APPH E6101x Site Information

Plasma Physics 1

Prof. Michael Mauel
Email: mauel@columbia.edu

General

Welcome to the APPH E6101x class information site.

This is the first 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 much more important than short range forces. Plasma dynamics is often dominated by "collective" motion involving the correlated motion of large populations of neighboring particles. Since plasma motion generates electric and magnetic fields, plasma behavior exhibits sometimes very 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. Kinetic description of plasmas. Collisional Boltzmann equation (and collision operators in Fokker-Planck forms.) Classical transport equations and collisional relaxation processes. Linear electrostatic and electromagnetic waves in field-free plasmas. Vlasov equation and Landau damping.

APPH 6101 requires a prior experience with electromagnetics (and some electrodynamics) and partial differential equations. The formal prerequisites are APPH E3300y Applied Electromagnetism and APMA E3102y Applied Mathematics II: Partial Differential Equations. The goal of this course is to provide a solid understanding of both the fundamental aspects of plasma physics and introduce students to research problems in the fields of laboratory and space plasma physics.

Textbook

The primary course textbook is Plasma Physics by Alexander Piel of Christian-Albrechts-University, Kiel, Germany. This is an excellent introduction to plasma physics, and we will be following the outline of textbook in the course.

I will also refer to other textbooks, and many of these books are available to Columbia University students via CLIO.  These are:

  1. Plasma Physics : An Introduction to Laboratory, Space, and Fusion Plasmas by Alexander Piel (2nd ed. 2017; Springer). Online here
  2. Introduction to plasma physics : with space, laboratory and astrophysical applications by Donald A. Gurnett and Amitava Bhattacharjee (2nd Ed. 2017; Cambridge Univ Press). Online here
  3. Plasma physics : An introduction by Richard Fitzpatrick (2nd ed. 2022; CRC Press). Online here
  4. Introduction to Plasma Physics and Controlled Fusion by Francis F. Chen (3rd ed. 2016; Springer). Online here
  5. The Physics of Plasmas by T.J.M. Boyd and J.J. Sanderson (2003, Cambridge). Online here.  
  6. Plasma Physics and Fusion Energy by Jeffrey P. Freidberg (Cambridge Unive Press, 2007). Online here
  7. Magnetically Confined Fusion Plasma Physics Ideal MHD theory by Linjin Zheng (Morgan & Claypool Publishers, 2019). Online here
  8. Fusion Reactor Design: Plasma Physics, Fuel Cycle System, Operation and Maintenance by Takashi Okazaki (17 November 2021, Wiley-VCH GmbH). Online here
  9.  Basic Space Plasma Physics by Wolfgang Baumjohann and Rudolf A. Treumann (3rd Edition, World Scientific 2022). Only  intro online here.
  10. Space Plasma Physics : 1 Stationary Processes by Akira Hasegawa and Tetsuya Sato. (1st ed. 1989, Springer Berlin Heidelberg). Online here
  11. Theory of Space Plasma Microinstabilities by S. Peter Gary (Cambridge University Press, 2005). Online here
  12. Magnetohydrodynamic Stability of Tokamaks by Hartmut Zohm (Wiley 2014). Online here
  13. Introduction to Plasma Physics by R.J. Goldston (CRC Press, 1995). Online here
  14. Plasma Physics via Computer Simulation by C K Birdsall and A B Langdon (Taylor & Francis, 2004). Online here
  15. Plasma waves by D.G. Swanson (Second edition, CRC Press, 2003). Online here

Everyone can have access to these textbooks. As guidance and for  clarity, this semester's syllabus will follow both the outline and content contained in the Alexander Piel's book.

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

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

Piel 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 415 Schapiro [SCEP] Building.

Grading

A student's grade for the course will be based primarily on two closed-book quizzes (25% each) and one final exam (50%). The quiz dates will be October 12 and 26.

I will also assign weekly homework assignments that will not "officially" count for your final grade. Completing these homeworks will be the most important action you can take to learn the material. Homeworks are due at the beginning of the following class period.

Lectures

This Web Site is a convenient resource for APPH E6101x. (I will also link to materials on the Columbia CourseWorks site for APPH E6101x. This will be especially the case for video lectures when I must be away from campus. After logging into to CourseWorks, you must select "AP 6101" to view and download materials.)

Lecture Date Subjects
Sept6
Sept 11
  • Charged particle motion in a magnetic field
  • Chapter 3 in Piel: Single Particle Motion in Electric and Magnetic Fields
Sept 13
  • Lecture 3 Notes
  • Guiding center theory and magnetic drifts (and a handout may be useful)
  • Trapped particle orbits, the magnetic mirror, planteary magnetospheres
  • Magnetized plasma torus, the tokamak
  • Rotational transform and rational surfaces
  • Adiabatic invariants and Chaotic orbits
Sept 18
  • Lecture 4 Notes (Adiabatic Invariants and Magnetic Drifts in the Tokamak)
  • ... and summarizing previous lectures
Sept 20
  • Lecture 5 Notes: (Adiabatic Invariants and Magnetic Drifts in the Tokamak)
  • including "banana orbits"!
Sept 25

Sept 27

VIDEO

Lecture 

  • Prof. Mauel is away from campus: Video Lecture in CourseWorks  
Oct 3
Oct 5
Oct 11

---- Quiz 1 -----

Oct 16-18
  • Prof. Mauel at IAEA Conference. See https://www.iaea.org/events/fec2023
  • Maybe: video lectures and updates about conference
  • Chapter 6 in Piel: Plasma Waves
  • Waves in a plasma (Chapter 6): Lecture10-Waves
Oct 23
Oct 25
10/30 - 11/3

Annual Meeting of the APS Division of Plasma Physics

Nov 6 Holiday: Election Day
Nov 8
Nov 13
  • (Monday) ------ Quiz 2 ------
Nov 15
  • Bohm Sheath Criterion
  • Waves in bounded plasma
  • Notes about Probes (Plasma1-Lecture-14-Probes.pdf)

 

Nov 20
Nov 22 Holday: Thanksgiving (no classses)
Nov 27
Nov 29

Not used in 2023:

Dec 4, 6
Dec 11
Dec 18
  • FINAL EXAM (1-4pm)

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


Professor Michael E. Mauel
Department of Applied Physics
Columbia University

Go to Prof. Mauel's HomePage