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Introduction to Beam Physics and Accelerator Technology
Dr. Giulio Stancari
Fermi National Accelerator Laboratory
A lecture series for undergraduate and graduate students within the High Energy Physics Laboratory class of Prof. Massimiliano Fiorini at the University of Ferrara, Italy, April 915, 2019.
General material
 Syllabus
 Student contact sheet
 Lecturer's slides:
 Textbooks:
 Fermilab Operations Department, Concepts Rookie Book
 Edwards and Syphers, An Introduction to the Physics of High Energy Accelerators (Wiley, 1992)
 Sessler and Wilson, Engines of Discovery: A Century of Particle Accelerators (World Scientific, 2nd ed., 2014)
 Exercises, problems and homework
 Practice report
 Final report
Lecture 1
(April 9)
Contents
Introduction. Student interests, background, course of study, contact information. Fill out contact sheet. Discuss syllabus and exercises.
Overview of the field of accelerator physics: research areas, applications, concept map, resources for young researchers.
Introduction to Fermilab. Beam physics and accelerator technology at Fermilab: superconducting rf, magnets, computation, beam physics.
Activities in class:
 strength of dipole magnet vs. current
 quadrupole magnet gradient vs. current; analogy with focusing in light optics
 transition between electric and magnetic steering and focusing at large particle velocities
Materials
Optional resources
 Operation of the Fermilab accelerator complex is described in detail in the Rookie Books.
Lecture 2
(April 10)
Contents
Relativistic kinematics. Magnetic rigidity.
Evolution of particle accelerators: electrostatic machines, cyclotrons, linacs, betatrons, synchrotrons, phase stability, transition energy.
Exercise: tandem accelerator
Activities in class:
 centerofmass energy of collider vs. fixed target
 de Broglie wavelength vs. kinetic energy
 definition of terms: phase stability
Materials
Optional resources
Lecture 3
(April 11)
Contents
Evolution of accelerators: weak and strong focusing, colliders.
Synchrotron radiation. Dissipated power and cooling effect. Intense sources of ultraviolet and X rays.
Applications: medical diagnostics, hadron therapy, industry, defense, ...
Luminosity. Link between nuclear and particle physics and accelerator physics. Fixed target and collider configurations. Crossing angles. Time structure. Instantaneous vs. average vs. integrated. Invariant formulation of event rate. Typical cross sections. Experiment data taking time. Pileup rate.
Exercise in class:
 overlap integral for collision of equal Gaussian bunches. Numerical examples.
Activities in class:
 luminosity optimiziation, store time, turnaround time, luminosity lifetime
 centerofmass energy and luminosity of various colliders
 brief discussion of practice report
Materials
 Landau and Lifshits, The Classical Theory of Fields, Course of Theoretical Physics (Book 2), (ButterworthHeinemann, 1980), Par. 12.
 Highenergy Collider Parameters from the 2014 Review of Particle Physics
 Herr and Muratori, CERN2006002, p. 361
 Concepts Rookie Book
Optional resources
 Grafstrom and Kozanecki, Progr. Part. Nucl. Phys. 81, 97 (2015)
Lecture 4
(April 12)
Contents
Separation of transverse and longitudinal dynamics.
Longitudinal dynamics. Phase stability. Motion in phaseenergy plane. Transition energy. Phaseslip factor. Synchrotron frequency. Buckets.
Numerical simulation of longitudinal dynamics. Effect of voltage on bucket area. Effect of synchronous phase. Phase portraits below and above transition.
Phasespace portraits. Fixed points. Flows. Stable and unstable fixed points.
Exercise in class: acceleration and longitudinal dynamics in the Tevatron
Accelerators as dynamical systems. Continuous and discrete descriptions. Review of Newtonian, Lagrangian, and Hamiltonian dynamics. Coordinates and conjugate momenta. Phase space. Phase portraits.
Exercise in class: Hamiltonian description and phase space of the harmonic oscillator.
Dissipative systems. Nonlinear and chaotic dynamics. Examples of phasespace plots (sextupole, octupole, McMillan lens).
Materials
 Any good introduction to classical mechanics: Goldstein, Landau, Tabor, Lichtenberg and Lieberman, ...
 Edwards and Syphers, Ch. 2 and 3
 Calculation and visualization of longitudinal dynamics in R: script  plot1  plot2
Optional resources
 Regular and chaotic properties of the Chirikov standard map
Lecture 5
(April 15)
Contents
Introduction to linear transverse dynamics. Coupled and uncoupled systems. Coordinates. Normalized gradients. Transfer matrix of drift and quadrupole.
Limitations of the model: coupling, nonlinearities, self fields.
Linear transverse dynamics. Transfer matrices. Stability condition.
Exercise: stability of FODO cell.
Equations of motion. Hill's equation and solutions. CourantSnyder parameterization: amplitude function, betatron tune. Invariants. Definitions of emittance.
Qualitative discussion of dispersion and chromaticity. Lattice imperfections, resonances, tune diagram.
Nonlinearities in accelerators: magnet imperfections, self fields, beambeam forces. Consequences: tune spread, dynamic aperture.
A second look at the concept map.
Resources for students: books, schools, internships, theses.
Discussion and expectations for the Final report.
Materials
 Edwards and Syphers, Ch. 3 and 8
Optional resources

Henon, Numerical Study of Quadratic AreaPreserving Mappings, Quarterly of Applied Mathematics XXVII, 291 (1969)

McMillan, A Problem in the Stability of Periodic Systems, in Topics in Modern Physics: A Tribute to Edward U. Condon, edited by W. E. Brittin and H. Odabasi (Colorado Associated University Press, 1971)

Chirikov, A Universal Instability of ManyDimensional Oscillator Systems, Phys. Rep. 52, 263 (1979)

Nonlinear transverse tracking: R scripts for tracking and plotting; phasespace portraits with sextupole (Q = 0.31), octupole (Q = 0.127 and Q = 0.618); McMillan lens (Q = 0.25, Q = 0.31, and Q = 0.618)

Shiltsev et al., Tevatron Electron Lenses: Design and Operation, Phys. Rev. ST Accel. Beams 11, 103501 (2008)

Stancari, Applications of Electron Lenses: Scraping of HighPower Beams, BeamBeam Compensation, and Nonlinear Optics, arXiv:1409.3615 (2014)
Reference material
General overviews and textbooks
 Chao, Am. J. Phys. 74, 855 (2006)
 Handbook of Accelerator Physics and Engineering, edited by A. W. Chao, K. H. Mess, M. Tigner, and F. Zimmermann (2nd ed., World Scientific, 2013)
 Edwards and Syphers, An Introduction to the Physics of High Energy Accelerators (Wiley, 1992)
 Syphers and Zimmermann, Accelerator Physics of Colliders, in the 2014 Review of Particle Physics
 Humphries, Principles of Charged Particle Acceleration (Wiley, 1986)
 Humphries, Charged Particle Beams (Wiley, 1990)
 Reiser, Theory and Design of Charged Particle Beams (2nd ed., WileyVCH, 2008)
 Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley, 1993)
Books on 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
Internships
 Fermilab internships
Journals and preprints
Conference proceedings
Scientific computing
These web sites describe a common and efficient paradigm for scripting, computation, visualization, documentation, and reproducible research:
 Software Carpentry
 University of Washington, HighPerformance Scientific Computing
 R for scripting, data analysis, and visualization
 Sage for mathematics
 git for version control
Updated