Skip to main content

FED3220 Motion of Charged Particles, Collision Processes and Basis of Transport Theory II 8.0 credits

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FED3220 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Perturbation theory of charged particle motion and adiabatic invariants. Drift motion of guiding centre. Particle motion in toroidal geometry in presence of static radial and toroidal electric fields. Stochastisation of the orbits by asymmetries, Poincaré plots, Chirikov criterion. Collision processes. Relaxation processes by Coulomb collisions with a background plasma. Interactions by time dependent fields (including wave-particle interactions; resonance interactions) superadiabatic oscillations, collisionless absorption and stimulated emission processes. Brownian motions – Monte Carlo methods for describing particle motion. Curvilinear coordinate system with application to charged particle motion. Basis of analytic mechanics with application to charged particle motion in curvilinear coordinate system. 

Intended learning outcomes

When completing the course, the student should be able to:

Describe particle motion in terms of drift motion of guiding centre,

Understand the concept of adiabatic invariants, knowledge of particle orbits in toroidal geometries in presence of static electric fields. Stochastisation of orbits by asymmetries.

Know how to use Poincaré plots and standard mapping for analysing regular and stochastic orbits, Chirikov criterion for determining stochastisation, and KAM surfaces. Understand how Coulomb collisions affect the motion of single particles and how relaxation towards isotropic thermal plasmas takes place.

Be familiar with the concept of stochastic differential equations and how to use it for solving diffusion equations. The most important collision processes in plasma including nuclear reactions.

Understand the basis of curvilinear coordinate system: covariant and contra variant representation, differentiation in curvilinear coordinate system, flux coordinate system, Clebsch representation of magnetic field and coordinate system suitable for analysing guiding centre motion.

Understand the basis of classical mechanics: Lagrange equation, Hamilton equation, canonical transformation, cyclical coordinates, action-angle variables, Lagrange and Hamiltonian equations of motion of charged particles.

Literature and preparations

Specific prerequisites

No information inserted

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

No information inserted

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F

Examination

  • EXA1 - Examination, 8.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Final writen and oral exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted

Contact

Thomas Jonsson

Postgraduate course

Postgraduate courses at EECS/Fusion Plasma Physics