Electrodynamics and synchroton radiation
Code: 100173Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Physics | OP | 4 |
Contact lecturer
- Name :
- Emili Bagan Capella
- Email :
- emili.bagan@uab.cat
Group languages
You can consult this information at the end of the document.
Prerequisites
There are no formal prerequisites. However, it is recommended that students have successfully completed the Electromagnetism course and the compulsory Mathematics courses of the Bachelor's Degree in Physics.
Objectives
The course is divided into two parts. The first part presents the most important aspects of the Lagrangian and Hamiltonian formulations of classical electrodynamics. Maxwell's equations are rederived from first principles (the principle of relativity, the principle of least action, etc.). Conservation laws, gauge invariance, and the equations of motion of a charged particle in an electromagnetic field are also studied.
The second part deals with the radiation emitted by relativistic particles. It begins with an introduction to the concept of radiation. The radiation emitted by relativistic charges, including Bremsstrahlung, is studied in depth, with particular emphasis on the cases of linear accelerators and synchrotrons. The spectrum and other properties of synchrotron radiation are also examined. Finally, a brief introduction to the quantization of the electromagnetic field is presented.
The objective of the first part of the course is for students to acquire a structured and unified understanding of classical electrodynamics, together with the background needed to gain a deeper understanding of advanced topics such as the quantum theory of radiation. The objective of the second part is to provide a broad, yet reasonably in-depth, understanding of both the theoretical foundations and selected applied aspects of radiation from relativistic particles, including linear accelerators, synchrotron light sources, and their experimental applications.
Learning outcomes
- Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
- Working in groups, assume shared responsibilities and interact professionally and constructively with others, showing absolute respect for their rights.
- Distinguish between the assumptions implicit in a given problem and the consequences of eliminating these and, therefore, learning to generalize solutions.
- Describe how Maxwell's equations are obtained from first principles such as relativity and the principle of least action.
- Describe the importance of gauge invariance in electrodynamics.
- Describe the production of radiation through relativistic particles.
- Describe field effects in load movement.
- Obtain the equations of motion and evolution for interacting relativistic particles.
- Calculate Lagrangean-conserved quantities with relativistic scalar and vector fields.
- Pose and solve the equation of motion for a load in certain simple electromagnetic fields.
- Calculate the power radiated by accelerated relativistic particles.
- Illustrate, in other scientific fields, the applicability of the methodology developed.
- Recognise the theoretical foundations underpinning the quantum theory of radiation.
- Recognise the importance of gauge invariance in formulating the standard model of fundamental interactions.
- Recognise the theoretical foundations underpinning the operation of particle accelerators and radiation production.
- Use approximate methods to decouple the evolution of complex systems into simpler parts.
- Correctly use linear and tensor algebra in non-Euclidean spaces.
- Handle and solve partial differential equations.
- Use group theory in describing symmetries.
- Identify situations in which a change or improvement is needed.
Contents
Special relativity (covariant notation). Lagrangian and Hamiltonian formulations of classical electrodynamics. Interaction Lagrangian. Charges in electromagnetic fields. Gauge invariance. Free-field Lagrangian. Maxwell's equations in covariant and vector form. Energy-momentum tensor. Symmetries and conservation laws. The Poynting vector.
Liénard-Wiechert potentials. General aspects of radiation from relativistic particles. Larmor's formula and its relativistic generalization. Bremsstrahlung. Linear accelerators. Synchrotron radiation. General properties of synchrotron radiation. Angular distribution. Spectrum of synchrotron radiation. Polarization of the radiation. Integrated spectral distribution. Quantization of the electromagnetic field (Gupta-Bleuler formalism).
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Individual Work | 92 | 3.68 | 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 |
| Theory and Problem Classes | 49 | 1.96 | 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 |
Lectures and problem-solving sessions covering the topics of the syllabus. Two problem sets will be assigned. They will be taken into account in the assessment if they contribute to improving the final grade.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Problem Delivery | 20% | 0 | 0 | 3, 4, 6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22 |
| First partial | 40-50% | 3 | 0.12 | 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 |
| Second partial | 40-50% | 3 | 0.12 | 1, 2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20 |
| Final examination | 100% | 3 | 0.12 | 1, 5, 6, 7, 9, 10, 11, 12, 14, 16, 19, 20, 21 |
Continuous assessment: Two examinations (each consisting of a theory part and a problem-solving part) and two problem-set submissions will be required. The grade for each midterm, N (out of 10), will be calculated from the grade of the corresponding problem set, L (out of 2), and the examination grade, E (out of 10), according to the formula:
N = L + (10 − L) · E / 10
The final grade will be the average of the two midterm grades, provided that each of them is at least 3.5 out of 10.
Students who do not pass the course through continuous assessment, as well as those who wish to improve their final grade, may take the final examination. This examination will cover the entire course. Its grade, which does not include the problem-set submissions, will replace the continuous assessment grade only if it is higher.
Single assessment: Students who have opted for the single assessment modality must complete a final assessment consisting of a theory examination (45%), in which they will answer a series of questions covering the course contents, and a problem-solving examination (45%), in which they will solve a set of problems. In addition, they must submit a problem set (10%), prepared in advance at home, and defend it on the day of the examination by explaining its solutions in detail and answering any questions that may be asked. All these assessment activities will take place on the same day, at the same time and in the same location as the second midterm examination of the continuous assessment.
Bibliography
J.D. Jackson Classical Electrodynamics John Wiley & Sons
L.D. Landau , E. M. Lifshitz Classical Theory of Fields Pergamon Press
J. Costa Quintana, F. López Aguilar, Interacción electromagnética. Teoría Clásica. Reverté, 2007.
E. Bagan, Notes d'Electrodinàmica clàssica. UAB (Serie Materials, Num. 47) 1998.
J. Llosa, A. Molina, Relativitat Especial amb aplicacions a l'electrodinàmica clàssica. Publicacions i Edicions Universitat de Barcelona, 2004.
P.J. Duke, Synchrotron Radiation : Production and properties. OUP Oxford (Series on Synchrotron Radiation), 2008.
E. Bagan, Problemes d'Electrodinàmica clàssica, UAB (Serie Materials, Num. 51) 1998.
Software
No particular programary is used in this course.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |