Postgraduate Plasma Physics
Lectures, Imperial College

ADVANCED PLASMA THEORY

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

**Alexander Schekochihin**

ADVANCED PLASMA THEORY

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

his powers have been exerted for their pleasure and instruction.

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.*

Introduction/preview of the course (notes: pdf, 1.3 Mb).

Linear kinetics: Langmuir waves, Landau damping/instability (notes: pdf, 1.3 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.

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)

Quasilinear theory (notes: pdf, 1.1 Mb).

There will be no lecture on Wednesday 13.02.08

Quasilinear relaxation in 1D (notes: pdf, 1.8 Mb).

Lecture on Wednesday 27.02.08 cancelled, apologies.

Hydrodynamic and MHD turbulence: phenomenological scaling theories.

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

Weak turbulence theory: introduction (notes: pdf, 3.8 Mb).