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
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.
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.
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.
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.
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)
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.
These web sites describe a common and efficient paradigm for scripting, computation, visualization, documentation, and reproducible research:
Last update: 5 Jun 2015 by G. Stancari