General Prerequisites:
Course Term: Michaelmas
Course Lecture Information: 28 lectures
Course Overview:
28 lectures.
Course weight: 1.75 units
Areas: CMT, Astro, foundational course.
Sequel: Advanced Fluid Dynamics (HT), Collisionless Plasma Physics (TT), Collisional Plasma Physics(TT),
Galactic and Planetary Dynamics (HT).
Lecturers: Dr Paul Dellar, Dr Jean-Baptiste Fouvry, Prof Alex Schekochihin
Method of assessment: Choose from Written Exam in HT week 0 OR homework completion.
This a Physics course. Additional course materials such as problem sheets, homework hand in, and lecture recording can be found at the Canvas site at:
https://canvas.ox.ac.uk/courses/110068 Lectures can be accessed from this link, but if you need a direct link to lectures they can be found at:
https://canvas.ox.ac.uk/courses/110068/external_tools/496
Course weight: 1.75 units
Areas: CMT, Astro, foundational course.
Sequel: Advanced Fluid Dynamics (HT), Collisionless Plasma Physics (TT), Collisional Plasma Physics(TT),
Galactic and Planetary Dynamics (HT).
Lecturers: Dr Paul Dellar, Dr Jean-Baptiste Fouvry, Prof Alex Schekochihin
Method of assessment: Choose from Written Exam in HT week 0 OR homework completion.
This a Physics course. Additional course materials such as problem sheets, homework hand in, and lecture recording can be found at the Canvas site at:
https://canvas.ox.ac.uk/courses/110068 Lectures can be accessed from this link, but if you need a direct link to lectures they can be found at:
https://canvas.ox.ac.uk/courses/110068/external_tools/496
Learning Outcomes:
Course Synopsis:
Part I (9 lectures). Kinetic theory of gases. Timescales and
length scales. Hamiltonian mechanics of N particles. Liouville’s Theorem.
Reduced distributions. BBGKY hierarchy. Boltzmann—Grad limit and truncation of BBGKY equation for the 2-particle distribution assuming a short-range potential. 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.
Part II (10 lectures). Kinetic theory of plasmas and quasiparticles. Kinetic description of a plasma: Debye shielding, micro- vs. macroscopic fields, Vlasov-Maxwell equations. Klimontovich’s version of BBGKY (non-examinable). Plasma frequency. Partition of the dynamics into equilibrium and fluctuations. Linear theory: initial-value problem for the Vlasov-Poisson system, Laplace-tranform solution, the dielectric function, Landau prescription for calculating velocity integrals, Langmuir waves, Landau damping and kinetic instabilities (driven by beams, streams and bumps on tail), Weibel instability (non-examinable), sound waves, their damping, ion-acoustic instability, ion-Langmuir oscillations. Energy conservation. Heating. Entropy and free energy. Ballistic response and phase mixing. Role of collisions. Elements of kinetic stability theory. Quasilinear theory: general scheme. QLT for bump-on-tail instability in 1D. Introduction to quasiparticle kinetics.
Part III (9 lectures). Kinetic theory of self gravitating systems.
Unshielded nature of gravity and implications for self-gravitating systems. Virial theorem, negative specific heat and impossibility of thermal equilibrium. Escape, impact of fluctuations. Mean-field approximation, angle-action variables, self-consistent potential, biorthonormal potential-density pairs. Relaxation driven by fluctuations in mean-field. Long-time response to initial perturbation. Fokker-Planck equation. Computation of the diffusion coeffcients in terms of resonant interactions. Application to a tepid disc.
length scales. Hamiltonian mechanics of N particles. Liouville’s Theorem.
Reduced distributions. BBGKY hierarchy. Boltzmann—Grad limit and truncation of BBGKY equation for the 2-particle distribution assuming a short-range potential. 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.
Part II (10 lectures). Kinetic theory of plasmas and quasiparticles. Kinetic description of a plasma: Debye shielding, micro- vs. macroscopic fields, Vlasov-Maxwell equations. Klimontovich’s version of BBGKY (non-examinable). Plasma frequency. Partition of the dynamics into equilibrium and fluctuations. Linear theory: initial-value problem for the Vlasov-Poisson system, Laplace-tranform solution, the dielectric function, Landau prescription for calculating velocity integrals, Langmuir waves, Landau damping and kinetic instabilities (driven by beams, streams and bumps on tail), Weibel instability (non-examinable), sound waves, their damping, ion-acoustic instability, ion-Langmuir oscillations. Energy conservation. Heating. Entropy and free energy. Ballistic response and phase mixing. Role of collisions. Elements of kinetic stability theory. Quasilinear theory: general scheme. QLT for bump-on-tail instability in 1D. Introduction to quasiparticle kinetics.
Part III (9 lectures). Kinetic theory of self gravitating systems.
Unshielded nature of gravity and implications for self-gravitating systems. Virial theorem, negative specific heat and impossibility of thermal equilibrium. Escape, impact of fluctuations. Mean-field approximation, angle-action variables, self-consistent potential, biorthonormal potential-density pairs. Relaxation driven by fluctuations in mean-field. Long-time response to initial perturbation. Fokker-Planck equation. Computation of the diffusion coeffcients in terms of resonant interactions. Application to a tepid disc.