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Introduction to Beam Physics and Accelerator Technology

Dr. Giulio Stancari
Fermi National Accelerator Laboratory

April 17-28, 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.

People and accelerators at Fermilab

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, small-group 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

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. Center-of-momentum 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: Cockcroft-Walton, 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 phase-energy plane. Transition energy. Phase-slip 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. Courant-Snyder parameterization: amplitude (beta) functions, betatron tune. Emittance.

Dispersion. Chromaticity. Lattice imperfections. Resonances. Tune diagram. Nonlinearities in accelerators: magnet imperfections, self fields, beam-beam forces. Tune spread generation. Dynamic aperture.

Slides: [Transverse dynamics]

Lecture 6

Seminar on current research topics. Research at IOTA/FAST. Nonlinear integrable optics. Single-electron 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 student’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

Accelerator and beam physics

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

Journals and preprints

Conference proceedings

Scientific computing tools

Contact

If you have any questions or comments, please do not hesitate to contact me.

Giulio Stancari in the IOTA control room

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
email address

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