Accelerator Physics
A.Y. 2026/2027
Learning objectives
The course gives a general description of the accelerators and introduces the fundamental concepts of the transversal and longitudinal
focalization. A detailed derivation of the periodic focusing structure FODO is given.
The characteristic and limits of the colliders are illustrated
focalization. A detailed derivation of the periodic focusing structure FODO is given.
The characteristic and limits of the colliders are illustrated
Expected learning outcomes
At the end of the course the students are expected to:
- be able to understand the characteristic of a circular accelerator (synchrotron)
- design a FODO cell and calculate the properties of the matched beam
- have the knowledge of the principal properties of the high energy proton colliders
- be able to understand the characteristic of a circular accelerator (synchrotron)
- design a FODO cell and calculate the properties of the matched beam
- have the knowledge of the principal properties of the high energy proton colliders
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1) General characteristics of accelerators. Historical development of accelerators: electrostatic, circular and linear accelerators. In particular: cyclotron, betatron, synchrotron and linac. Energy loss due to radiation.
2) Equations of motion. Transverse dynamics in a magnetic field. Linear motion, focusing, transfer matrix and beam matrix. Emittance. Adiabatic damping. Longitudinal dynamics, phase stability and electric fields.
3) Magnetic quadrupoles. Matching and periodic transport.
4) Hill's equations. Transfer matrix and stability. Matching and eigen-ellipses. The FODO cell.
5) Resonances. Theory and classification.
6) Colliders. Luminosity. The LHC as an example.
7) Limits of synchrotrons and colliders. Collective effects: space charge, tune shift and beam-beam effects. Luminosity decay.
8) Scaling laws for synchrotrons and colliders. The CERN accelerator chain.
9) Main technologies developed for modern accelerators:
a) RF cavities
b) Magnets
c) Collimators and absorbers
d) Plasma accelerators
e) Accelerators for light sources: synchrotron radiation, FELs and inverse Compton scattering
2) Equations of motion. Transverse dynamics in a magnetic field. Linear motion, focusing, transfer matrix and beam matrix. Emittance. Adiabatic damping. Longitudinal dynamics, phase stability and electric fields.
3) Magnetic quadrupoles. Matching and periodic transport.
4) Hill's equations. Transfer matrix and stability. Matching and eigen-ellipses. The FODO cell.
5) Resonances. Theory and classification.
6) Colliders. Luminosity. The LHC as an example.
7) Limits of synchrotrons and colliders. Collective effects: space charge, tune shift and beam-beam effects. Luminosity decay.
8) Scaling laws for synchrotrons and colliders. The CERN accelerator chain.
9) Main technologies developed for modern accelerators:
a) RF cavities
b) Magnets
c) Collimators and absorbers
d) Plasma accelerators
e) Accelerators for light sources: synchrotron radiation, FELs and inverse Compton scattering
Prerequisites for admission
Second-order differential equations
Fundamentals of electromagnetism
Fundamentals of electromagnetism
Teaching methods
Lectures
Discussion of the characteristics and design of modern energy-frontier colliders, plasma accelerators and accelerators for light sources.
Visit to the LASA Laboratory.
Discussion of the characteristics and design of modern energy-frontier colliders, plasma accelerators and accelerators for light sources.
Visit to the LASA Laboratory.
Teaching Resources
Lecture notes (booklet by Prof. G. Bellomo) and other material, including slides prepared by the course lecturers
Books: Edwards, Syphers - An Introduction to the Physics of High Energy Accelerators. Wiley & Sons. - Available in the library
- K. Wille - The Physics of Particle Accelerators: An Introduction. Oxford University Press. - Available in the library
Books: Edwards, Syphers - An Introduction to the Physics of High Energy Accelerators. Wiley & Sons. - Available in the library
- K. Wille - The Physics of Particle Accelerators: An Introduction. Oxford University Press. - Available in the library
Assessment methods and Criteria
A written report on one technology and one specific type of accelerator (4-5 pages), followed by an oral examination of about 60-80 minutes on fundamental topics such as:
- Magnetic quadrupoles: equations of motion, transfer matrix, thin-lens approximation
- Periodic structures: Hill's equations, lattice stability, Twiss matrix, beta function, beam matching
- FODO lattice and beam matching
- Resonances
- Longitudinal beam stability
- Luminosity
- Main technologies (magnets, RF cavities, collimators)
Lectures and seminars by specialists from CERN and other laboratories are also planned.
- Magnetic quadrupoles: equations of motion, transfer matrix, thin-lens approximation
- Periodic structures: Hill's equations, lattice stability, Twiss matrix, beta function, beam matching
- FODO lattice and beam matching
- Resonances
- Longitudinal beam stability
- Luminosity
- Main technologies (magnets, RF cavities, collimators)
Lectures and seminars by specialists from CERN and other laboratories are also planned.
PHYS-01/A - Experimental Physics of Fundamental Interactions and Applications - University credits: 3
PHYS-03/A - Experimental Physics of Matter and Applications - University credits: 3
PHYS-03/A - Experimental Physics of Matter and Applications - University credits: 3
Lessons: 42 hours
Professor(s)
Reception:
Monday 2-4 pm
LASA Laboratory or Physics Department (please send an e-mail)