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
2019 LECTURES (28 hours) Lindemann LT Monday 10:0011:30 (weeks 1,2,7,8) Monday 10:3011:30 (weeks 3,4) Monday 16:0018:00 (weeks 1,2) Monday 16:3018:00 (weeks 3,4,5,6,7,8) Tuesday 12:0013:00 (weeks 1,2,3,4) Tuesday 12:0013:30 (weeks 7,8) CLASSES A. Wood Rm (week 4), 501 DWB (weeks 7, 9) Wednesday 16:0018:00 (weeks 4, 7) Thursday 16:0018:00 (week 9) EXAM in week 0 of Hilary Term 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 14.10.19  Tue
22.10.19) 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 14.10.19) Lectures 23 (16:0018:00; Mon 14.10.19) Lecture 4 (12:0013:00; Tue 15.10.19) Lecture 5+ (10:0011:30; Mon 21.10.19) Lectures 67 (16:0018:00; Mon 21.10.19) Lecture 8 (12:0013:00; Tue 22.10.19) 
Problem Class 1 16:0018:00 on Wed 6.11.19 (week 4) in Audrey Wood Room Homework due 23:59 Sun 3.11.19 to Toby Adkins (in Merton) 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 28.10.19  Mon
18.11.19) 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 16:0018:00 on Wed 27.11.19 (week 7) in DWB Seminar Room (501) Homework due 23:59 Sun 24.11.18 to Toby Adkins (in Merton) The latest version of the typed notes is available here. Check back for upadtes! Reading: 

Lecture 9 (10:3011:30; Mon 28.10.19) Kinetic
description of a plasma: Debye shielding, micro vs. macroscopic
fields, VlasovLandauMaxwell equations. Lecture
Notes sec 1.11.6

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+ (16:3018:00; Mon
28.10.19) Basic properties of the Landau
collision integral.
Plasma frequency. Slow equilibrium and fast fluctuations. 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. Lecture
Notes sec 1.83.1

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), but I am planning to cover this in my TT2020 followon course. 

Lecture
11 (12:0013:00; Tue 29.10.19)
Linear
theory cont'd: Landau
prescription
for calculating velocity integrals. Solving
the plasma dispersion relation in the slow damping/growth limit.
Langmuir waves. Landau damping.
Lecture
Notes sec 3.23.5


Lecture 12 (10:3011:30; Mon 4.11.19) Linear
theory cont'd: Landau damping and
kinetic
instabilities, sound waves, their damping, ionacoustic instability. Lecture
Notes sec 3.5, 3.73.9


Lecture 13+ (16:3018:00; Mon 4.11.19) Linear
theory cont'd:
ionLangmuir oscillations. Summary of longitudinal waves. Beam
instabilities. You are ready to do Q1, 2, 3/4 of the Problem Set Energy conservation. Heating. Entropy and free energy. Perturbed distribution function: ballistic response and phase mixing. Lecture
Notes sec 3.1011, 5.15.4

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

Lecture 14 (12:0013:00; Tue 5.11.19) Phase
mixing: role of collisions; coarsegraining. Structure of the perturbed
distribution near a resonance: the Casevan Kampen mode. You are ready to do Q68 of the Problem Set Lecture
Notes sec 5.55.6
Note added on 16.11.19:
I have just uploaded a version of the notes with amended sec 5.7, where
the way in which free energy is conserved for Landaudamped Langmuir
oscillations is worked out carefully (and the stray factor of 2, which
I mentioned in the lecture, sorted out). A feature that becomes
explicit in this calculation is the presence of oscillating flows
alongside theoscillating electric fields  cf. also the corresponding
parts of the QLT (sec 7.57.6).


Lecture 15+ (16:3018:00; Mon 11.11.19) Quasilinear
theory: general scheme. QLT
for bumpontail instability in 1D. You are ready to do Q9, 10, or 11 of the Problem Set Lecture
Notes sec 6.1,6.36.6

Krall
& Trivelpiece sec 10 Kadomtsev sec I.3 Sagdeev & Galeev sec II2 (...and read on for more advanced topics) 

Lecture
16+ (16:3018:00; Mon
18.11.19) Quasiparticles. Lecture
Notes sec 7.1

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
25.11.19  Tue 3.12.19) 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 17+ (10:0011:30; Mon 25.11.19) Lecture 18+ (16:3018:00; Mon 25.11.19) Lecture 19+ (12:0013:30; Tue 26.11.19) Lecture 20+ (10:0011:30; Mon 2.12.19) Lecture 21+ (16:3018:00; Mon 2.12.19) Lecture 22+ (12:0013:30; Tue 3.12.19) 
Problem Set 3: you will
find it on JB Fouvry's webpage Problem Class 3 16:0018:00 on Thu 12.12.19 (week 9) in DWB Seminar Room (501) Homework due 23:59 on Tue 10.12.19 to Toby Adkins (in Merton) JB Fouvry's webpage for this part of the course, including lecture notes and problem set J. Binney's 2018 Lecture Notes 

ADVANCED
TOPICS in PLASMA PHYSICS Prof Alexander Schekochihin TA: Toby Adkins Coronavirus (aka Trinity) Term 2020 LECTURES (8 hours) email Alex Schekochihin to receive Zoom link Tuesday and Friday 17:0018:00 (weeks 14) 

KINETICS of QUASIPARTICLES 
Lecture
1 (17:0018:00; Tue 28.04.20)
Reminder: QLT in the language of quasiparticles. Weak turbulence:
kinetic equations for weakly interacting waves  3wave and 4wave
interactions.
Lecture
Notes sec 7.17.2.2

Problem Set: see Lecture
Notes Due: Sunday week 5 to Toby Adkins 

Lecture
2 (17:0018:00; Fri 1.05.20)
WT cont'd: kinetic equations for Langmuirsound turbulence, induced
scattering, and "real" collisions. Statatistical mechanics of
Quasiparticles. Validity of WT.
Lecture
Notes sec 7.2.37.4


LANGMUIR TURBULENCE 
Lecture
3 (17:0018:00; Tue 5.05.20)
Zakharov equations. Hamiltonian form thereof. Derivation of WT kinetic
equations via perturbation and randomphase approximation.
Lecture
Notes sec 8.1, 8.38.4.2



Lecture
4 (17:0018:00; Fri 8.05.20) Solution of WT equations. Direct and inverse cascades. Break down of WT.
Lecture
Notes sec 8.4.38.4.7

Topics I have no time to cover,
but advise you to read about: modulational instability, Langmuir
collapse, strong Langmuir turbulence.
Lecture
Notes sec 8.58.6


NONLINEAR STABILITY (THERMODYNAMICS of COLLISIONLESS PLASMA) 
Lecture
5 (17:0018:00; Tue 12.05.20)
General scheme of the thermodynamic method. Gardner's theorem and
Helander's minimumenergy thermodynamics. Kruskal and Oberman's
thermodynamics of small perturbations. Fowler's thermodynamics of
finite perturbations.

I will not, alas, have time to teach linear stability, but your can
read what I hope is a coherent, and reasonably short, introduction to
this topic in my notes. Lecture
Notes sec 4


COLLISIONLESS RELAXATION & PHASESPACE TURBULENCE 
Lecture
6 (17:0018:00; Fri 15.05.20) LyndenBell's statistical mechanics for collisionless plasma. QL derivation of a "collisionless collision integral".
Lecture
Notes sec 10.110.2.1


Lecture 7 (17:0018:00; Tue 19.05.20)
Microgranulation ansatz. KadomtsevPogutse, LenardBalescu and Landau's
collision integrals. Interpretation of "collisionless collision
integrals" and open questions. Intro to plasma echo. Lecture
Notes sec 10.2.211.1


Lecture 8 (17:0018:00; Fri 22.05.20) TBD 