoup on a pu réaliser la véritable complexité de ce type de machines. Ceci est particulièrement vrai des questions de la production et conservation de remittance des faisceaux ainsi que pour les sections de focalisation finale. Le SLC n'est cependant pas un vrai collisionneur linéaire en ce sens que les deux faisceaux sont co-accélérés dans le même linac; puis deux arcs et systèmes de focalisation finale les amènent en collision au point d'interaction. Il a cependant démontré la faisabilité de ce type de machines. Les enseignements tirés du SLC n'auraient certainement pas pu être obtenus par d'autres moyens. L'autre défi des collisionneurs e+e~ de haute énergie est la luminosité requise pour l'investigation d'événements très rares. La prochaine génération de machines aura besoin d'une luminosité comprise entre 1033 et 1034 cm~2s~l. Il y a trois paramètres principaux à la luminosité: la fréquence de répétition des collisions, la population de chaque faisceau et la surface d'intersection des deux faisceaux au point d'interaction. Les deux premiers paramètres sont les points forts des machines circulaires. Le courant circulant, propor- tionnel au produit de la population du faisceau par la fréquence de répétition, peut être assez élevé bien que soumis à des limitations. Au LEP la fréquence de révolution est de l'ordre de 104 Hz et la population typique d'un paquet en mode de collision est.
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