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Introduction to Beam Physics and Accelerator Technology
Dr. Giulio Stancari
Fermi National Accelerator Laboratory
April 1728, 2023
Welcome!
This is a lecture series for undergraduate and graduate students in physics at the University of Ferrara, Italy.
All course materials can be found here at bitbucket.org/gist/apufe23.
Table of Contents
Audience
This course is for undergraduate and graduate students in physics. Prerequisites include classical mechanics, electromagnetism and special relativity at the undergraduate level.
Motivation
Why study accelerator physics?

First of all, it is rewarding. It puts you in touch with fundamental science, such as nuclear and particle physics, and with exciting applications, such as medical diagnostics and treatment.

It is also a challenging and diverse field. It brings together researchers with a variety of skills, including mathematics, physics, engineering and computing. You will likely find areas that match your strengths and inclinations.

Accelerators are important tools in many fields of science and technology. Scientists and engineers who use them in their research need to know how they work to design experiments, to analyze data, and to explore new applications.

Finally, the field offers several theses, internships, fellowships and job opportunities. If you like the topics discussed in this course, there is probably a career path for you!
Learning objectives
In this course, students

learn about the historical evolution of particle accelerators

become familiar with the main concepts

develop the ability to make quantitative estimates of basic phenomena and design parameters

critically review articles from the literature
Methodology
Lectures include slides, smallgroup activities and discussion sessions.
Schedule
We will meet from 15:00 till 18:00 (Europe/Rome time zone) on these dates:
 Tuesday April 18
 Wednesday April 19
 Thursday April 20
 Friday April 21
 Wednesday April 26
 Thursday April 27
Lectures will be held in person in room C200 at INFN and Department of Physics and Earth Science of the University of Ferrara, Italy.
Assessment
Students will be evaluated according to the following criteria:

Attendance (24%) is a key part of the course. Active participation is highly encouraged: ask questions and contribute to the discussions!

Homework (32%) consists of a set of questions and problems. Examples are discussed in class. Solutions can be prepared individually or as a group, but each student must turn in a scan of his or her own handwritten copy to receive credit. All homework is due Friday, June 30.

Critical Paper Review (24%). You are asked to choose an article from a list of papers and to prepare a report according to the process discussed in class. The paper review is due Friday, June 30.

Oral Exam (20%, for undergraduate students only). You will be asked to discuss some of the concepts presented during the lectures and to summarize your paper review.
Textbooks

Edwards and Syphers, An Introduction to the Physics of High Energy Accelerators (Wiley, 1992) (available online with permission of the author)

Fermilab Operations Department, Concepts Rookie Book (2020)

Sessler and Wilson, Engines of Discovery: A Century of Particle Accelerators (World Scientific, 2nd ed., 2014)
Contents
Lecture 1
Introduction of lecturer and students. Motivation, objectives, methodology, assessments, resources.
Overview of the course: history, applications, concept map.
Review of classical mechanics. Newtonian, Lagrangian and Hamiltonian approaches. Phase space. Example of the harmonic oscillator.
Review of relativistic kinematics. Main definitions: velocity parameters, momentum, energy. Four vectors. Centerofmomentum energy. Relations between momentum, energy and velocity spread.
Review of electromagnetism. Maxwell's equations and Lorentz force. Magnetic rigidity.
Slides: [Introduction] [Reviews]
Lecture 2
Review of electromagnetism. Magnetic materials. Functions and design of dipole and quadrupole magnets.
Historical evolution of particle accelerators and related discoveries. Motivation: conversion of energy to mass; secondary beams; microscopic probes. Direct voltage acceleration: CockcroftWalton, Van de Graaff, tandem. Resonant acceleration: cyclotrons, linacs. Induction acceleration: betatrons. Synchrotrons and phase stability.
Slides: [Historical evolution]
Lecture 3
Historical evolution. Alternating gradient. Strong focusing. Colliders: advantages, challenges and advances in the understanding of beam physics. Superconductivity applied to accelerators. Current research topics.
Applications of accelerators. Overview: nuclear and particle physics; biology, chemistry and material science; medicine; archeology and art; industrial processes; defense; energy and environment. Synchrotron radiation sources. Medical applications. Examples from fine arts.
Critical paper review. Motivation. Methods. Examples. Review of Cockcroft and Walton's papers. List of papers for assignment.
Slides: [Applications] [Critical review]
Lecture 4
Experiment design and luminosity. Fixed target and collider configurations. Crossing angles. Time structure. Instantaneous vs. average vs. integrated luminosity. Invariant formulation of event rate. Typical cross sections. Experiment data taking time.
Longitudinal dynamics and acceleration. Phase stability. Motion in phaseenergy plane. Transition energy. Phaseslip factor. Synchrotron frequency. Buckets. Introduction to nonlinear dynamics and chaos.
Slides: [Luminosity] [Longitudinal dynamics]
Lecture 5
Transverse dynamics and focusing. Coupled and uncoupled systems. Coordinates. Normalized magnetic gradients. Transfer matrices. Beam transport. Stability conditions. Equations of transverse motion. Hill's equation. CourantSnyder parameterization: amplitude (beta) functions, betatron tune. Emittance.
Dispersion. Chromaticity. Lattice imperfections. Resonances. Tune diagram. Nonlinearities in accelerators: magnet imperfections, self fields, beambeam forces. Tune spread generation. Dynamic aperture.
Slides: [Transverse dynamics]
Lecture 6
Seminar on current research topics. Research at IOTA/FAST. Nonlinear integrable optics. Singleelectron dynamics. Undulator radiation. Optical stochastic cooling.
Resources and next steps. Textbooks. Literature. Schools. Internships. Research opportunities.
Expectations. Homework. Critical paper review. Oral exam.
Slides: [Current research] [Conclusions]
Academic integrity
This course promotes high academic standards and integrity. Students are expected to conduct themselves as academic professionals.
All work submitted is expected to be the studentâ€™s own. Information drawn from other sources must be properly cited. At the discretion of the instructor, work that is not the student's own or information that lacks clear attribution may be considered invalid for course evaluation and for the attribution of credits.
Special needs and accommodations
Accommodations will be made for students with special needs. University policies can be found here.
Resources
General overviews and textbooks
Mechanics, electromagnetism, relativity

Goldstein, Poole, and Safko, Classical Mechanics, 3rd ed. (Addison Wesley, 2002)

Landau and Lifshitz, Mechanics (Elsevier, 1976)

Taylor and Wheeler, Spacetime Physics, 2nd ed. (Freeman, 1992)

Purcell and Morin, Electricity and Magnetism, 3rd ed. (Cambridge, 2013)

Landau and Lifshitz, The Classical Theory Of Fields, 4th ed. (ButterworthHeinemann, 1987)

Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)
Accelerator and beam physics

M. Sands, The Physics of Electron Storage Rings: An Introduction, SLAC121 (1970)

S. Humphries, Principles of Charged Particle Acceleration (Wiley, 1986)

S. Humphries, Charged Particle Beams (Wiley, 1990)

D. Edwards and M. Syphers, An Introduction to the Physics of High Energy Accelerators (Wiley, 1992) (available online with permission of the author)

A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley, 1993)

A. W. Chao, Am. J. Phys. 74, 855 (2006)

M. Reiser, Theory and Design of Charged Particle Beams (2nd ed., WileyVCH, 2008)

Handbook of Accelerator Physics and Engineering, edited by A. W. Chao, K. H. Mess, M. Tigner, and F. Zimmermann (2nd ed., World Scientific, 2013)

S. Y. Lee, Accelerator Physics (4th ed., World Scientific, 2019)

A. W. Chao, Lectures on Accelerator Physics (World Scientific, 2020)

Accelerator Physics of Colliders, HighEnergy Collider Parameters and Neutrino Beam Lines at HighEnergy Proton Synchrotrons in the 2021 Review of Particle Physics

Handbook of Accelerator Physics and Engineering, edited by A. W. Chao, M. Tigner, H. Weise and F. Zimmermann (3rd ed., World Scientific, 2023)
Nonlinear dynamics and chaos

Amaldi, La fisica del caos (Zanichelli, 2011), with additional materials

Gleick, Chaos (Penguin, 2008)

Ruelle, Chance and Chaos (Princeton, 1993)

Strogatz, Nonlinear Dynamics and Chaos (2nd ed., Westview, 2014)

Hirsch, Smale, and Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos (3rd ed., Academic Press, 2012)

Thompson and Stewart, Nonlinear Dynamics and Chaos (Wiley, 2002)

Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, 1989)

Lichtenberg and Lieberman, Regular and Chaotic Dynamics (Springer, 1992)
Particle Accelerator Schools
 US Particle Accelerator School (USPAS)
 CERN Accelerator School (CAS)
 Joint Universities Accelerator School (JUAS)
Internships
 Fermilab internships
Journals and preprints
Conference proceedings
Scientific computing tools
 R for scripting, data analysis, and visualization
 SageMath and SageMathCell for numerical and symbolic mathematics
 SageMathCell and WolframAlpha for online computations
 git for version control
Contact
If you have any questions or comments, please do not hesitate to contact me.
Dr. Giulio Stancari
Fermi National Accelerator Laboratory
Mail Stop 339
PO Box 500
Batavia IL 60510
USA
+1 630 840 3934
home.fnal.gov/~stancari
Updated