Dr. Giulio Stancari*Fermi National Accelerator Laboratory*

*A lecture series for undergraduate and graduate students within the High Energy Physics Laboratory class of Dr. Massimiliano Fiorini at the University of Ferrara, Italy, May 18-22, 2015. This class follows the introduction to accelerators given by Prof. Erhard Steffens, May 11-15, 2015.*

General material | Lecture 1 | Lecture 2 | Lecture 3 | Lecture 4 | Lecture 5 | Reference material

- Syllabus
- Student contact sheet
- Lecturer's slides
- Exercises, problems and homework
- Practice report
- Final report

(May 18)

Introduction. Lecturer experience, teaching style, teaching philosophy. Student interests, background, course of study, contact information. Fill out contact sheet. Discuss syllabus.

Overview of the field of accelerator physics: concept map, applications.

The Fermilab accelerator complex: sources, RFQ, Linac, Booster, Recycler, Main Injector, neutrino and muon experiments. Limitations. Upgrade options.

Beam physics research at Fermilab. The IOTA/ASTA facility. Beam physics and accelerator technology at Fermilab: superconducting rf, magnets, computation, beam physics.

Brief overview of longitudinal dynamics. Phase stability. Time structure of beams.

Clarifications on injection and extraction. Choppers and kicker magnets. Combined-function magnets. Magnetic rigidity.

Exercises in class: relativistic kinematics; Booster rf system frequencies.

- Concepts Rookie Book, Ch. 4.
- slides

- Operation of the Fermilab accelerator complex is described in detail in the Rookie Books.

(May 19)

Luminosity. Link between nuclear and particle physics and accelerator physics. Fixed target and collider configurations. Crossing angles. Time structure. Instantaneous vs. average vs. integrated.

Definitions. Invariant formulation.

Exercises in class: Overlap integrals in fixed-target experiment and in collision of equal bunches. Numerical examples. Typical cross sections. Experiment data taking time. Pile-up rate.

Homework: plot of collider luminosities. Optimization in colliders: store time, turn-around time, luminosity lifetime.

- Landau and Lifshits,
*The Classical Theory of Fields*, Course of Theoretical Physics (Book 2), (Butterworth-Heinemann, 1980), Par. 12. - High-energy Collider Parameters from the 2014 Review of Particle Physics
- Herr and Muratori, CERN-2006-002, p. 361

- Grafstrom and Kozanecki, Progr. Part. Nucl. Phys.
**81**, 97 (2015)

(May 20)

Accelerators as dynamical systems. Continuous and discrete descriptions. Review of Hamiltonian dynamics. Coordinates and conjugate momenta. Phase space. Phase portraits.

Exercise in class: harmonic oscillator equations. Phase-space portraits. Fixed points. Flows. Stable and unstable fixed points.

Dissipative systems. In accelerators: scattering, synchrotron radiation, cooling.

Separation of transverse and longitudinal dynamics in accelerators. Coupled and uncoupled lattices.

Longitudinal dynamics. Phase stability. Motion in phase-energy plane. Transition energy. Phase-slip factor. Synchrotron frequency. Stationary buckets.

Numerical simulation of longitudinal dynamics. Effect of voltage on bucket area. Effect of synchronous phase. Phase portraits below and above transition.

Exercise in class: acceleration and synchrotron frequency in Tevatron.

Homework: exploration of Chirikov's standard map.

- Any good introduction to classical mechanics (Goldstein, Landau, Tabor, Lichtenberg and Lieberman, ...)
- Edwards and Syphers, Ch. 2
- slides
- Calculation and visualization of longitudinal dynamics in R: script | plot

- Regular and chaotic properties of the Chirikov standard map

(May 21)

Discussion of practice report. Writing definitions. Writing of the short essay. Examples.

Linear transverse dynamics. Definitions. Normalized gradients. Equations of motion. Transfer matrices. Stability. Courant-Snyder parameterization. Invariants. Single-particle and beam emittance.

Qualitative discussion of dispersion and chromaticity.

Nonlinearities in accelerators: magnet imperfections, space charge, beam-beam forces. Consequences: tune spread, dynamic aperture.

Examples of numerical tracking with sextupoles, octupoles, McMillan lens.

- Edwards and Syphers, Ch. 3
- slides

Henon,

*Numerical Study of Quadratic Area-Preserving 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 Many-Dimensional Oscillator Systems*, Phys. Rep.**52**, 263 (1979)Nonlinear transverse tracking: R scripts for tracking and plotting; phase-space 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*)

(May 22)

Definitions of emittance: single-particle vs. beam; rms or beam fraction; geometrical and normalized.

More on sources and consequences of nonlinearities in accelerators.

Quantitative examples of self fields and intensity effects: space-charge force in long Gaussian bunch; beam-beam force in colliders; space-charge limited diode.

Electron lenses and their applications: beam-beam compensation, collimation, nonlinear integrable optics.

Discussion of final report.

Accelerator resources. Schools, internships, theses.

Conclusions.

- Edwards and Syphers, Ch. 3
- slides
- problem sets
- Herr and Muratori, CERN-2006-002, p. 361
- Humphries,
*Charged Particle Beams*, Secs. 5.1, 5.2, and 5.5.

- Shiltsev et al.,
*Tevatron Electron Lenses: Design and Operation*, Phys. Rev. ST Accel. Beams**11**, 103501 (2008) - Stancari,
*Applications of Electron Lenses: Scraping of High-Power Beams, Beam-Beam Compensation, and Nonlinear Optics*, arXiv:1409.3615 (2014)

- 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., Wiley-VCH, 2008) - Chao,
*Physics of Collective Beam Instabilities in High Energy Accelerators*(Wiley, 1993)

- 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)

- Fermilab internships

These web sites describe a common and efficient paradigm for scripting, computation, visualization, documentation, and reproducible research:

- Software Carpentry
- University of Washington, High-Performance Scientific Computing
- R for scripting, data analysis, and visualization
- Sage for mathematics
- git for version control

*Last update: 5 Jun 2015 by G. Stancari*