PHYS 626 -- Fundamentals of Plasma Physics --
Fall 2009
I. Course Description
The UAF Catalog listing for PHYS 626:
"Single charge particle motion in the electromagnetic fields, plasma
kinetic theory, Vlasov equations for collisionless plasmas,
magnetohydrodynamic equations, linear plasma waves and instabilities,
nonlinear plasma waves and instabilities."
In terms of the content of the textbook
(which you must have and bring
to classes), we will cover most topics from Chapter 1 to 6, 8, and
10 (i.e., we are skipping Chapters 7, 9, and 11). We will
also not cover everything in these chapters, due to the fact that we
only have
a limited
amount of time, not because other topics are not important. At the end
of this syllabus, there is a tentative schedule which lists topics we
plan to
cover in more details. This is subject to change. So you should
check frequently the online version of this page:
http://www.gi.alaska.edu/~chungsangng/phys626/phys626.html.
II. Course Goals
The main goal of this course is to
introduce you to the fundamental concepts, phenomena, and theories of
plasmas, at the beginning graduate level. Applications and examples
will be mainly on aspects of space physics, with occasional reference
to laboratory plasmas, such as in thermal nuclear fusion devices.
Emphasis will be on the theoretical aspects of the subject. However,
relevant experimental or observational data will also be pointed out so
as to compare with theories.
III. Student Learning Outcomes
- Know how to solve assigned problems in the covered
Chapters of the textbook.
- Be able to solve problems at the difficulty level of recent PhD
plasma physics comprehensive exam questions.
- Obtain good understandings on useful concepts, as well as
theoretical and mathematical tools related to plasma physics that can
help students to conduct their own graduate research
IV. Textbook, Reading Assignments, and References
You must have a copy of the textbook:
Introduction
to
Plasma
Physics, by D. A. Gurnett and A. Bhattacharjee,
Cambridge, 2005 (ISBN 0 521 36730 1 paperback). It is very important
that you read the Section(s) covered by each lecture and try to follow
derivations
before you come to that lecture. Please
refer to the schedule below (subject to change) for such reading
assignments. You should bring your textbook to the lectures.
There are many other excellent plasma textbooks and references. I
understand you may not have time to do more further reading. It is also
not essential for getting a good grade in this course. However, if you
have time and want to learn more for your own good, you may look up
lists of references and "Further reading" for titles of more reading
materials. You should be able to obtain most of them through the
library (may need to recall or use the Interlibrary Loan).
You will find it extremely useful to
have some mathematical references,
handbooks, or tables. There are many options available from the
Internet,
but you should be cautious about the accuracy of information obtained
there.
One recommendation is
Abramowitz
and
Stegun:
Handbook of Mathematical Functions, which can be
downloaded freely. Another one is the
NRL
Plasma Formulary, which you can order a free
copy or download it online.
V. Lectures
The class is for 3 credits, and so 3
hours per week are devoted to
lectures. Based on the reading schedule listed below, you should have
read (and try to derive) the material in the text before coming to each
day's lecture.
You are also expected to contribute to discussion in class about
physical concepts and mathematical derivations. I will not have time to
read through all the text and work out all derivations, but will only
highlight
those points that are important or difficult. You must cover the rest
of the text and ask for help if you encounter difficulties. I reserve
the right to assign homework or exam questions over materials listed in
Reading Assignments, even if it was not covered explicitly in lecture.
Note: some
lecture notes will be available for download via the course home page (
http://www.gi.alaska.edu/~chungsangng/phys626/phys626.html)
by
clicking
at the dates of the lectures in the schedule. These notes
are
not to replace
the lectures
themselves or the textbook.
VI. Attendance and participation
Since this is a small class, there is no need to keep a formal
attendance record. However, participation is counted towards 5% of the
final grade. Again, due to the tedious nature of keeping track of
participation and that I will recognize everyone in this small class,
no formal record will be kept for participation. The final
participation grade will be given based on my general impression of
your participation level. You are encouraged to check with me during
the course to see if your participation level is acceptable.
Participation is based on attendance, asking questions, and
contributing to discussion in class, as well as coming to my office
hour to ask questions and to discuss physics. Of course, you can
impress me the most by pointing out errors I made in derivations, or
helping me out when I get stuck.
VII. Homework
Doing homework is most important
factor in doing well
in this class. There will be approximately one homework set assigned
per week,
usually on Fridays, and is usually due in the following Friday before
class. However, you should
work on your homework as early as possible before a deadline so that
you
can have time to ask for help if you encounter difficulties in solving
these
problems. Late homework will not be accepted.
To emphasize the importance of doing
homework, homework
grade
will count towards 60% of the total grade of the course, excluding the
assignment
with the lowest grade.
Most homework questions will be
assigned from those
questions in the textbook. Some questions may be selected from other
sources, as well as past comprehensive exams. Your submission of any
homework problem
cannot simply be a one-line statement of the answer. You need to show
steps of how you used the method leading to that answer. I will grade
the
homework based on the method used, as well as the answer. Therefore,
you should submit your partially finished work. This will help you
getting partial credit, and let me identify your difficulties. If some
homework problems are found to be too difficult, adjustment to the
homework grades will be made. Also,
your work should be clean and clear enough for me to understand.
While it is good for you to have
discussion with classmates or search
the Internet for additional information, your submitted homework should
be of your own, but not a direct copy from another source. Keep in mind
that you will be required to do similar questions on your own during
exams. In addition, it is against the UAF Honor Code to misrepresent
work which is not your own. Plagiarism on homework or on an exam will
result in a failing grade.
Solutions to the homework problems
will be emailed to you after the due
date. Therefore, late homework will not be accepted. The homework
assignments will be given in class, and on the course website (click on
links within the Schedule).
VIII. Examinations
There will be one one-hour in-class
midterm exam on Friday November 6th,
and a two-hour final exam on Wednesday December 16th from 8 to 10 AM.
Both are closed book exams. Calculators, computers, and
communication devices are also not allowed. However, special
or unusual formula
or integrals essential to a particular question will be written
down for that question. Midterm exam counts towards 10% of the total
grade. The final exam counts towards 25%
of the total grade. You must not miss the midterm exam
and the
Final Exam (except for documented illness or family emergency
).
Some questions in the exams will be
similar to those you have seen in homework. This is to make sure that
you don't just copy homework answers without truly understanding
how to answer on your own. Thus, it is
important to review homework sets and solutions before the exams. Exam
questions will be graded based on the method used, as well as the
answer. Therefore, you should write down explicitly and clearly step by
step how you come up with your answers. This
will help you getting partial credit.
IX. Grading
The final grade will be composed of:
Participation
|
5 %
|
|
Midterm exam
|
10 % |
Mandatory |
| Final exam: |
25 % |
Mandatory |
Homework
|
60 % |
Homework set with lowest grade dropped
|
| Total: |
100 % |
|
The course will be graded approximately on the following
scale:
>
85 %
|
A
|
80 %
-- 85 %
|
A-
|
75 % -- 80 %
|
B+
|
70 % -- 75 %
|
B
|
65 % -- 70 %
|
B-
|
60 % -- 65 %
|
C+
|
55 % -- 60 %
|
C
|
50 % -- 55 %
|
C-
|
45 % -- 50 %
|
D+
|
40 % -- 45 %
|
D
|
35 % -- 40 %
|
D-
|
< 35 %
|
F
|
Note that the passing grade for graduate students is B.
Therefore, in order to pass this course, you should get almost full
scores in homework and participation and to get enough points in exams.
X. Getting Help
My office hours are 10:20 AM - 11:20
AM
on Monday, Wednesday, and Friday. I will be at Reichardt 108 during
these
office hours. Canceled office hours will be announced in class or by
email. If you need to see me outside these office hours, please set up
a time by appointment to come to my office at Elvey 706E. These are
hours set aside
especially to help you - do not feel like you are imposing or cheating
by coming in. If you have problems that need immediate attention,
please send me an e-mail or give me a call at my office phone number.
I have set up a home page for the
course:
http://www.gi.alaska.edu/~chungsangng/phys626/phys626.html.
I
may
put additional materials that may be helpful to you later on. So,
please
come back often, especially to check any changes in the schedule. The
UAF Blackboard site for this course will be made available to students,
but will not be used to provide communication about this course.
XI. Disabilities Services
The Physics Department will work with
the Office of Disabilities
Services (203 WHIT, 474-5655) to provide reasonable accommodation to
students with disabilities.
XII. Tentative Schedule
Below is a tentative schedule (subject to change):
Day
|
Text (Reading
Assignment)
|
Topics
|
Homework due
(coverage)
|
9/4 F
|
1 - 2.3
|
Course Introduction; Debye length; Plasma
frequency
|
|
9/9 W
|
2.4 - 2.8
|
Cyclotron frequency;...;
Representative plasma parameters
|
|
9/11 F
|
3.1 - 3.2
|
Single particle motions; E x B drift
|
|
9/14 M
|
3.3 - 3.4
|
Gradient and curvature drifts; Motion in a
magnetic mirror field
|
|
9/16 W
|
3.5 - 3.6
|
Motion in a time varying magnetic field;
Adiabatic invariants
|
|
9/18 F
|
4.1 |
Fourier representation of waves
|
HW1 due
|
9/21 M
|
4.2
|
General form of the dispersion relation |
|
9/23 W
|
4.3
|
Waves in a cold uniform unmagnetized plasma
|
|
9/25 F
|
4.4 - 4.4.1
|
Waves in a cold uniform
magnetized plasma; Parallel propagation
|
HW2 due
|
9/28 M
|
4.4.1.1 - 4.4.1.3
|
Whistlers, Ion cyclotron
whistlers; Faraday rotation
|
|
9/30 W
|
4.4.2 - 4.4.3
|
Perpendicular propagation;
Hybrid resonances; Oblique propagation
|
|
10/2 F
|
4.4.4
|
CMA diagram
|
HW3 due
|
10/5 M
|
5.1 - 5.2
|
The distribution function; The
Boltzmann and Vlasov equations
|
|
10/7 W
|
5.3 - 5.4.2
|
Solutions based on constants of
the motion; The moment equations
|
|
10/9 F
|
5.4.3 - 5.4.4
|
Energy equation; The closure
problem
|
HW4 due
|
10/12
M
|
5.5
|
Electron and ion pressure waves
|
|
10/14
W
|
5.6 - 5.7
|
Collisional drag force;
Ambipolar diffusion
|
|
10/16
F
|
6.1
|
The basic equations of MHD
|
HW5 due
|
10/19
M
|
6.2 - 6.3 |
Magnetic pressure; Magnetic
field convection and diffusion |
|
10/21
W
|
6.4 - 6.5
|
The energy equation;
Magnetohydrodynamic waves |
|
10/23
F
|
6.6 - 6.6.3 |
MHD stability; Force-free
equilibria |
HW6 due
|
10/26
M
|
6.6.4
|
Force balanced equilibria |
|
10/28
W
|
6.7 - 6.7.2 |
MHD stability; Interchange
instabilities |
|
10/30
F
|
6.7.3 - 6.7.5 |
The linear force operator; The
normal mode method; Energy principle |
HW7 due
|
11/2 M
|
|
review
|
|
11/4 W
|
|
review
|
|
11/6
F
|
|
Midterm exam (in class)
|
|
11/9 M
|
6.7.6 - 6.7.7
|
A more useful form for dW; The Rayleigh-Taylor instability |
|
11/11
W
|
6.8
|
Magnetic reconnection |
|
11/13
F
|
8.1 - 8.1.1 |
Electrostatic waves in a hot
unmagnetized plasma; The Vlasov approach |
HW8 due
|
11/16
M
|
8.1.2
|
Cold beam instabilities |
|
11/18
W
|
8.2 - 8.2.1
|
The Landau approach; Laplace
transforms |
|
11/20
F
|
8.2.2
|
Dispersion relation for a plasma
of hot electrons and immobile ions
|
HW9 due
|
11/23
M
|
8.2.3 - 8.2.5
|
Cauchy velocity distribution
function; Physics of Landau Damping
|
|
11/25 W
|
8.3
|
The plasma dispersion function
|
|
11/30 M
|
8.4
|
The dispersion relation for a
multi-component plasma
|
HW10 due
|
12/2 W
|
8.5 - 8.5.3
|
Stability; Gardner's theorem;
Nyquist criterion; Penrose condition
|
|
12/4 F
|
8.5.4
|
Some kinetic instabilities
|
|
12/7 M
|
10.1
|
Non-linear effects; Quasi-linear
theory
|
|
12/9 W
|
10.1.2
|
Bump-on-tail instability
|
|
12/11 F
|
10.2
|
Stationary non-linear
electrostatic potentials
|
|
12/14 M
|
|
Summary, review |
|
12/16 W
|
|
Final (8 AM to 10 AM)
|
|