A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). 
Michaelmas
Term 2021 LECTURES (28 hours) Monday 10:0011:30 (weeks 1,2,3,4,7,8) Monday 16:0018:00 (weeks 1,2,7,8) Tuesday 12:0013:00 (weeks 1,2,7,8) Tuesday 12:0013:30 (weeks 3,4) Friday 16:0018:00 (weeks 5,6) in Lindemann LT CLASSES TBA Course materials, reading suggestions, scheduling notices, problem sets to appear below. 
A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). 

PART I: KINETIC THEORY OF GASES 
9
hours (Mon 11.10.21  Tue 19.10.21)
Dr Paul
Dellar
Timescales and length scales. Hamiltonian
mechanics of N particles. Liouville’s Theorem.
Reduced distributions. BBGKY hierarchy.
BoltzmannGrad limit and truncation of BBGKY
equation for the 2particle distribution assuming a
shortrange potential. Boltzmann's collision
operator and its conservation properties.
Boltzmann's entropy and the Htheorem.
MaxwellBoltzmann distribution. Linearised collision
operator. Model collision operators: the BGK
operator, FokkerPlanck operator. Derivation of
hydrodynamics via ChapmanEnskog expansion.
Viscosity and thermal conductivity.
The objective of this part of the course is to introduce the basic language of kinetic theory and show how, starting from a kinetic description, one can construct fluid equations for a collisional system close to Maxwellian equilibrium. Lecture 1+ (10:0011:30; Mon 11.10.21) Lectures 23 (16:0018:00; Mon 11.10.21) Lecture 4 (12:0013:00; Tue 12.10.21) Lecture 5+ (10:0011:30; Mon 18.10.21) Lectures 67 (16:0018:00; Mon 18.10.21) Lecture 8 (12:0013:00; Tue 19.10.21) 
Problem Class 1 Tue 2.11.21 @17:0019:30 in D. Sciama LT Homework due by midnight 31.10.21 to Toby Adkins via Canvas Lecture Notes Paul Dellar's webpage for this part of the course, including lecture notes, problem set, and reading suggestions 

PART II: KINETIC THEORY OF PLASMAS & QUASIPARTICLES 
10
hours (Mon
25.10.21  Fri 19.11.21) Prof Alexander Schekochihin Kinetic description of a plasma:
Debye shielding, micro vs. macroscopic fields,
VlasovMaxwell equations. Klimontovich’s version of
BBGKY (nonexaminable). Plasma frequency. Partition
of the dynamics into equilibrium and fluctuations.
Linear theory: initialvalue problem for the
VlasovPoisson system, Laplacetranform 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, sound waves, their damping,
ionacoustic instability, ionLangmuir oscillations.
Energy conservation. Heating. Entropy and free
energy. Ballistic response and phase mixing. Role of
collisions; coarsegraining. Elements of kinetic
stability theory. Quasilinear theory: general
scheme. QLT for bumpontail instability in 1D.
Introduction to quasiparticle kinetics.
The main new set of concepts in this part of the course, compared to Part I, is about the behaviour of a system that has not only particles but also fields: how do they exchange energy? how do they interact? 
Problem Set 2: you will find it in the Lecture Notes Problem Class 2 Tue 23.11.21 @17:0019:30 in D. Sciama LT Homework due by midnight 21.11.21 to Toby Adkins via Canvas The latest version of the typed notes is available here. Check back for upadtes! Reading: 

Lecture 9+ (10:0011:30; Mon
25.10.21) Kinetic description of a plasma:
Debye shielding, micro vs. macroscopic fields,
VlasovLandauMaxwell equations. Basic properties of the
Landau collision integral. Plasma frequency. Slow
equilibrium and fast fluctuations. Lecture Notes sec
1.11.6, 1.82.3

Klimontovich
sec 4, 5, 11 (his version of BBGKY etc.) Helander sec 3 (coll. operator) Helander sec 4 (fluid eqns) Braginskii (ChapmanEnskog for plasma, original derivation) 

Lecture 10+ (12:0013:30; Tue
26.10.21) Outline of the hierarchy of
approximations: linear, quasilinear, weak turbulence,
strong turbulence.
Linear theory: initialvalue problem for the VlasovPoisson system, Laplacetransform solution, the dielectric function, plasma dispersion relation. Landau prescription for calculating velocity integrals. Solving the plasma dispersion relation in the slow damping/growth limit. Lecture Notes sec
2.33.3

Zakharov
et
al.; Nazarenko (general scheme of weak turbulence theory) Kadomtsev; Sagdeev & Galeev (from linear to QL to WT for plasma) Landau's paper (original derivation) Hazeltine & Waelbroeck sec 6.3, 6.4 Alexandrov et al. sec 2, 4 (all the waves catalogued, with an emphasis on plasma as a dielectric) Sec 4 of my Notes is extracurricular material. You can read it if you like (after Lecture 10, you will know all you need to know to read it) 

Lecture 11+ (10:0011:30; Mon
1.11.21) Linear theory cont'd: Langmuir
waves. Landau damping and kinetic instabilities. Sound
waves, their damping, ionacoustic instability,
ionLangmuir oscillations. Summary of longitudinal
waves. Hydrodynamic beam instability.
You are ready to do Q1, 2, 3/4 of the Problem Set Lecture Notes sec
3.43.5, 3.811, 3.7


Lecture 12+ (12:0013:30; Tue 2.11.21) Energy
conservation. Heating. Entropy and free energy.
Perturbed distribution function: ballistic response and
phase mixing. Role of collisions; coarsegraining. You are ready to do Q68 of the Problem Set Lecture Notes sec
5.15.5

Hazeltine &
Waelbroeck sec 6.2 (Landau damping and phase mixing without Laplace transforms) 

Lectures 1314 (16:0018:30; Fri
12.11.21) Structure of the perturbed
distribution near a resonance: the Casevan Kampen mode. Quasilinear theory: general scheme. QLT for bumpontail instability in 1D: plateau, spectrum of waves. Lecture Notes sec
5.6, 6.1


Lectures 1516 (16:0018:00; Fri
19.11.21) QLT for bumpontail instability in
1D.
You are ready to do Q9, 10, or 11 of the Problem Set Reformulation of QLT in quasiparticle formalism. Lecture Notes sec
6.36.6, 7.1

Krall & Trivelpiece
sec 10 Kadomtsev sec I.3 Sagdeev & Galeev sec II2 (...and read on for more advanced topics) Tsytovich sec 3, 5, 7 (on plasmon kinetics and beyond) Peierls's and Ziman's books (on electrons and phonons in metals) 

PART III: KINETIC THEORY OF SELFGRAVITATING SYSTEMS 
9
hours (Mon 22.11.21  Tue 30.11.21) Dr
JeanBaptiste Fouvry
Unshielded nature of gravity and implications
for selfgravitating systems. Meanfield
approximation with simple examples. Negative
specific heat and impossibility of thermal
equilibrium. Relaxation driven by fluctuations in
mean field. Evaporation. Angleaction variables.
Potentialdensity pairs. Longtime response to
initial perturbation. FokkerPlanck equation.
Computation of the diffusion coefficients in terms
of resonant interactions. Application to a tepid
disc.
Here again there are particles (stars) and fields (gravitational). The key feature is that there are no collisions at all and one must understand the behaviour of a kinetic system that is not close to a Maxwellian equilibrium. Lecture 16+ (10:0011:30; Mon 22.11.21) Lectures 1718 (16:0018:00; Mon 22.11.21) Lecture 19 (12:0013:00; Tue 23.11.21) Lecture 20+ (10:0011:30; Mon 29.11.21) Lectures 2122 (16:0018:00; Mon 29.11.21) Lecture 23 (12:0013:00; Tue 30.11.21) 
Problem Set 3:
you will find it on JB Fouvry's webpage Problem Class 3 Tue 7.12.21 @10:0012:00 in Fisher Room Homework due by midnight 5.12.21 to Toby Adkins via Canvas JB Fouvry's webpage for this part of the course, including lecture notes and problem set J. Binney's 2018 Lecture Notes 

COLLISIONLESS PLASMA PHYSICS Dr Plamen Ivanov & Prof Alexander Schekochihin TA: TBA Hilary & Trinity Terms 2021 LECTURES (18 hours) TBA 
