Physics 520
Plasma Physics
Spring
Term, 2006
Professors:
Joan Marler and Matt Stoneking
Catalog course description:
Plasma physics is the
study of hot, ionized gases. A plasma, being a collection of charged particles
interacting with each other over long distances via electric and magnetic
forces, exhibits a wide array of complex behavior including waves and
instabilities. Plasmas occur abundantly in space and in the earth's ionosphere.
One of the applications of plasma physics is the production of electric power
from nuclear fusion. Topics covered in this course include motion of charged
particles in electric and magnetic fields, plasma kinetic theory, fluid models,
waves and instabilities, wave-particle interactions (Landau damping), plasma
confinement and transport.
Text: Introduction
to Plasma Physics with Space and Laboratory Applications, by Donald A.
Gurnett and Amitava Bhattacharjee,
Office hours:
Prof. Marler: TBA
Prof. Stoneking: TBA
Appointments can be made to meet with
instructors at other times.
Grading policy:
Grades will be
assigned based on the following elements, weighted as indicated:
Midterm
Exam: 25%
Final
Exam: 30%
Problem sets: 25%
Problem Presentations
/ Article Discussions: 20 %
Exams:
The midterm exam will be a take home
exam. The final exam will be cumulative
and will take place during the regularly scheduled final exam time (Tuesday, 11
December,
Problem sets:
Problem sets will be assigned almost
every week (probably ~8 total), and will usually be due in class on Thursday of
each week. Students are encouraged to
collaborate on problem solutions, but each student must submit his own write-up
of solutions and each student must participate in the solution of each problem.
Problem Presentations:
Each student
will have at least two opportunities to present problem solutions in class
(usually on a Tuesday). Students who are
scheduled to present a problem should meet with an instructor on the previous
day to rehearse the presentation.
Article Discussions:
Plasma physics
is an active area of research. There
will be weekly discussions (usually on Thursdays) of recent plasma physics
articles that deal with experimental or observational results. Students are expected to read the assigned
articles and participate in discussion.
Schedule:
The following is a tentative schedule of
topics to be covered in this course.
There will be occasional digressions to review and introduce background
material necessary to understand plasma physics that may necessitate revision
of this schedule.
Introduction
The
introduction to plasma physics includes a review of necessary background
material and an overview of the rest of the course. As a prototypical example
of the collective behavior of plasma particles, we will derive the
characteristic distance over which localized electrostatic potentials are
screened out by neighboring charges (Debye shielding), and the characteristic
oscillation frequency for a plasma (the plasma frequency).
Week ONE
Day
1: Tuesday 28 March
Introduction
to plasmas, brief history of plasma physics, landscape of plasma models, distribution
functions, the Boltzmann distribution, the Maxwellian velocity distribution, the
thermal velocity, the Debye shielding length, and the plasma frequency.
Unit
I: Single-Particle Motion
During
this unit we will derive particle trajectories in a) uniform magnetic fields,
b) uniform electric and magnetic fields, c) curved/non-uniform magnetic fields,
and d) time-varying electric and magnetic fields. Single particle trajectories
(or drifts) represent a microscopic description of plasma behavior with
specified fields. To accurately describe the influence of many neighboring
particles on each other, however, requires the reduced fluid or statistical
models that comprise the bulk of this course.
Day
2: Thursday 30 March
Gyro-motion
of charged particle in magnetic field, the ExB drift, the general FxB
drift/gravitational drift, grad-B drift, and curvature drift.
Week TWO
Day
3: Tuesday 4 April
The
mirror force, magnetic moment conservation (adiabatic invariants), and magnetic
mirrors.
Unit
II: Cold Plasma Waves
The
character of plasma waves depends on the frequency of the wave relative to a
set of characteristic frequencies and on the direction of propagation with
respect to the magnetic field.
Particular wave characteristics can be obtained by taking limits of a
unified solution of the wave equation that treats the plasma as an anisotropic
dielectric medium.
Day
4: Thursday 6 April
General
wave characteristics, Fourier analysis of waves, phase velocity, group
velocity, sound waves, electromagnetic waves in dielectric materials, waves in
a cold unmagnetized plasma.
Week THREE
Monday
10 April: Physics Colloquium
Heating the Solar Corona: A hot topic in
plasma astrophysics
Christopher Watts,
Day
5: Tuesday 11 April
The
cold plasma dispersion relation in a uniform, magnetized plasma. High frequency waves propagating parallel to B (O-mode, X-mode, wave polarization,
upper hybrid resonance, left and right cutoffs). High frequency waves propagating parallel to B (R-mode, L-mode, whistlers, electron
cyclotron resonance).
Day
6: Thursday 13 April
Plasma
interferometry, Faraday rotation. Low
frequency waves. Alfven waves, analogy
to mass-loaded string, lower hybrid frequency.
Unit
III: Kinetic Theory and the Fluid Equations
Kinetic
theory is a statistical description that describes the evolution of the phase
space (velocity and real space) distribution of plasma particles. The fluid equations are obtained by taking
moments of the equations governing the phase space distribution.
Week FOUR
Day
7: Tuesday 18 April
Distribution
functions, moments of the distribution function, the Boltzmann equation and the
Vlasov equation.
Day
8: Thursday 20 April
Derivation of the fluid equations, the
Bohm-Gross dispersion relation, ion acoustic waves.
Unit
IV: Magnetohydrodynamics
Magnetohydrodynamic
theory provides a simple plasma description that unites the two fluid equations
into a single conducting fluid model.
Week FIVE
Day
9: Tuesday 25 April
The
MHD model, magnetic pressure.
Day
10: Thursday 27 April
Alfven
waves revisited, MHD equilibrium.
Takehome
MIDTERM EXAM handed out
Week SIX
Day
11: Tuesday 2 May
MHD
stability, magnetic reconnection.
Thursday
4 May MIDTERM READING PERIOD no class
Unit
V: Electrostatic Waves and Landau Damping
To
understand some plasma behavior it is necessary to use a more complete
description than is provided by the fluid models. Kinetic theory is a
statistical description that describes the evolution of the velocity and real space
distribution of plasma particles. Such a description is necessary to understand
the interaction of plasma particles with waves in the plasma (Landau damping
and two-stream instability for example).
Week SEVEN
Day
12: Tuesday 9 May
The
Vlasov solution for warm plasma waves and the Landau approach.
Day
13: Thursday 11 May
The
plasma dispersion function.
Unit
VI: Collisional Processes
Plasma
particles experience both long range (many body) forces due to bulk currents
and charge accumulations and short range (two body) forces. The short range
encounters (collisions) influence the rate at which particle density gradients
are smoothed out (diffusion) and determine the electrical resistivity of the
plasma. We will discuss an appropriate plasma description that can include
these effects.
Week EIGHT
Day
14: Tuesday 16 May
Coulomb
collisions and multiple small-angle collisions
Day
15: Thursday 18 May
Spitzer
resistivity, collisional time scales, diffusion, and plasma transport
Unit
VII: Non-neutral Plasmas
Week NINE
Day
16: Tuesday 23 May
Penning-Malmberg
traps and the physics of electron plasmas
Day
17: Tuesday 25 May
Positron
plasmas and atomic physics
Unit VIII: Nuclear Fusion
One
of the most interesting and important applications of plasma physics is the
potential generation of electric power from nuclear fusion reactions. This unit provides a very brief introduction
to this important topic.
Day
18: Tuesday 30 May
Lawson
criterion and progress to date on development of a nuclear fusion reactor.
Day
19: Thursday 1 June
Plasma
heating. Plasma diagnostics. Overview of experimental fusion plasma
physics.
Final Exam: Tuesday, 6
June,