PHY691 spring 2023

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Class meet time and dates Instructors
  • 2 x 1hr20 weekly, Tu Th 7:00PM-8:20PM. Starts Tu 23 Jan 2024.
  • Courses will be held in person, at PHYSICS P117 WESTCAMPUS.
  • Prof. François Méot

High Tech Tools

  • Accelerators produced the first man-made high energy particle beams a century ago. Over that century, they have been at the forefront of high-tech, subject to frantic development. Accelerators today are the inescapable tools of research, medicine, industry, under a variety of forms, from small things to gigantic machines and installations, including

- cyclotrons, synchrotrons for the production of cancer tumor therapy beams,

- electron storage rings for the production of UV and X-ray beams,

- linear accelerators for the production of laser X-rays,

- colliders for nuclear and particle physics research: the largest tools ever built !

- microtrons, betatrons and other wham- bam- slam-atrons for industrial applications.

  • Two examples of challenging R&D areas, these days:

- The Electron Ion Collider at BNL, a worldwide collaboration for a facility based on tens of accelerators of different types: high-energy synchrotrons, Linacs, polarized particle sources, beam lines of all sorts,

- FLASH radio-therapy, an emerging cancer tumor treatment technique which holds the promise of affordable access to ion-beam cancer-tumor therapy for anyone in need, and requires an as yet never reached radiation dose of 100s of Gy in a fraction of a second flash.

Course Overview

  • This course is An Introduction to Particle Accelerators, Hands On, based on beam optics and beam dynamics computer simulations.
  • During this course we will manipulate/guide/accelerate to the speed of light charged particles and particle beams, using computer models of various accelerators: cyclotron, synchrotron, FFAGs, linac etc. Our objective: learn about these various acceleration methods, how they work, beam optics, design and engineering aspects, understand their applications. We will do this in a virtual world of accelerator and beam simulations on computer, just like accelerator physicists and designers do in laboratories.
  • This will allow discovering the basic theoretical and practical aspects of their main technological components: magnets and radio-frequency cavities. Learning the principles of beam dynamics via numerical simulations will involve a couple of dedicated, popular accelerator simulation codes. With these we will, as time allows, manipulate beams in cyclotrons, produce synchrotron radiation, accelerate polarized ion beams, watch the dance of particle spins, etc.
  • In confronting basic accelerator theory with numerical simulation outcomes, the course introduces to a wide variety of applied mathematics and numerical methods, from ODE solving to Fourier analysis to interpolation techniques. Popular software tools will be used such as gnuplot (plotting), latex (writing your reports, your slide presentations), ...
  • This course fosters programming, computing and system software skills, knowledge of computer languages. In a general manner, it will require the students to carry out some programming, program debugging sometimes, and other computer science tasks, as part of the game.
  • So... Yes! You'll be using your laptop, it will be your main tool. Preferred systems: linux. MAC is ok. Otherwise, a linux emulator or equivalent capabilities. A Fortran compiler is needed, gfortran for instance. Have gnuplot operational on your system. The use of such tools as python for interfacing and/or data post processing is welcome.

Course Content

  • During the course we will navigate through the following list of topics, as time allows, and not necessarily in this order :

- early 1900s electrostatic components, the AGS "electric analog", today's storage rings

- early 1930s cyclotron, isochronous cyclotron, CW acceleration, 1960s spin dynamics

- 1940's betatron, betatron motion, induction acceleration

- 1944's microtron, racetrack microtron, more spin dynamics

- 1945's synchro-cyclotron, longitudinal stability, synchronous acceleration

- 1945's weak focusing pulsed synchrotron

- 1950s and XXI-st century strong focusing synchrotron, storage rings, depolarizing resonances

- 1955s FFAG accelerators

- XXI-st century mass separators, mass spectrometers, beam lines

  • Numerical experiments will include a variety of beam optics and beam dynamics topics drawn from such themes as

- focusing, periodic stability, acceleration,

- phase space motion,

- non-linear dynamics, resonances, defects and tolerances

- production of synchrotron radiation, Poynting vector, spectral brightness,

- polarization and Siberian snakes,

- radio-biological/medical beam manipulations,

- in-flight particle decay of short-lived particles,

- beam purification, mass separators.

Learning Goals

  • The course will prepare graduate students with no prior experience for the understanding of the dynamics of charged particle beams, and of the design of particle accelerators. Running computer programs has a variety of goals : applying numerical methods to solve problems for which analytical methods have limitations; producing, collecting, analyzing and understanding numerical simulation data; presenting and reporting results using appropriate media. This course will allow students to reach an appropriate level of knowledge to thrive in the field of particle accelerator R&D, if so desired.
  • Following completion of this study/computer lab period, students will have learned/increased their knowledge, in various domains, including

- The history of particle accelerators

- Beam optics

- Physics and dynamics of charge particle beams, their manipulation

- Application of accelerators: medical, X-ray source, the quest for fundamental particles

- Synchrotron radiation, spin dynamics and other Siberian snakes

- Programing, debugging, using big computer codes

- Many other aspects of particle accelerator science and technology

- And reporting: via real-world style of scientific written reports, and via slide presentations.

Textbook and suggested materials

  • Recommended readings in preparation for the course:

- In "CAS - CERN Accelerator School : 5th General Accelerator Physics Course", Yellow-Report CERN-94-01, (

 A brief history and review of accelerators, P.J. Bryant, (pp.1-14),

- In CASE PHY554 (

 Lectures 4-7 and 13-14, by Profs. V.N. Litvinenko, Y. Jing, Yue Hao.
  • Documents taken from the "Course Schedule" below, as needed, will complete these readings.


  • Students, rather than the instructor! will be active most of the time during the course: constructing accelerators, manipulating and accelerating particle beams, discussing their progress, programming/debugging. Home work will be largely based on pursuing or "finishing" the studies undertaken during the course. A preferred way of returning the "home work" will be under the form of short written scientific-style reports, or slide presentations to the class, or both, by individuals or 2~3 student teams.
   Participation during the class - 40% of the grade
   Completion of homework assignments - 40% of the grade
   Homework return reports and/or slides: document and presentation quality - 40% of the grade
   (The total is 120%, yes)

Course Schedule

  • The course schedule will follow the "Course Content" above, yet not necessarily in that order, as time allows, and with much flexibility as to the topics and the time spent on each topic, depending on the difficulty, students' interest, etc.


  • Beam Optics

Particle Accelerators: An Introduction

Tooling and Methods for Particle Trajectory Simulations

Lorentz Force Solver Engine: Getting Started

  • Electrostatic Systems

Electrostatic Systems - Theory Reminder / Computer Lab work

     [[media: |Computer Lab work - Solutions]]

  • Cyclotron, Classical


Classical Cyclotron - Theory Reminder / Computer Lab work

Computer Lab work - Solutions of exercises 3.1 to 3.3

  • Cyclotron, Relativistic

Relativistic Cyclotron - Theory Reminder / Computer Lab work

     [[media: |Computer Lab work - Solutions]]

  • Betatron; Microtron; Synchro-cyclotron


Theory Reminder / Computer Lab work

  • Weak Focusing Synchrotron; Synchrotron Radiation Light


Theory Reminder / Computer Lab work

    Computer Lab work - Exercises
    [[media:|Computer Lab work - Solutions]]

  • Synchrotron, Strong Focusing


Theory Reminder / Computer Lab work

  • Scaling FFAG


Theory Reminder / Computer Lab work

     [[media:|Computer Lab work - Solutions]]

  • Linear FFAG


Theory Reminder / Computer Lab work

  • Beam Line; Spectrometer; Mass Separator


Theory Reminder / Computer Lab work

  • Documentation

Beam Optics, An Introduction

Linear Transport, Brief Reminder