Accelerator Physics
A.Y. 2025/2026
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 can be attended as a single course.
Course syllabus and organization
Single session
Lesson period
Second semester
Course syllabus
1) Basic Characteristics of accelerators. History of accelerators: electrostatics, cyclotron, betatron, synchrotron, linac.
2) Motion equation, transverse dynamics in magnetic field. Linear motion, focusing, transfer matrix, and beam matrix. Emittance. Adiabatic damping. Longitudinal dynamics, phase stability.
3) Quadrupoles, matching and periodic transport
4) Hill equations, Transfer matrix and stability. Matching , eigen-ellipses, FODO cell.
5) Resonance. Theory and classifications.
6) Colliders. Luminosity. LHC example.
7) Limits in synchrotrons and colliders. Collective effects: space charge, tune shift, beam-beam effects, luminosity decay..
8) Scaling law for synchrotron and colliders. The CERN accelerator chain.
9) Main technology for modern accelerators:
a) RF cavities
b) Magnets
c) Collimators and absorbers
d) Plasma accelerators
e) Accelerators for light sources: Synchrotron light, FEL and inverse Compton
2) Motion equation, transverse dynamics in magnetic field. Linear motion, focusing, transfer matrix, and beam matrix. Emittance. Adiabatic damping. Longitudinal dynamics, phase stability.
3) Quadrupoles, matching and periodic transport
4) Hill equations, Transfer matrix and stability. Matching , eigen-ellipses, FODO cell.
5) Resonance. Theory and classifications.
6) Colliders. Luminosity. LHC example.
7) Limits in synchrotrons and colliders. Collective effects: space charge, tune shift, beam-beam effects, luminosity decay..
8) Scaling law for synchrotron and colliders. The CERN accelerator chain.
9) Main technology for modern accelerators:
a) RF cavities
b) Magnets
c) Collimators and absorbers
d) Plasma accelerators
e) Accelerators for light sources: Synchrotron light, FEL and inverse Compton
Prerequisites for admission
II order differential equations
Fundamnets of electromagnetism
Fundamnets of electromagnetism
Teaching methods
Lectures
Discussion of characteristics and design of modern energy frontier accelrators, plasma accelerators and light sources.
Visit to LASA lab
Discussion of characteristics and design of modern energy frontier accelrators, plasma accelerators and light sources.
Visit to LASA lab
Teaching Resources
Lectures note (Booklet Prof. G. Bellomo) and other documents - lectures slides by teachers
Books:
- Edwards, Syphers - An Introduction to the Physics of High Energy Accelerators. Wiley&Sons editors. - 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 editors. - Available in the library
-K. Wille - The physics of particle accelerators. An introduction- Oxford University Press - Available in the library
Assessment methods and Criteria
Written report on a technology and on a specific type of accelerator (4-5 pages), and an oral examination of about 60-80 minutes covering 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 foreseen.
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 foreseen.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor(s)