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Accelerator Physics Third Edition Preface Accelerator science took off in the 20th century. Accelerator scientists invent many in- novative technologies to produce and manipulate high energy and high quality beams that are instrumental to progresses in natural sciences. Many kinds of accelerators serve the need of research in natural and biomedical sciences, and the demand of applications in industry. In the 21st century, accelerators will become even more important in applications that include industrial processing and imaging, biomedical research, nuclear medicine, medical imaging, cancer therapy, energy research, etc. Accelerator research aims to produce beams in high power, high energy, and high brilliance frontiers. These beams addresses the needs of fundamental science research in particle and nuclear physics, condensed matter and biomedical sciences. High power beams may ignite many applications in industrial processing, energy production, and national security. Accelerator Physics studies the interaction between the charged particles and elec- tromagnetic field. Research topics in accelerator science include generation of elec- tromagnetic fields, material science, plasma, ion source, secondary beam production, nonlinear dynamics, collective instabilities, beam cooling, beam instrumentation, de- tection and analysis, beam manipulation, etc. The textbook is intended for graduate students who have completed their graduate core-courses including classical mechanics, electrodynamics, quantum mechanics, and statistical mechanics. I have tried to emphasize the fundamental physics behind each innovative idea with least amount of mathematical complication. The textbook may also be used by advanced undergraduate seniors who have completed courses on classical mechanics and electromagnetism. For beginners in accelerator physics, one begins with Secs. 2.I–2.IV in Chapter 2, and follows by Secs. 3.I–3.II in Chapter 3 for the basic betatron and synchrotron motion. The study continues onto Secs. 2.V, 2.VIII, and 3.VII for chromatic aberration and collective beam instabilities. After these basic topics, the rf technology and basic physics of linac are covered in Secs. 3.V, 3.VI, 3.VIII in Chapter 3. The basic accelerator physics course ends with physics of electron storage rings in Chapter 4, and some advanced topics of free electron laser and beam-beam interaction in Chapter 5. For beginners, one should pay great attention to the Floquet transformation of Sec. 2.II that can be used to solve Hill’s equation with perturbations. Similarly, some scaling properties of bunch longitudinal distribution in Sec. 3.II are handy for beam vii viii PREFACE manipulation, data analysis, and machine design. The Hamiltonian formalism and canonical transformation, often used to solve particle motion in this book, can provide a better physics picture in beam dynamics. In this revised edition, I include some recently published information on beam ma- nipulation and detection methods, advanced data analysis. I revise some homework problems, and correct mis-prints in the second Edition. The homework is designed to solve a particular problem by providing step-by-step procedures to minimize frustra- tion. The answer is usually listed at the end of each homework problem so that the result can be used in practical design of accelerator systems. I take this opportunity to enhance the content of Sec. 2.VII. Your comments and criticisms to this revised edition are appreciated. S.Y. Lee Bloomington, Indiana, U.S.A. June 10, 2011 ix Preface to Second Edition Since the appearance of the first edition in 1999, this book has been used as a text- book or reference for graduate-level “Accelerator Physics” courses. I have benefited from questions, criticism and suggestions from colleagues and students. As a re- sponse to these suggestions, the revised edition is intended to provide easier learning explanations and illustrations. Accelerator Physics studies the interaction between the charged particles and elec- tromagnetic field. The applications of accelerators include all branches of sciences and technologies, medical treatment, and industrial processing. Accelerator scientists in- vent many innovative technologies to produce beams with qualities required for each application. This textbook is intended for graduate students who have completed their gradu- ate core-courses including classical mechanics, electrodynamics, quantum mechanics, and statistical mechanics. I have tried to emphasize the fundamental physics behind each innovative idea with least amount of mathematical complication. The textbook may also be used by undergraduate seniors who have completed courses on classical mechanics and electromagnetism. For beginners in accelerator physics, one begins with Secs. 2.1–2.4 in Chapter 2, and follows by Secs. 3.1–3.2 for the basic beta- tron and synchrotron motion. The study continues onto Secs. 2.5, 2.8, and 3.7 for chromatic aberration and collective beam instabilities. After these basic topics, the rf technology and basic physics of linac are covered in Secs. 3.5, 3.6, 3.8 in Chapter 3. The basic accelerator physics course ends with physics of electron storage rings in Chapter 4. I have chosen the Frenet-Serret coordinate-system of (ˆx, s,ˆ zˆ) for the transverse radially-outward, longitudinally-forward, and vertical unit base-vectors with the right- hand rule:z ˆ =x ˆ sˆ. I have also chosen positive-charge to derive the equations of betatron motion for× all sections of the Chapter 2, except a discussion of -signs in ± Eq. (2.22). The sign of some terms in Hill’s equation should be reversed if you solve the equation of motion for electrons in accelerators. The convention of the rf-phase differs in linac and synchrotron communities by φlinac = φsynchrotron (π/2). To be consistent with the synchrotron motion in Chapter 3, I have chosen the− rf-phase convention of the synchrotron community to describe the synchrotron equation of motion for linac in Sec. 3.8. x PREFACE TO SECOND EDITION In this revised edition, I include two special topics: free electron laser (FEL) and beam-beam interaction in Chapter 5. In 2000, several self-amplified spontaneous emission (SASE) FEL experiments have been successfully demonstrated. Many light source laboratories are proposing the fourth generation light source using high gain FEL based on the concept of SASE and high-gain harmonic generation (HGHG). Similarly, the success of high luminosity B-factories indicates that beam-beam in- teraction remains very important to the basic accelerator physics. These activities justify the addition of two introductory topics to the accelerator physics text. Finally, the homework is designed to solve a particular problem by providing step-by-step procedures to minimize frustrations. The answer is usually listed at the end of each homework problem so that the result can be used in practical design of accelerator systems. I would appreciate very much to receive comments and criticism to this revised edition. S.Y. Lee Bloomington, Indiana, U.S.A. November 2004 xi Preface to First Edition The development of high energy accelerators began in 1911 when Rutherford discov- ered the atomic nuclei inside the atom. Since then, high voltage DC and rf acceler- ators have been developed, high-field magnets with excellent field quality have been achieved, transverse and longitudinal beam focusing principles have been discovered, high power rf sources have been invented, high vacuum technology has been improved, high brightness (polarized/unpolarized) electron/ion sources have been attained, and beam dynamics and beam manipulation schemes such as beam injection, accumula- tion, slow and fast extraction, beam damping and beam cooling, instability feedback, etc. have been advanced. The impacts of the accelerator development are evidenced by many ground-breaking discoveries in particle and nuclear physics, atomic and molecular physics, condensed-matter physics, biomedical physics, medicine, biology, and industrial processing. Accelerator physics and technology is an evolving branch of science. As the tech- nology progresses, research in the physics of beams propels advancement in accelerator performance. The advancement in type II superconducting material led to the devel- opment of high-field magnets. The invention of the collider concept initiated research and development in single and multi-particle beam dynamics. Accelerator develop- ment has been impressive. High energy was measured in MeV’s in the 1930’s, GeV’s in the 1950’s, and multi-TeV’s in the 1990’s. In the coming decades, the center of mass energy will reach 10-100 TeV. High intensity was 109 particles per pulse in the 1950’s. Now, the AGS has achieved 6 1013 protons per pulse. We are looking for 1014 protons per bunch for many applications.× The brilliance of synchrotron radiation was about 1012 [photons/s mm2 mrad2 0.1% (∆λ/λ)] from the first-generation light sources in the 1970’s. Now, it reaches 1021, and efforts are being made to reach a brilliance of 1029 1034 in many FEL research projects. − This textbook deals with basic accelerator physics. It is based on my lecture notes for the accelerator physics graduate course at Indiana University and two courses in the U.S. Particle Accelerator School. It has been used as preparatory course material for graduate accelerator physics students doing thesis research at Indiana University. The book has four chapters. The first describes historical accelerator development. The second deals with transverse betatron motion. The third chapter concerns
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