*This page was last updated 16 Mar 2020.*

Notes 1: System and Freezing-in Law — *posted 06 Jan 2020*

Notes 2: Conservation Laws, Virial Theorem and Self-Confinement — *posted 06 Jan 2020*

Notes 3: Linear Waves in MHD — *posted 06 Jan 2020*

Notes 4: Energy Principle and Ideal Instabilities — *posted 23 Jan 2020*

Notes 5a: Non-Ideal MHD I — Basic Reconnection — *revised notes posted 07 Feb 2020*

Notes 5b: Non-Ideal MHD II — Flux Expulsion and Homogenization — *revised version posted 07 Feb 2020*

Notes 5c: Non-Ideal MHD III — Basics of Magnetic Helicity — *revised version posted 07 Feb 2020*

Notes 5d: Non-Ideal MHD III — Taylor Relaxation and its Dynamics — *posted 07 Feb 2020*

Notes 6a: Wave Interactions — *posted 10 Feb 2020*

Notes 6b: Basics of Turbulence — *posted 10 Feb 2020*

Notes 6c: Detailed Notes on Turbulence — *posted 10 Feb 2020*

Notes 7a: MHD Turbulence 1 — *posted 10 Feb 2020*

Notes 7b: MHD Turbulence 2 — *posted 10 Feb 2020*

Notes 8: Nonlinear Alfven Waves — *revised notes posted 12 Mar 2020*

Toward Investigation of Diffusive Shock Acceleration Mechanism in a Magnetized Collisionless Shock Wave in LArge Plasma Device (LAPD) — Feng-Jen Chang — *posted 16 Mar 2020*

Hyper Resistivity in Presence of Stochastic Fields — Chang-Chun Chen — *posted 16 Mar 2020*

Magnetoluminescence — Jung-Tsung Li — *posted 16 Mar 2020*

EMHD Explanation of Ionization Wave Propagation
in Strong Magnetic Field Region — Haotian Mao — *posted 16 Mar 2020*

What to Expect When Getting an MRI — Rebecca Masline — *posted 16 Mar 2020*

Where My Glitches At? Pulsar Magnetohydrodynamics and Superfluid Glitches — Jacob Saret — *posted 16 Mar 2020*

Ambipolar Diffusion and Implications for Star Formation — Kielan Wilcomb — *posted 16 Mar 2020*

Lecture 1: Basic Equations, Alfven's Theorem, Freezing-in — *posted 18 January 2018*

Lecture 2: Conservation Laws, Virial Theorem, Self-confinement and Collapse — *posted 18 January 2018*

Lecture 3: Linear Waves in MHD — *posted 18 January 2018*

Lecture 4: Reduced Models — *posted 29 January 2018*

Lecture 5: Introduction to DNLS and Collisionless Shocks — *posted 29 January 2018*

Lecture 6: Simple Ideas in Non-Ideal MHD — *posted 29 January 2018*

Lecture 7: Non-Ideal MHD II — Flux Expulsion and Homogenization — *posted 12 February 2018*

Lecture 8: Magnetic Helicity, Taylor Relaxation, Mean Field Theory — *posted 15 February 2018*

Lecture 9: Notes on Wave Interactions — *posted 22 February 2018*

Lecture 10: MHD Turbulence I — *posted 01 March 2018*

Lecture 11: MHD Turbulence II — *posted 05 March 2018*

Lecture 12: Energy Principle and Ideal Instabilities — *posted 01 March 2018*

Lecture 13: Introduction to Cosmic Ray Dynamics — *posted 19 March 2018*

Lecture 1: Basics of MHD - *posted 2 March 2015*

Lecture 2: Conservation Laws in MHD - *posted 2 March 2015*

Lecture 3: Linear Waves in MHD - *posted 2 March 2015*

Lecture 3a: Reduced MHD - *posted 2 March 2015*

Supplement-Reduced MHD - *reposted 8 April 2015*

Basics of Gas Dynamic and MHD Shocks - *posted 13 April 2015*

Lecture 4: Foundations of Wave Kinetics - *posted 2 March 2015 *

Lecture 5: Energy Principle and Stability - *posted 2 March 2015*

Lecture 6: Simple Ideas in Non-Ideal MHD I - *posted 2 March 2015*

Lecture 7: Non-Ideal MHD II - *posted 2 March 2015*

Lecture 7a: Homogenization and Expulsion - *posted 2 March 2015 *

Lecture 8: Stochastic Magnetic Fields and Relaxation - *posted 2 March 2015*

Lecture 9: A Very Brief Intro to Mean Field Electrodynamics - posted 2 March 2015

Lecture 9a: Quasilinear Theory I - *posted 2 March 2015 *

Lecture 9b: Quasilinear Theory II - *posted 2 March 2015 *

Lecture 9c: See Chapter 3 for Quasilinear Theory Discussion - *posted 2 March 2015 *

Lecture 10: Nonlinear Waves, Shocks and Turbulence - An Introduction - *posted 2 March 2015*

Lecture 10a: Nonlinear Waves - *posted 2 March 2015*

Lecture 10b: "Nonlinear Plasma" by "Wave Kinetics" - *posted 2 March 2015*

"Hydromagnetic Stability of a Plasmas" - B.B. Kadomtsev

"MHD Description of Plasma" - Russell M. Kulsrud

"The Variational Principle for Problems of Ideal Magnetohydrodynamic Stability" - Ira B. Bernstein

"Relaxation and Magnetic Reconnection in Plasmas"- J.B. Taylor

"On Steady Laminar Flow with Closed Streamlines at Large Reynolds Number" - G.K. Batchelor

"How Rapidly is a Passive Scalar Mixed Within Closed Streamlines?" - P.B. Rhines and W.R. Young

Electron Heat Transport in a Tokamak with Destroyed Magnetic Surfaces" - A.B. Rechester and M.N. Rosenbluth

A New Look at the Instability of a Stratified Horizontal Magnetic Field - D.W. Hughes and F. Cattaneo

Magnetic Buoyancy and the Boussinesq Approximation - E.A. Spiegel and N.O. Weiss

PV Homogenization - Peter B. Rhines and William R. Young

The Expulsion of Magnetic Flux by Eddies - N.O. Weiss

50 years of fusion research - Dale Meade

The Physics Basis of ITER Confinement - F. Wagner

Pseudo-three dimensional turbulence in magnetized nonuniform plasma - Akira Hasegawa and Kunioki Mima

A collisional drift wave description of plasma edge turbulence - Masahiro Wakatani and Akira Hasegawa

A quarter-century of H-mode studies - F. Wagner

Low Frequency Modes in Confined Plasmas - K. Itoh, S.-I. Itoh and A. Fukuyama

Turbulence in Toroidal Systems - B.B. Kadomtsev and O.P. Pogutse

Zonal Flows: From Wave Momentum and Potential Vorticity Mixing to Shearing Feedback Loops and Enhanced Confinement - P.H. Diamond

Zonal flows in plasma-a review" - P.H. Diamond, S.-I. Itoh, K. Itoh and T.S. Hahm

Vorticity dynamics, drift wave turbulence, and zonal flows: a look back and a look ahead - P.H. Diamond, A. Hasegawa and K. Mima

Eddy Motion in the Atmosphere - G.I. TaylorMultiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers - D.G. Dritschel and M.E. McIntyre

The General Circulation of the Atmosphere - Isaac M. Held and GFD/2000 Fellows

Gravitational Resistive Instability of an Incompressible Plasma in a Sheared Magnetic Field - K.V. Roberts and J.B. Taylor

High mode number stability of an axisymmetric toroidal plasma - J.W. Connor, R.J. Hastie and J.B. Taylor

Shear, Periodicity, and Plasma Ballooning Modes - J.W. Connor, R.J. Hastie, and J.B. Taylor

Nonlinear growth of the tearing mode - P.H. Rutherford

Intro to Mixing Length Theory - Douglas Gough; D.O. Gough and E.A. Spiegel

Reviews of Plasma Physics - B.B. Kadomtsev

Electron Magnetohydrodynamics - A.S. Kingsep, K.V. Chukbar, V.V. Yankov

From Reconnection to Relaxation: A Pedagogical Tale of Two Taylors - P.H. Diamond

Cooperative Phenomena and Shock Waves in Collisionless Shocks - R.Z. Sagdeev

Notes by Jiacong Li and P.H. Diamond - *posted 06-25-15*

Turbulence theory is a huge and vital subject. In 218B, we only scratch the surface. For additional reading, see below:

**A) Fluid/Navier-Stokes Turbulence**

i.) "Turbulence: The Legacy of A.N. Kolmogorov", - U. Frisch, C.U.P. - superb, *short* book

ii.) Kulsrud: 11.7, 11.8 - summary of basics

iii.) Diamond, Itoh, Itoh: 2.3 - summary of basics

iv.) Frisch, Sulem, Nelkin '78 - good basic OV of cascades and fractal intermittency. Accessible

A Simple Dynamically Model of Intermittent Fully Developed Turbulence - Uriel Frisch, Pierre-Louis Sulem and Mark Nelkin

v.) Falkovich, et *al.*, 2001 - review of particle dispersion in turbulence. Difficult, but worth it.

Particles and Fields in Fluid Turbulence - G. Falkovich, K. Gawedzki and M. Vergassola

**B) MHD Turbulence**

i.) Kulsrud: 11.9 - basics

ii.) Diamond, Itoh, Itoh: 9.1, 9.2 - basics; 9.3 - steepening of Alfven waves

iii.) Goldreich, Sridhar '95, '97: basic papers. GS'97 is particularly accessible

Toward a Theory of Interstellar Turbulence II. Strong Alfvenic Turbulence - P. Goldreich and S. Sridhar

Magnetohydrodynamic Turbulence Revisited - P. Goldreich and S. Sridhar

iv.) Pouquet, Frisch, Leorat '78: classic paper on strong MHD turbulence

Strong MHD Helical Turbulence and the Nonlinear Dynamo Effect - A. Pouquet, U. Frisch and J. Leorat

v.) Pouquet '78: classic paper on 2D MHD turbulence

On Two-Dimensional Magnetohydrodynamics Turbulence - A. Pouquet

vi.) Galtier, et *al.*, 2000: technical but useful paper on wave interactions in MHD turbulence

A Weak Turbulence Theory for Incompressible Magnetohydrodynamics - S. Galtier, S.V. Nazarenko, A.C. Newell and A. Pouquet

- - Kulsrud, Chapter 7 - presents an introductory exposition of the Energy Princple.

Some additional material may be found at:

- - Rayleigh-Taylor notes I, II (posted)

- Supplementary Notes on Energy Principle

- Kadomtsev Review Article (posted)

- Kulsrud Review Article (posted)

- R.B. White, "Theory of Tokamak Plasmas", Chapter 4

For Kinetic Energy Principles:

- - Binney and Tremaine, Chapter 5: 5.2, 5.4

- R. Kulsrud and J.W.-K. Mark, Ap. J. 160, 471 (1970)

- J. Goodman, Ap. J. 329, 612 (1988)

- M.D. Kruskal and C. Oberman, Phys. Fluids 1, 275 (1958)