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
2020 LECTURES (28 hours) Monday 10:0011:30 (weeks 2,3,4,7,8) Monday 16:0018:00 (weeks 2,3,7,8) Monday 16:3018:00 (weeks 4,5,6) Tuesday 12:0013:00 (weeks 2,3,4,7,8) Tuesday 16:3018:00 (weeks 3,4) on ZOOM (links by email from Jasmine, not public) Virtual blackboard for Part II (plasma) lectures Virtual blackboard for Part III (GD) lectures CLASSES Tuesday 16:0018:00 (weeks 5, 7), 14:0016:00 (week 9) on ZOOM (link by email from Jasmine or Toby) 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 19.10.20  Tue
27.10.20) 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 19.10.20) Lectures 23 (16:0018:00; Mon 19.10.20) Lecture 4 (12:0013:00; Tue 20.10.20) Lecture 5+ (10:0011:30; Mon 26.10.20) Lectures 67 (16:0018:00; Mon 26.10.20) Lecture 8 (12:0013:00; Tue 27.10.20) 
Problem Class 1 Tuesday 10.11.20 at 16:0018:00 Homework due by 11:59 on 6.11.20 to Toby Adkins 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 (Tue 27.10.20  Mon
16.11.20) 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 Tuesday 24.11.20 at 16:0018:00 Homework due by 11:59 on 20.11.20 to Toby Adkins The latest version of the typed notes is available here. Check back for upadtes! Reading: 

Lecture 9+ (16:3018:00; Tue 27.10.20) Kinetic
description of a plasma: Debye shielding, micro vs. macroscopic
fields, VlasovLandauMaxwell equations. Basic properties of the Landau
collision integral. Plasma frequency. Lecture
Notes sec 1.11.6, 1.82.1

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+ (10:0011:30; Mon 2.11.20) 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 2.23.1

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+ (16:3018:00; Mon 2.11.20)
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 and
kinetic
instabilities. Sound waves.
Lecture
Notes sec 3.23.5, 3.8


Lecture 12 (12:0013:00; Tue 3.11.20) Linear
theory cont'd: damping of sound waves, 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 3.911, 3.7


Lecture 13+ (16:3018:00; Tue 3.11.20) 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) 

Lecture 14+ (16:3018:00; Mon 9.11.20) 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, 6.1,6.36.4

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

Lecture
15+ (16:3018:00; Mon
16.11.20) QLT in 1D con'd: energy of resonant and nonresonant particles, heating of the thermal bulk.
You are ready to do Q9, 10, or 11 of the Problem Set Reformulation of QLT in quasiparticle formalism. Lecture
Notes sec 6.56.6, 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
23.11.20  Tue 1.12.20) 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 23.11.20) Lectures 1718 (16:0018:00; Mon 23.11.20) Lecture 19 (12:0013:00; Tue 24.11.20) Lecture 20+ (10:0011:30; Mon 30.11.20) Lectures 2122 (16:0018:00; Mon 30.11.20) Lecture 23 (12:0013:00; Tue 1.12.20) 
Problem Set 3: you will
find it on JB Fouvry's webpage Problem Class 3 Tuesday 8.12.20 at 14:0016:00 Homework due by 11:59 on 4.12.20 to Toby Adkins 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 Information below is for TT2020, to be updated for TT2021 closer to the time 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)
Phasespace turbulence under the "shortsudden" approximation.
Stochastic echo. Adkins' solution in 1D and the effect of
collisions.Implications for collisionless relxation. Lecture
Notes sec 11.211.4
