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PHY 691: Computational Accelerator Physics



Class meet time and dates Instructors

2 x 1hr25min weekly (total 2hrs50min). Starts Wed. 10 Feb.
Courses will be held under Zoom. A link will be sent to registered students.
Much flexibility on day & time: to be agreed upon with Pr. F. Méot

Prof. François Méot


Course Overview

  • This course is An Introduction to Particle Accelerators, Hands On, based on computer-laboratory work - the essential of the time of the course.
  • During this course we will manipulate/guide/accelerate to the speed of light charged particles and particle beams, in most of these style of accelerators. The objective: learn about them, 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 their labs, working as a team.
  • This will allow discovering the basic theoretical and practical aspects of their main technological components: magnets and radio-wave cavities. Learning the principles of beam dynamics via numerical simulations will involve a couple of dedicated, popular accelerator simulation codes. With these we will manipulate beams in medical cyclotrons, produce synchrotron radiation proper to condensed matter research, accelerate polarized ion beams for nuclear physics research and watch their spins dance, 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), python.
  • 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 need your laptop, it will be your essential tool. Preferred system: linux. Otherwise, a linux emulator or equivalent capabilities. A Fortran compiler is needed. Have gnuplot operational on your system.

Course Content

  • During the course we will navigate, in the manner described in the "Course Overview" above, through the following list of topics, as time allows :

- cyclotron, transverse stability, CW acceleration,

- betatron, betatron motion, induction acceleration,

- synchro-cyclotron, longitudinal stability,

- pulsed synchrotron, weak and strong focusing,

- particle colliders, spin dynamics,

- light source, synchrotron radiation damping, insertion devices, synchrotron light,

- recirculating and energy recovery linear accelerators,

- electrostatic accelerators,

- beam lines, mass spectrometers.

  • Numerical experiments - the every day's task - will include a variety of beam physics and dynamics topics drawn from such themes as

- focussing, periodic stability, acceleration,

- phase space motion,

- non-linear dynamics, resonances, defects and tolerances

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

- polarization and other Siberian snakes,

- radio-biological/medical beam manipulations,

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

- beam purification, spectrometry.

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 attain a level of knowledge needed to thrive in the field of particle accelerator R&D.
  • 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 other 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, (*%22&f=reportnumber&sf=chronologicalorder&so=a&sp=CERN&rm=):

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

- In CASE PHY554 (

Lectures 1 to 7 and Lecture 9, by Profs. V.N. Litvinenko and Y. Jing
  • Documents taken from the "Course Schedule" below, as needed, will complete these readings.


  • Students 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.
  • Students, in a duo~trio team, will have to complete a research project over the duration of the lecture session. This project will be returned at the end of the session (in May), under the form of a detailed slide presentation. Or instead, under the form a scientific journal-style article. Or both. This will be discussed in due time.
   Participation during the class - 30% of the grade
   Homework assignments - 30% of the grade
   Project (May) - 60% of the grade
   (The total is 120%, yes)

Research Project

  • The research project represents 60% of the final grade.

A project has to begin with a bibliographical research. Consider this as 30% of the time devoted to the project. The quality of, and written reporting on, this preliminary bibliographical research, will represent a substantial part in the final grade.

A project will be chosen from this list: PHY689_projects.pdf.

However, personal initiative is welcome: anyone attracted in a particular accelerator application, not found in that list, is encouraged to make a proposal.

  • The general conduct of a project is the following:

- document the accelerator you have chosen: history, principles, current status;

- document the user's side of the particle beam (e.g., medical application, beam collision and QCD, beam collision and HEP, synchrotron radiation, etc.);

- set up a list of the parameters defining the accelerator, including beam injection, acceleration, extraction or collision;

- from this list build a simulation of the accelerator in a beam optics program;

- produce accelerator optics parameters and a handful of beam dynamics studies, including comparison with theory.

  • Students are encouraged to work on the research project by team

Dedicated short status presentations (slides) will be held over the duration of the course.

  • The project will be concluded by

- a detailed slide presentation

- or a detailed written report

- or both,

to be completed in due time sometime in May.

Course Schedule

  • The course schedule will follow the "Course Content" above, as time allows, and with much flexibility as to the topics and the time spent on a topic, depending on the difficulty, students' interest, etc.


  • Period 0:

Introduction to this 14 week course

A choice of accelerator optics projects

Introduction to the Planet of the Accelerators

A stepwise particle tracker engine: getting started


  • Period 1: Cyclotron


Classical Cyclotron - Theory Reminder / Computer Lab work

Computer Simulations - Solutions (1)

Relativistic Cyclotron - Theory Reminder / Computer Lab work


  • Period 2: synchro-cyclotron, betatron


Theory Reminder / Computer Lab work


  • Period 3: synchrotron, weak focusing


Theory Reminder / Computer Lab work


  • Period 4: synchrotron, strong focusing



  • Period 5: Fixed-Field Alternating Gradient Accelerators - Scaling FFAG


Theory Reminder / Computer Lab work


  • Period 6: Fixed-Field Alternating Gradient Accelerators - Linear FFAG


Theory Reminder / Computer Lab work


  • Period 6: Light source



  • Period 7: Circular collider



  • Phase 8: Spectrometry


Theory Reminder / Computer Lab work


  • Various material

Lab work reporting: Latex material and template for a "Lab. Tech. Note" style of report

Zgoubi Python interfacing: Introduction to PyZgoubi, AGS booster example (Kiel Hock)

Lab work exercises and solutions - will be documented as the course proceeds.