APPH E6102y Site Information

Plasma Physics 2

Prof. Michael Mauel
Email: mauel@columbia.edu

General	Welcome to the APPH E6102y class information site. This is the second semester of a two-semester sequence in plasma physics. Plasma physics is the study of "luminous matter", matter that has been heated sufficiently or prepared specially in order to be ionized. In plasma long-range electromagnetic forces are more important than short range forces. Plasma dynamics is dominated by "collective" motion of large populations of neighboring particles. Electric and electromagnetic waves propagate at speeds that resonate with particles and allow energy and momentum exchange. Plasma motion and the self-consistent electric and magnetic fields exhibit beautiful nonlinear physics. Plasma is studied in the laboratory and in space. Most of the visible universe is in the plasma state. Laboratory generated plasma are used to studied the fundamental properties of high-temperature matter, and they are employed for many valuable applications like surface processing and lighting. Integrated circuits are manufactured using plasma processing, and plasma displays are status symbols of today's world of entertainment. Controlled fusion energy research reflects the remarkable success of plasma physics. The controlled release of more than 10 MW of fusion power has occurred within the strong confining fields of tokamak devices, and the world is now building the first experimental fusion power source, called ITER. Topics covered include: Motion of charged particles in space- and time-varying electromagnetic fields. Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities. Quasilinear theory. Introduction to drift-kinegtic and gyro-kinetic theory. APPH 6102 requires prior experience with plasma physics. The formal prerequisites are APPH E6101 Plasma physics. The goal of this course is to provide a working understanding of plasma physics and prepare students for research.

Welcome to the APPH E6102y class information site.

This is the second semester of a two-semester sequence in plasma physics. Plasma physics is the study of "luminous matter", matter that has been heated sufficiently or prepared specially in order to be ionized. In plasma long-range electromagnetic forces are more important than short range forces. Plasma dynamics is dominated by "collective" motion of large populations of neighboring particles. Electric and electromagnetic waves propagate at speeds that resonate with particles and allow energy and momentum exchange. Plasma motion and the self-consistent electric and magnetic fields exhibit beautiful nonlinear physics.

Plasma is studied in the laboratory and in space. Most of the visible universe is in the plasma state. Laboratory generated plasma are used to studied the fundamental properties of high-temperature matter, and they are employed for many valuable applications like surface processing and lighting. Integrated circuits are manufactured using plasma processing, and plasma displays are status symbols of today's world of entertainment. Controlled fusion energy research reflects the remarkable success of plasma physics. The controlled release of more than 10 MW of fusion power has occurred within the strong confining fields of tokamak devices, and the world is now building the first experimental fusion power source, called ITER.

Topics covered include: Motion of charged particles in space- and time-varying electromagnetic fields. Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities. Quasilinear theory. Introduction to drift-kinegtic and gyro-kinetic theory.

APPH 6102 requires prior experience with plasma physics. The formal prerequisites are APPH E6101 Plasma physics. The goal of this course is to provide a working understanding of plasma physics and prepare students for research.

Textbook	There will be no textbook for the course. Instead, we will make frequent use of journal publications. For those who want a well-rounded textbook, I recommend Introduction to Plasma Physics (2nd Edition) by Don Gurnett (University of Iowa) and Amitava Bhattacharjee (Princeton University). Don Gurnett is a well known space plasma physicists and plasma wave expert. Bhattacharjee has worked in many areas of magnetized plasma physics, including magnetic fusion, plasma astrophysics, theory, and high-performance computation. Since Columbia's plasma physics program has a focus on fusion energy, I also recommend an introductory textbook (undergraduate-level) by Garry McCracken and Peter Stott: Fusion: The Energy of the Universe. McCracken has made pioneering studies of tokamak plasma confinement. He's an expert on plasma wall interactions and worked at Alcator CMOD and JET. Peter Stott is also a leading expert on tokamak fusion confinement, having worked at PPPL, JET, and most recently working on ITER diagnostic systems. Another (graduate-level) textbook on the same subject is Plasma physics and fusion energy, by Jeffrey P. Freidberg (Cambridge University Press, 2007) ISBN 9780521851077. Available online to Columbia University students at CLIO. Indeed, all three books are available online for Columbia University students: see CLIO. Occasionally, I will present numerical illustrations of plasma physics using Mathematica. Mathematica is available to all students through Columbia University. Most frequently, I will distribute published journal articles that illustrate the scientific progress and discoveries in the field of plasma physics.

Textbook

There will be no textbook for the course. Instead, we will make frequent use of journal publications.

For those who want a well-rounded textbook, I recommend Introduction to Plasma Physics (2nd Edition) by Don Gurnett (University of Iowa) and Amitava Bhattacharjee (Princeton University). Don Gurnett is a well known space plasma physicists and plasma wave expert. Bhattacharjee has worked in many areas of magnetized plasma physics, including magnetic fusion, plasma astrophysics, theory, and high-performance computation.

Since Columbia's plasma physics program has a focus on fusion energy, I also recommend an introductory textbook (undergraduate-level) by Garry McCracken and Peter Stott: Fusion: The Energy of the Universe. McCracken has made pioneering studies of tokamak plasma confinement. He's an expert on plasma wall interactions and worked at Alcator CMOD and JET. Peter Stott is also a leading expert on tokamak fusion confinement, having worked at PPPL, JET, and most recently working on ITER diagnostic systems.

Another (graduate-level) textbook on the same subject is Plasma physics and fusion energy, by Jeffrey P. Freidberg (Cambridge University Press, 2007) ISBN 9780521851077. Available online to Columbia University students at CLIO.

Indeed, all three books are available online for Columbia University students: see CLIO.

Occasionally, I will present numerical illustrations of plasma physics using Mathematica. Mathematica is available to all students through Columbia University.

Most frequently, I will distribute published journal articles that illustrate the scientific progress and discoveries in the field of plasma physics.

Curnett and Bhattacharjee Plasma Physics Cover

Instructor & Class Time	Feel free to contact me, Prof. Mike Mauel, anytime. I also try to answer my emails frequently. If you have have question (even if you're stuck on a homework problem), send me an email. Lectures will be held every Monday and Wednesday afternoon, 1:10-2:25 PM, in Room 327, S. W. Mudd Building.

Instructor & Class Time

Feel free to contact me, Prof. Mike Mauel, anytime. I also try to answer my emails frequently. If you have have question (even if you're stuck on a homework problem), send me an email.

Lectures will be held every Monday and Wednesday afternoon, 1:10-2:25 PM, in Room 327, S. W. Mudd Building.

Grading

A student's grade for the course will be based on two take-home exams and two research and writing assignments: one midterm paper and one final paper. These papers must follow the style used for publication in Physics of Plasmas. You will clearly deescribe in your own words a plasma physics topic or question and then review the topic or present an answer to the question.

Student Projects:

Wave Particle Interactions

William Boyes
Jalaluddin Butt
Xu Chu
Rohan Mahnot
Devan Massin
Marco Andres Miller
Aaron Tran
Xuxin Zhang

Student Projects:

Low-Frequency Drift and MHD Instabilities

William Boyes
Jalaluddin Butt
Xu Chu
Rohan Mahnot
Devan Massin
Marco Andres Miller
Aaron Tran
Xuxin Zhang

Lectures

This Web Site is a convenient resource for APPH E6102y. (I will also link to materials on the Columbia CourseWorks site for APPH E6102y.)

*Lecture Date*	*Subjects*
Wed Jan 22	Introduction to course, grading policies, and First Assignment
Mon Jan 27	Collisionless Damping of Nonlinear Plasma Oscillations Physics of Fluids 8, 2255 (1965); https://doi.org/10.1063/1.1761193 Lecture 2 Notes
Wed Jan 29	Lecture 3 Notes
Mon Feb 3	Read "The collisionless nature of high-temperature plasmas," by T. M. O’Neil and F. V. Coroniti, Rev. Mod. Phys. 71, S404 (1999) [https://doi.org/10.1103/RevModPhys.71.S404] Papers to Discuss: "Collisionless Damping of Electrostatic Plasma Waves," J. H. Malmberg and C. B. Wharton, Phys. Rev. Lett. 13, 184 (1964); [https://doi.org/10.1103/PhysRevLett.13.184] "Landau Waves: An Experimental Fact," H. Derfler and T. C. Simonen, Phys. Rev. Lett. 17, 172 (1966); [https://doi.org/10.1103/PhysRevLett.17.172] Some Investigations of Nonlinear Behavior in One-Dimensional Plasmas Physics of Fluids 11, 1506 (1968); [https://doi.org/10.1063/1.1692136] J. M. Dawson, R. Shanny "Nonlinear Development of the Beam-Plasma Instability," Physics of Fluids 13, 2422 (1970); [https://doi.org/10.1063/1.1693255] W. E. Drummond, J. H. Malmberg, T. M. O'Neil, J. R. Thompson In-class problem: electrostatic plasma wave in a warm plasma. Lectue 4 Notes
Wed Feb 5	T.B.D.
Mon Feb 10	Assignment: Ch. 11: Quaslinear Theory: Lecture Notes 5 Email titles and citations for at least two published articles related to wave-particle interactions in plasma. Include with your email a proposed title and subject of your midterm paper. Academic Writing for Graduate Students (3rd Edition) by John Swales and Christine Feak is a very nice workbook for graduate student writing practice. Here's a chapter on writing research reports.
Wed Feb 12	Lecture Notes 6 A simple Mathematica notebook for the standard map. Please take note of Tom Stix's textbook titled Waves in Plasmas (2nd Edition). Chapter 16 is all about quasilinear diffusion.
Mon Feb 17	Read Ch. 10: Wave particle interactions in a magnetized plasma Lecture 7 Notes
Wed Feb 19	Lecture 8 Note: Whistler Waves and Cyclotron Heating Old notes (1988) about wave-energy density in a disperive medium. In-class worksheet: electromagnetic ordinary wave
Mon Feb 24	Lecture 9: Alfvén Waves
Wed Feb 26	Nonlinear Wave-Particle PIC Simulation: Mathematica Notebook (14-Plasma_PIC-2020.nb)
Mon Mar 2	Lecture 10: Discussion of scientific papers From the 2016 DPP Meeting: Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas, Jungpyo Lee, John Wright, Nicola Bertelli, Erwin F. Jaeger, et al. Physics of Plasmas 24, 052502 (2017); [https://doi.org/10.1063/1.4982060] Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear, Zhen-Zhen Ren, Feng Wang, G. Y. Fu, Wei Shen et al., Physics of Plasmas 24, 052501 (2017); [https://doi.org/10.1063/1.4981935]
Wed Mar 4	*T.B.D.*
Mon Mar 9	Lecture 11 Notes DUE: Abstract, Outline, and Approach for your Midterm Paper
Wed Mar 11	Lecture 12 *Discussion: Midterm Papers*
Mon-Fri Mar 16-20	Classes Canceled: Academic Recess
Mon Mar 23	Midterm Assignment DUE: Submit by email a "journal article" on your selected topic of wave-particle interactions. Your paper must have an abstract, introduction, description of physics, summary and reference list. Lecture 14: Introduction to Low-Frequency Fluctuatuions and Transport
Wed Mar 25	Lecture 15
Mon Mar 30	Lecture 16: Introduction to Drift Waves
Wed Apil 1	Lecture 17: Collisional Drift Waves Read the classic and important paper (50th anniversary year): Collisional Drift Waves—Identification, Stabilization, and Enhanced Plasma Transport Physics of Fluids 11, 2426 (1968); https://doi.org/10.1063/1.1691833 H. W. Hendel, T. K. Chu, and P. A. Politzer
Mon Apr 6	Lecture 18: Collisionless Drift Waves See: "Physical Mechanism for the Collisionless Drift Wave Instability," by D. M. Meade, Physics of Fluids 12, 947 (1969); [https://doi.org/10.1063/1.1692583]
Wed Apr 8	Lecture 19: Electromagnetic Response: What is parallel electric field?
Mon Apr 13	Lecture 20: Introduction to Interchange, Ballooning, and Kink Modes Assignment: Email titles and citations for at least two published articles related to two-fluid low-frequency dynamics in a torodial magnetized plasma. Include with your email a proposed title and subject of your midterm paper.
Wed Apr 16	T.B.D.
Mon Apr 20	Lecture 21: Reduced MHD in a Large Aspect Ratio Tokamak Reference: Chapter 5 of Boris Kadomtsev's Tokamak Plasma: A Complex Physical System
Wed Apr 22	Lecture 22: Grad-Shafranov Equilibrium (and More Kink Modes)
Mon Apr 27	Lecture 23: Kink Mode Calculations See also Mathematica notebook: Kink_Mode_Plasma-II.nb
Wed Apr 29	Lecture 24: Resistive MHD and Tearing Modes and Introduction to Resistive Wall Modes (RWM)
Mon May 3	Final Assignment DUE (but students may request extensions): Submit by email a "journal article" on your selected topic of two-fluid low-frequency dynamics in a torodial magnetized plasma. Your paper must have an abstract, introduction, description of physics, summary and reference list.

NRL Plasma Formulary	The NRL Plasma Formulary has been the mini-Bible of plasma physicists for the past 25 years. It is an eclectic compilation of mathematical and scientific formulas, and contains physical parameters pertinent to a variety of plasma regimes, ranging from laboratory devices to astrophysical objects. Download a PDF copy here. (This is very good to have handy!)

NRL Plasma Formulary

The NRL Plasma Formulary has been the mini-Bible of plasma physicists for the past 25 years. It is an eclectic compilation of mathematical and scientific formulas, and contains physical parameters pertinent to a variety of plasma regimes, ranging from laboratory devices to astrophysical objects.

Download a PDF copy here. (This is very good to have handy!)

Plasma Science Links	Matt Stoneking's (and Clint Sprott's) plasma physics bibliography Access to the Physics of Plasmas (Requires CU password.) Access to Physical Review Letters (Requires CU password.) Access to Nuclear Fusion (Requires CU password.) APS Division of Plasma Physics Yahoo's search list for Plasma Physics Wikipedia's page for Plasma Physics Fusion Energy Research The Franklin Institute's "Energy Hotlist" PPPL NIF ITER The "Fire Place" (News and information about fusion energy research.) IAEA Tim Eastman's Outreach Sites: Tim Eastman's "Plasmas International" Tim Eastman's "Perspectives on Plasmas" site Space Weather… spaceweathercenter.org Today's space weather spaceweather.com Rice University's links to space weather NASA's International Solar-Terrestrial Physics (ISTP)

Plasma Science Links

Matt Stoneking's (and Clint Sprott's) plasma physics bibliography
Access to the Physics of Plasmas (Requires CU password.)
Access to Physical Review Letters (Requires CU password.)
Access to Nuclear Fusion (Requires CU password.)
APS Division of Plasma Physics
Yahoo's search list for Plasma Physics
Wikipedia's page for Plasma Physics
Fusion Energy Research
- The Franklin Institute's "Energy Hotlist"
- PPPL
- NIF
- ITER
- The "Fire Place" (News and information about fusion energy research.)
- IAEA
Tim Eastman's Outreach Sites:
- Tim Eastman's "Plasmas International"
- Tim Eastman's "Perspectives on Plasmas" site
Space Weather…
- spaceweathercenter.org
- Today's space weather
- spaceweather.com
- Rice University's links to space weather
- NASA's International Solar-Terrestrial Physics (ISTP)

Course Weblog	Since Fall 2004, I have decided to keep a "weblog" (also known as a "blog") about my academic work. When I started, the weblog was intended only for APPH E4010x Introduction to Nuclear Science. I am not sure if anything important will be recorded there. The blog is like an instructor's diary. Based on my experience from last year, the weblog was essentially unused by students except for the occasional glance. (Students are too busy to read this stuff, and I'm too busy to write anything interesting!) Nevertheless, the link to my (personal) course blog is here. I am no longer providing frequent updates. I also have a link to this page from Columbia's CourseWorks site under the APPH E6102y links.

Course Weblog

Since Fall 2004, I have decided to keep a "weblog" (also known as a "blog") about my academic work. When I started, the weblog was intended only for APPH E4010x Introduction to Nuclear Science. I am not sure if anything important will be recorded there. The blog is like an instructor's diary. Based on my experience from last year, the weblog was essentially unused by students except for the occasional glance. (Students are too busy to read this stuff, and I'm too busy to write anything interesting!)

Nevertheless, the link to my (personal) course blog is here. I am no longer providing frequent updates.

I also have a link to this page from Columbia's CourseWorks site under the APPH E6102y links.

Professor Michael E. Mauel
Department of Applied Physics
Columbia University

Go to Prof. Mauel's HomePage

APPH E6102y Site Information

Plasma Physics 2

Collisional Drift Waves—Identification, Stabilization, and Enhanced Plasma Transport