ECG 734 Plasma II – Plasma Kinetic Theory
CATALOG DATA
Plasma parameters; Elementary statistics and the random walk problem; Method of Lagrange
multipliers; Maxwell-Boltzmann distribution law; Klimontovich equation;Plasma kinetic
equation; Liouville equation; BBGKY Hierarchy; Lenard-Balescu equation; Bogoliubov’s
hypothesis; Fokker-Planck equation; Krook model; Collisionless and Collisional Plasmas; Vlasov
equation; Landau damping.
PREREQUISITE
Prerequisites: EE 330 or consent of instructor.
TEXTBOOK(s)
1. J.A. Bittencourt, Fundamentals of Plasma Physics 3rd ed., Springer Verlag, New York,
2004. (Employs a kinetic approach with intermediate details) ISBN 0-387-20975-1
2. Dwight Nicholson, Introduction to Plasma Theory, Krieger Publishing, Malabar, Florida,
1983. (recommended for its statistical mechanics approach to plasmas) ISBN 0-894-64677-X
References:
1. S. Chandrasekhar, Plasma Physics, The University of Chicago Press, Chicago, 1960.
2. Dwight Nicholson, Introduction to Plasma Theory, Krieger Publishing, Malabar, Florida,
1983.
3. D.C. Montgomery and D.A. Tidman, Plasma Kinetic Theory, McGraw Hill, 1964.
4. Kenro Miyamoto, Plasma Physics for Nuclear Fusion, MIT Press, Cambridge, 1976.
5. S.R. Seshadri, Fundamentals of Plasma Physics, Elsevier, New York, 1973.
6. Juda Leon Shohet, The Plasma State, Academic Press, New York, 1971.
7. F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, vol. 1, 2 ed. Plenum
Press, 1984.
8. Paul M Bellan, Fundamentals of Plasma Physics, Cambridge University Press, 2006.
COORDINATOR (pls. list all faculty who have/would instruct this course)
Professor Robert A. Schill, Jr.
PREREQUISITE BY TOPIC
1. Engineering Electromagnetics I
TOPICS*
 Plasma Parameters
 Debye shielding
 Plasma frequency and cyclotron frequency
 Binary collisions
 Ensemble averaging, mean free path
 Coulomb binary collision and collision frequency
 Collective behavior and criteria for plasma
 Rutherford scattering cross-section
 Mind map of different kinetic theory approaches
 Elementary Statistics and the Random Walk Problem
 Binomial probability distribution
 Mean values
 Gaussian distribution function density
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 Probability of several variables
Method of Lagrange Multipliers
Nomenclature – Classical Systems
 State of system
 Generalized coordinates and velocities (momentums)
 Degrees of freedom
 Holonomic and Nonholonomic systems
 Phase space
 Various types of ensembles
 Principle of detailed balance
Formal Development of the Maxwell-Boltzmann Distribution Law
Plasma Kinetic Theory I
 Derivation of the Klimontovich equation
 Plasma kinetic equation
Plasma Kinetic Theory II
 Derivation of the Liouville equation
 BBGKY Hierarchy.
Plasma Kinetic Theory III
 Derivation of the Lenard-Balescu equation
 Bogoliubov’s hypothesis
 Fokker-Planck equation
 Krook model
Collisionless and Collisional Plasmas
 Derivation of the Vlasov equation
 Linear and nonlinear Landau damping
 BGK modes
 Case-Van Kampen modes
 Alternative intuitive derivation of the Fokker-Planck equation (Trubnikov’s technique)
COURSE OUTCOMES
Upon completion of the course, students will be able to:
 Conceptually and analytically apply the kinetic theory to a plasma system
 Apply statistical mechanics to analyze the probability that an event will occur
COMPUTER USAGE
MATLAB minimal.
GRADING
Homework assignments; One midterm; One final exam.
COURSE PREPARER AND DATE OF PREPARATION
Robert A. Schill, Jr., Last update date November 14, 2012