Postgraduate Plasma Physics Lectures, Imperial College


(Spring Term 2008: lectures on Wednesdays, 1:00-3:00pm, 741 Blackett)

Alexander Schekochihin


The lecturer should give the audience full reason to believe that all
his powers have been exerted for their pleasure and instruction.

Michael Faraday.

Here I will post some information on the material we have covered in the past lectures, plans for the upcoming lectures, suggestions for additional reading, original references, problem sheets, scheduling notices etc.

Note that my presentation will not necessarily be based on the reading suggestions below. These are given simply so that you know where to look for an alternative (and in many cases much more extensive) account of the material discussed in class.

Reading Suggestions

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 13.02.08

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 review (1-2) and references therein

Kolmogorov's original paper: A. N. Kolmogorov, Dokl. Akad. Nauk 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. N. Kolmogorov and the founding of the Russian school of turbulence.
Moffatt, Ann. Rev. Fluid Mech. 34, 19 (2002) on G. K. Batchelor and the Cambridge school of turbulence.
Here is a wonderful illustration of turbulence as multiscale disorder: this is a paper by Yokokawa et al. describing the biggest to date direct numerical simulation of 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. Astron. 7, 566 (1964) --- English translation of Iroshnikov's original paper
Kraichnan, Phys. Fluids 8, 1385 (1965) --- Kraichnan's original paper
Dobrowolny, Mangeney & Veltri, Phys. Rev. Lett. 45, 144 (1980) --- IK theory with imbalanced cascades (more + than - waves)
Higdon, Astrophys. J. 285, 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, 706 (1995) --- 3-wave interations defended
Ng & Bhattacharjee, Astrophys. J. 465, 845 (1996) --- 3-wave interactions demonstrated
Ng & Bhattacharjee, Phys. Plasmas 4, 605 (1997) --- more of the above

Goldreich & Sridhar, Astrophys. J. 438, 763 (1995) --- original GS paper on strong MHD turbulence
Goldreich & Sridhar, Astrophys. J. 485, 680 (1997) --- weak vs. strong turbulence (3-wave interactions acknowledged and further analysed)
Galtier et al., 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 (2003) --- another version of the weak-turbulence calculation (plus imbalance between + and - waves), previous work reexamined
Lithwick, Goldreich & Sridhar, Astrophys. J. 655, 269 (2007) --- GS theory with imbalanced cascades
Boldyrev, Phys. Rev. Lett. 96, 115002 (2006) --- a modification of GS theory that has anisotropy but a -3/2 spectrum

Lectures 10-11 (5.03.08)

Reduced MHD and the decoupling of Alfven-wave cascade.

Reading: this review (1-2) 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)