Undergraduate Course: Theoretical methods for fusion and astrophysical plasmas (PHYS11073)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | An introduction to theoretical and computational methods that underpin modern advancements in plasma physics. Emphasis is given to kinetic theory, with suitable applications to both magnetically confined fusion and astrophysical settings.
The syllabus is expected to be of interest to undergraduate and postgraduate students specialising in the physics (or applied mathematics) of gases and plasmas, astrophysics, and condensed matter.
The course will be taught through a combination of lectures (in S1) and a project-based component (in S2), with guest participation of UK Atomic Energy Authority expert staff. A substantial part of the learning experience will consist of directed independent learning. |
| Course description |
The first semester activities will establish the fundamental theoretical background. Key concepts and methods will be introduced during frontal lectures. Applications, including worked examples, will be presented during tutorials. The second semester will be mostly devoted to a significant group project, which will allow the students to specialise their interests in the plasma, astrophysical, or condensed matter direction.
Outline content:
1. Kinetic theory of gases
weeks 1-4 (Lectures: 8 hours + Tutorials: 4 hours)
Timescales and length scales. Hamiltonian mechanics of N particles. Liouville's Theorem. Reduced distributions. BBGKY hierarchy. Boltzmann's collision operator and its conservation properties. Boltzmann's entropy and the H-theorem. Maxwell-Boltzmann distribution. Linearised collision operator. Model collision operators: the BGK operator, Fokker-Planck operator. Derivation of hydrodynamics via Chapman-Enskog expansion. Viscosity and thermal conductivity.
2. Kinetic theory of plasmas
weeks 5-8 (Lectures: 8 hours + Tutorials: 4 hours)
Kinetic description of a plasma: Debye shielding and plasma frequency. Vlasov-Maxwell equations. Partition of the dynamics into equilibrium and fluctuations. Linear theory: initial-value problem for the Vlasov-Poisson system. Laplace-transform solution and dielectric function. Landau prescription for calculating velocity integrals. Landau damping and kinetic instabilities. Energy conservation and plasma heating. Ballistic response and phase mixing. Role of collisions. Elements of kinetic stability theory.
3. Kinetic theory of self-gravitating systems
weeks 9-11 (Lectures: 6 hours + Tutorials: 2 hours)
Unshielded nature of gravity and implications for self-gravitating systems. Mean-field approximation with simple examples of equilibria. Negative specific heat. Potential-density pairs. Jeans equations. Long-time response to initial perturbation. Applications of Fokker-Planck formalism to weakly collisional self-gravitating systems, including evaporation.
The second semester (S2) will be mostly devoted to a significant group project. Building upon the theoretical foundation established in S1, the project topics will be related to case studies in both magnetic confinement fusion and astrophysical settings - such as gyrokinetics models, fluid models of different complexity (to enhance connection with MHD courses), plasma instabilities, kinetic turbulence, and self-gravitating systems. The project will require significant theoretical and/or computational development, supplemented by independent literature exploration. The final goal is to produce a report of professional standard. To further strengthen the exposure of students to topics at the forefront plasma research, topical guest lectures will be delivered during the first weeks of Semester 2.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2026/27, Available to all students (SV1)
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Quota: 50 |
| Course Start |
Full Year |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 52,
Seminar/Tutorial Hours 20,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
124 )
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| Assessment (Further Info) |
Written Exam
0 %,
Coursework
50 %,
Practical Exam
50 %
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| Additional Information (Assessment) |
Practical Exam (individual viva): 50%
Coursework: Project report: 50%, including group moderation element (as suggested by the Student representatives that have been consulted)
Both Viva and Project components are 'must pass'. |
| Feedback |
Feedback will be given verbally during tutorials, as well ad during the Practical Exam (viva). Written feedback will be given on the final project report |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Acquire an understanding of fundamental principles of kinetic theory applied to gases, plasmas, and self-gravitating systems
- Offer evidence of such understanding via a succinct oral examination which will include quantitative reasoning
- Develop theoretical and computational methods to address a case study of contemporary relevance in plasma physics
- Communicate results, obtained working as a team, via a written report of a professional standard
- Reflect critically at the implications of fusion plasma physics in response to current technological and societal needs
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Reading List
- The Physics of Fluids and Plasmas, A. R. Choudhuri
- Introduction to Plasma Theory, D. R. Nicholson
- Fundamentals of Plasma Physics, P. M. Bellan
- Plasma Kinetic Theory, D. G. Swanson
- Introduction to Stellar Dynamics, L. Ciotti
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Anna Varri
Tel: (0131 6) 68 8465
Email: Anna.Varri@ed.ac.uk |
Course secretary | Mrs Gillian MacDonald
Tel: (0131 6)51 7525
Email: gillian.macdonald@ed.ac.uk |
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