The course aims to provide an overview of the physics of particle accelerators, and of the historical development of this discipline. The student will be finally in possession of the basic knowledge for the understanding and control of linear and circular accelerators, and for the design of new machines.

The attendance of the Course is recommended after passing the exams in Physics (Mechanics, Electrodynamics) and Mathematics of the first two years of the Bachelor's Degree Course. A good knowledge of electromagnetism and Special Relativity is highly recommended.

The Course introduces students to the Special Relativity and relativistic kinematics and dynamics of subatomic particles, to the concept of accelerator and the accelerated beam parameters. The main types of particle accelerators are exposed approximately following their historical development. The magnetic focusing concepts and accelerating radiofrequency are addressed analytically. The longitudinal and transverse dynamics of a single particle is treated in both linear and circular accelerators. Collective effects on the beam of accelerated particles include wakefields and emission of synchrotron radiation. Finally, the more 'recent free electron laser development is illustrated through the main equations characterizing the process. The course addresses the topics with frequent references to existing accelerators, both colliders and light sources.

Fundamentals of Particle Accelerator Physics, S. Di Mitri, Springer (Graduate Text in Physics). CERN Accelerator School - 94-01 CERN - Vol.I (edited by Turner, 1994).

Recalls of Special Relativity. Introduction to dynamics of relativistic particles. Lorentz force. Definition of parameters for the characterization of the quality of a beam of accelerated particles. Brightness of a particle collider. Historical roots and evolution of the accelerators. Electrostatic accelerators. Electromagnetic resonant accelerators: linear accelerator, the cyclotron. Electromagnetic accelerators non-resonant: the betatron. The synchrotron. The concept of the phase stability. The concept of strong focus. The storage rings. The light sources. Accelerators and resonant circuits structures. Factor transit time. Shunt Impedance. Factor of merit. Dynamic in a synchrotron. Synchronous particle. Longitudinal phase space. Dynamic in a Linac. Outline of traveling wave structures. Trajectories in phase space. Focusing and magnetic lattices. Field number. Alternating gradients. Magnetic field multipolar expansion. Beam transport in matrix representation. Hill equations. Floquet theorem. Concept of resonance and the operating point. Elements of Lagrangian and Hamiltonian dynamics. Conjugate variables. Canonical transformations. Hamiltonian of a conservative system. Invariants of Poincare'. Liouville Theorem (incompressible fluid). Geometric and normalized emittance. Properties of synchrotron radiation. Larmor formula for the radiated power. Spectrum and angular distribution of the synchrotron radiation. Robinson's theorem. Quantum excitation of longitudinal and transverse motion. Udulator. Free electron Laser.

The Course develops nominally within 48 hours of classroom teaching. The training includes written exercises with which to apply the theoretical concepts presented in the lectures.

The Course includes exercises in class that will contribute in part to the final evaluation of the student, in the examination.

Oral exam with frontal exposure to the blackboard by the student. Typically 4-6 questions are asked, covering a good part of the Course program.