UFDF040 Fundamentals of plasma physics

Faculty of Philosophy and Science in Opava
Summer 2020
Extent and Intensity
2/1/0. 0 credit(s). Type of Completion: dzk.
Teacher(s)
Claudio Cremaschini, Ph.D. (lecturer)
Claudio Cremaschini, Ph.D. (seminar tutor)
Guaranteed by
Claudio Cremaschini, Ph.D.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is intended to provide the fundamentals of plasma physics. Starting from basic properties of plasmas, subjects address issues concerning single-particle dynamics and the microscopic statistical description of plasmas, which provide the basis for the formulation of kinetic and fluid theories. Applications of the theory to astrophysical plasmas and introduction to relativistic kinetic theory for plasmas subject to electromagnetic radiation-reaction are proposed.
Syllabus
  • 1. Properties of plasmas
    - The plasma state and physical applications.
    - Langmuir frequency and Debye length.
    - The Debye screening effect.
    - Basic properties of plasma dynamics.
    2. Single-particle dynamics in plasmas
    - Motion of charges in uniform EM fields: Larmor frequency and magnetic moment.
    - Motion of charges in intense EM fields slowly-varying in time and space:
    guiding-center approximation and construction of gyrokinetic variables.
    - Gyrokinetic theory: gyrokinetic Lagrangian, equations of motion in gyrokinetic variables, drift velocities, adiabatic invariants, particle trapping phenomena.
    3. Microscopic statistical description (MSD)
    - Axiomatic formulation of MSD: definition of probability, probability density and axiom of conservation of probability.
    - Liouville equation.
    - Boltzmann-Shannon statistical entropy and principle of entropy maximization.
    - Reduced probability density and BBGKY hierarchy.
    4. Kinetic theory of plasmas
    - Kinetic descriptions of plasmas and kinetic distribution function.
    - Kinetic equations of Vlasov and Landau-Fokker-Planck.
    - Maxwellian distribution and kinetic equilibrium.
    - Construction of kinetic equilibrium and Chapman-Enskog solution method.
    5. Fluid and MHD descriptions
    - Fluid fields and velocity moment equations of the kinetic equation.
    - Equations of MHD.
    - The problem of closure conditions.
    - The ideal MHD and the Alfven theorem.
    - Fluid vs kinetic equilibria.
    6. Applications to astrophysical plasmas
    - Astrophysical background.
    - Kinetic equilibria in symmetric and non-symmetric systems.
    - Magnetic field representation.
    - Solution method and plasma kinetic regimes.
    - Construction of equilibrium kinetic distribution functions and physical properties.
    - Perturbative theory and Chapman-Enskog representation.
    - Maxwell's equations and kinetic dynamo.
    7. Relativistic theory
    - Relativistic dynamics of charges: the electromagnetic radiation-reaction effect.
    - Lorentz-Abram-Dirac and Landau-Lifschitz equations of motion: features and problems.
    - Radiation-reaction for classical finite-size charges.
    - Lagrangian formulation and variational equations of motion.
    - Asymptotic approximations and non-existence of point-particle limit.
    - Existence and uniqueness theorem.
    - Non-local Hamiltonian formulation.
    - Relativistic kinetic theory in the presence of radiation-reaction: Liouville and fluid equations.
    Habrman.txt
Literature
    recommended literature
  • Swanson D. G. Plasma Kinetic Theory. Boca Raton, FL: Taylor & Francis, 2008. info
  • Kulsrud R. M. Plasma Physics for Astrophysics. Princeton, NJ: Princeton Univ. Press, 2005. info
  • Goedbloed J. P. H., Poedts N. S. Principles of Magnetohydrodynamics. Cambridge: Cambridge Univ. Press, 2004. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attendance at lectures is recommended. It can be substituted by
the self-study of recommended literature and individual consultations.
The course is also listed under the following terms Winter 2013, Summer 2014, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Winter 2020, Summer 2021, Winter 2021, Summer 2022.
  • Enrolment Statistics (Summer 2020, recent)
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