Postgraduate Plasma Physics
Lectures, Imperial College
ADVANCED PLASMA THEORY
(Spring Term 2008: lectures on Wednesdays, 1:00-3:00pm, 741 Blackett)
The lecturer should
give the audience full
to believe that all
his powers have been exerted for their pleasure and instruction.
Here I will post some information on
covered in the past lectures, plans for the upcoming lectures,
for additional reading, original references, problem sheets, scheduling
Note that my presentation will not necessarily be based on the
suggestions below. These are given simply so
you know where to look for an alternative (and in many cases much more
account of the material discussed in class.
Lectures 1-2 (23.01.08)
Introduction/preview of the course (notes: pdf, 1.3 Mb).
Linear kinetics: Langmuir waves, Landau damping/instability (notes: pdf, 1.3 Mb).
Reading: Landau's original paper (pdf, 5.1 Mb)
Note that I did not have time to talk about ion-acoustic waves and the electron-current-driven instability, but this is a review of my last term's lecture, so just read about it in my notes or see these notes on Landau damping etc. from my lectures in Autumn 2006.
Lecture 3 (30.01.08) --- only one hour today because of the plasma open day, which starts at 2pm.
Energy conservation, heating, entropy, phase mixing (notes: pdf, 3 Mb).
Here are three papers that deal with aspects phase mixing:
Hammett, Dorland and Perkins, Phys. Fluids B 4, 2052 (1992)
Krommes & Hu, Phys. Plasmas 1, 3211 (1994)
Krommes, Phys. Plasmas 6, 1477 (1999)
Energy, heating, entropy and phase mixing in gyrokinetics;
Howes et al., Astrophys. J. 651, 590 (2006) --- treatment of entropy/heating closest to my lecture
Schekochihin et al., arXiv:0704.0044, but see this substantially revamped and updated preprint (2008)
Lectures 4-5 (6.02.08)
Phase mixing cont'd.
Quasilinear theory (notes: pdf, 1.1 Mb).
There will be no
lecture on Wednesday
Lectures 6-7 (20.02.08)
Quasilinear relaxation in 1D (notes: pdf, 1.8 Mb).
Lecture on Wednesday 27.02.08 cancelled, apologies.
Lectures 8-9 (5.03.08) --- these lectures are at 10am-12noon; they are self-contained and are also part of the morning lecture series
Hydrodynamic and MHD turbulence: phenomenological scaling theories.
Reading: Kolmogorov-1941 theory: Landau & Lifshitz §33-34; you can also use these lecture notes (sec 1; read on if interested)
MHD turbulence: this
and references therein
Kolmogorov's original paper: A. N. Kolmogorov, Dokl.
SSSR 30, 299 (1941) [reprinted Proc.
Roy. Soc. A 434, 9 (1991)].
Here are two interesting historical papers:
Yaglom, Ann. Rev. Fluid Mech. 26,
1 (1994) on A.
Kolmogorov and the founding of the Russian school of turbulence.
Moffatt, Ann. Rev. Fluid Mech. 34,
19 (2002) on G.
and the Cambridge school of turbulence.
illustration of turbulence as multiscale disorder: this is a paper by
et al. describing the biggest to date direct
turbulence done on the Earth Simulator in Japan.
Here are the some theory papers on MHD turbulence that trace the history of the debate:
P. S. Iroshnikov, Sov.
566 (1964) --- English
translation of Iroshnikov's original paper
Kraichnan, Phys. Fluids 8, 1385 (1965) ---
Dobrowolny, Mangeney & Veltri, Phys. Rev. Lett. 45, 144 (1980) ---
with imbalanced cascades (more + than - waves)
109 (1984) --- early
precursor of the GS theory
Sridhar & Golreich, Astrophys. J. 432, 612 (1994)
--- weak turbulence with 4-wave interactions (3-wave interactions argued empty)
Montgomery & Matthaeus, Astrophys. J. 447,
--- 3-wave interations defended
Ng & Bhattacharjee, Astrophys. J. 465, 845
--- 3-wave interactions demonstrated
Ng & Bhattacharjee,
Phys. Plasmas 4, 605 (1997) --- more of the above
Goldreich & Sridhar, Astrophys.
--- original GS paper on strong MHD turbulence
Goldreich & Sridhar, Astrophys. J. 485, 680
--- weak vs. strong turbulence (3-wave interactions acknowledged and further analysed)
J. Plasma Phys. 63, 447 (2000) --- formal weak turbulence calculation
Galtier et al., Astrophys. J. 564, L49 (2002)
a simpler version of the above
Lithwick & Goldreich, Astrophys. J. 582, 1220
--- another version of the weak-turbulence calculation (plus imbalance
+ and - waves), previous work reexamined
Lithwick, Goldreich & Sridhar, Astrophys. J. 655, 269 (2007) ---
theory with imbalanced cascades
Boldyrev, Phys. Rev.
115002 (2006) --- a
modification of GS theory that has anisotropy but a -3/2
Lectures 10-11 (5.03.08)
Reduced MHD and the decoupling of Alfven-wave cascade.
and references therein
Lectures 12-13 (12.01.08)
Weak turbulence theory: introduction (notes: pdf, 3.8 Mb).
Lectures 14-15 (19.01.08) --- these lectures are at 10am!
Lectures 16-17 (19.01.08)