Physics

Review of the fundamental laws of classical physics. Galileo's principle of relativity, Newtonian mechanics. Galilean transformations, absolute space and time. Maxwell's equations. Electromagnetic waves. Limits of classical mechanics and special relativity theory. Ether theory. Michelson and Morley experiment, alternative theories to explain the results. Lorentz transformations and relativistic kinematics. Concept of simultaneity, time dilation, length contraction. Transformation of velocities, relativistic dynamics, momentum, energy, transformation of forces. Maxwell's equations and Relativity. Transformations of charge and current densities, transformation of E and B fields and potentials. Field of a charge in uniform rectilinear motion. Covariance of Maxwell's equations. Relativistic electrodynamics and applications to particle accelerators. Equations of motion of a charge in an electromagnetic field in Cartesian and cylindrical coordinates. Accelerated charge in an electric field. Bending effects of the B field, cyclotron motion. Multipolar development of the magnetic field in magnetic devices for accelerators. Longitudinal and transverse dynamics of a particle beam. Synchrotron radiation. Accelerator technologies and systems. Radiofrequency accelerating systems. Focusing and bending systems in particle accelerators. Linear accelerators. Circular accelerators. Stability and control of particle beams.

The student must have basic knowledge of mechanics and electromagnetism No prerequisites are requested.

Notes distributed by the professor Textbooks specialized in particle accelerators, such as: S. Y. Lee, Accelerator Physics, World Scientific.

Lectures with exercises and numerical examples. In the event that, due to the pandemic emergency, it is not possible to carry out lessons in person, the course modality will be of the blended or remote type depending on the regulatory provisions.

Attendance at the course is optional

The written exam consists in exercises on relativity and radiation of an accelerated charge. The oral exam consists in a report/presentation of the student of one of the topics of the course with in-depth analysis and questions concerning other arguments

S. Y. Lee, Accelerator Physics, World Scientific. R. Resnick, Introduction to Special Relativity, John Wiley & Sons Inc.

Explanation of the theory lessons and carrying out of exercises that follow the course program on a classic blackboard, interactive white board, tablet with projection in the classroom, or through presentations.

Review of the fundamental laws of classical physics. Galileo's principle of relativity, Newtonian mechanics. Galilean transformations, absolute space and time. Maxwell's equations. Electromagnetic waves. Limits of classical mechanics and special relativity theory. Ether theory. Michelson and Morley experiment, alternative theories to explain the results. Lorentz transformations and relativistic kinematics. Concept of simultaneity, time dilation, length contraction. Transformation of velocities, relativistic dynamics, momentum, energy, transformation of forces. Maxwell's equations and Relativity. Transformations of charge and current densities, transformation of E and B fields and potentials. Field of a charge in uniform rectilinear motion. Covariance of Maxwell's equations. Relativistic electrodynamics and applications to particle accelerators. Equations of motion of a charge in an electromagnetic field in Cartesian and cylindrical coordinates. Accelerated charge in an electric field. Bending effects of the B field, cyclotron motion. Multipolar development of the magnetic field in magnetic devices for accelerators. Longitudinal and transverse dynamics of a particle beam. Synchrotron radiation. Accelerator technologies and systems. Radiofrequency accelerating systems. Focusing and bending systems in particle accelerators. Linear accelerators. Circular accelerators. Stability and control of particle beams.

The student must have basic knowledge of mechanics and electromagnetism No prerequisites are requested.

Notes distributed by the professor Textbooks specialized in particle accelerators, such as: S. Y. Lee, Accelerator Physics, World Scientific.

Lectures with exercises and numerical examples. In the event that, due to the pandemic emergency, it is not possible to carry out lessons in person, the course modality will be of the blended or remote type depending on the regulatory provisions.

Attendance at the course is optional

The written exam consists in exercises on relativity and radiation of an accelerated charge. The oral exam consists in a report/presentation of the student of one of the topics of the course with in-depth analysis and questions concerning other arguments

S. Y. Lee, Accelerator Physics, World Scientific. R. Resnick, Introduction to Special Relativity, John Wiley & Sons Inc.

Explanation of the theory lessons and carrying out of exercises that follow the course program on a classic blackboard, interactive white board, tablet with projection in the classroom, or through presentations.

FIRST PART: Relativistic Electrodynamics. 1- Principles of classical mechanics and electromagnetism Introduction, the principles of classical mechanics, the concept of absolute space and time, the Maxwell equations and the electromagnetic waves, the experiment of Michelson-Morley, the concept of ether. 2- Relativistic kinematics The Lorentz transformations, introduction to space-time, concept of simultaneity and proper time, relativistic invariant, Minkowski space, relativistic Doppler effect. 3- Relativistic dynamics Momentum, work and kinetic energy, equivalence of mass and energy, transformations of momentum and energy, pulse-energy quadrivector, transformations of forces. 4- Relativity and electromagnetism Transformations of charge and current density, the covariance concept and the transformations of fields, potential quadrivector, e.m. field of a relativistic point charge with constant velocity, retarded potentials. 5- Relativistic electrodynamics Brief review of analytical mechanics, the principle of virtual work, Lagrange equations, the Hamilton function, relativistic Hamiltonian of a charged particle. SECOND PART: Accelerator Physics. 1- Introduction to particle accelerators A brief history on particle accelerators, electrostatic accelerators, accelerators based on time varying fields, Cyclotrons, Betatrons and Linacs. 2- Beam dynamics Phase stability in synchrotrons, field index and weak focusing, strong focusing colliders and storage rings. 3- Accelerator devices and new acceleration techniques Dipoles, quadrupoles and sextupoles, RF cavities. 4- Transverse beam dynamics in circular accelerators Hamiltonian in Fernet-Serret coordinate system, Hill’s equation, transverse beam dynamics, matrix formalism, betatron function and tune, Courant-Snyder invariant and Twiss parameters. 5- Longitudinal beam dynamics in circular accelerators Electromagnetic fields in RF devices, standing wave and travelling wave structures, momentum compaction, slippage factor and transition energy, synchrotron oscillations with small and large amplitude.

Basic Physics and Basic electromagnetism courses

Notes from the teacher Material available on the web site https://classroom.google.com/c/MTc3OTM0NDMxOTg0

Lectures and visits

Attendance is optional, but recommended. If a student has not been able to carry out laboratory experiments for some reason, recovery days are to be arranged with the teacher.

The final exam is oral and includes the defence of review of topics studied in the course.

The course is based on traditional lectures in class, with some visits of didactic interest.

FIRST PART: Relativistic Electrodynamics. 1- Principles of classical mechanics and electromagnetism Introduction, the principles of classical mechanics, the concept of absolute space and time, the Maxwell equations and the electromagnetic waves, the experiment of Michelson-Morley, the concept of ether. 2- Relativistic kinematics The Lorentz transformations, introduction to space-time, concept of simultaneity and proper time, relativistic invariant, Minkowski space, relativistic Doppler effect. 3- Relativistic dynamics Momentum, work and kinetic energy, equivalence of mass and energy, transformations of momentum and energy, pulse-energy quadrivector, transformations of forces. 4- Relativity and electromagnetism Transformations of charge and current density, the covariance concept and the transformations of fields, potential quadrivector, e.m. field of a relativistic point charge with constant velocity, retarded potentials. 5- Relativistic electrodynamics Brief review of analytical mechanics, the principle of virtual work, Lagrange equations, the Hamilton function, relativistic Hamiltonian of a charged particle. SECOND PART: Accelerator Physics. 1- Introduction to particle accelerators A brief history on particle accelerators, electrostatic accelerators, accelerators based on time varying fields, Cyclotrons, Betatrons and Linacs. 2- Beam dynamics Phase stability in synchrotrons, field index and weak focusing, strong focusing colliders and storage rings. 3- Accelerator devices and new acceleration techniques Dipoles, quadrupoles and sextupoles, RF cavities. 4- Transverse beam dynamics in circular accelerators Hamiltonian in Fernet-Serret coordinate system, Hill’s equation, transverse beam dynamics, matrix formalism, betatron function and tune, Courant-Snyder invariant and Twiss parameters. 5- Longitudinal beam dynamics in circular accelerators Electromagnetic fields in RF devices, standing wave and travelling wave structures, momentum compaction, slippage factor and transition energy, synchrotron oscillations with small and large amplitude.

Basic Physics and Basic electromagnetism courses

Notes from the teacher Material available on the web site https://classroom.google.com/c/MTc3OTM0NDMxOTg0

Lectures and visits

Attendance is optional, but recommended. If a student has not been able to carry out laboratory experiments for some reason, recovery days are to be arranged with the teacher.

The final exam is oral and includes the defence of review of topics studied in the course.

The course is based on traditional lectures in class, with some visits of didactic interest.