Plasma Physics
Course Outline and Arrangements
Lecturer:
Prof. Sergey Lebedev –
Course:
Level 3
Website:
“Plasma Physics (2015-16)” on Blackboard Learn
Lectures:
26 in LT2
–
Revision Lecture –
Office hours:
1
1–2pm Tuesdays,
743 Blackett, x 47748, s.lebedev@imperial.ac.uk
11 weeks (12/01/16 – 23/03/16)
Summer Term, weeks 1–2, date & time TBD
1–2pm Fridays
(by appointment outside term)
Introduction and Aims
We live in a largely neutral world in which plasmas are seemingly rare. By contrast,
the majority of visible material in the universe exists at sufficiently high temperatures or
rarefied densities to be at least partially ionized, and is therefore plasma. Importantly,
plasmas behave differently to other states of matter and exhibit, so called, “collective
effects”. The physics of plasmas is important to a wide range of phenomena; the
evolution of stars & galaxies, the interaction of the solar wind with the Earth’s
magnetic field, industrial processes such as computer chip fabrication and the generation
of intense sources of electromagnetic radiation and energetic particles. Plasma
physics is also central to attempts to achieve controlled thermonuclear fusion as a future
energy source.
The aims of the course are to help you . . .
• Understand the broad range of physical phenomena which determine the behaviour
of plasmas & the importance of collective effects.
– Develop a qualitative understanding (ability to explain concepts, know terminology).
– Learn about theoretical models (often have to be simplified).
• Start learning how to think like a plasma physicist.
– Develop intuition for plasma behaviour; Pin-point key physics in a particular system.
– Get your head around conditions spanning over 20 orders of magnitude!
• Learn problem solving skills for plasma physics.
– Linearization of PDEs; Simplification of theoretical models to allow tractable, quantitative solution.
– Enhance your analytical abilities and physics problem-solving in general.
• Understand the principles and challenges involved in energy generation by
thermonuclear fusion.
• Understand the role of plasma in a range of naturally occurring phenomena &
laboratory applications.
Spring Term 2015–16
1
Plasma Physics
Course Outline & Arrangements
2 Outline Syllabus
∗
1. Basic properties of plasmas
[4 Lectures]
- Definition, occurrence & importance of plasmas, Debye shielding
- Quasi-neutrality, plasma parameter, plasma frequency, Larmor orbits (basics)
- Non-ideal plasmas
2. Thermonuclear fusion
- Nuclear reactions & cross sections, ignition & break-even
- Overviews; magnetic confinement fusion (MCF) & tokamaks,
inertial confinement fusion (ICF)
[3 Lectures]
3. Single particle motion
- Guiding centre drifts; E × B, curvature, gradient
- Magnetic moment (μ), conservation of μ, magnetic mirrors
[5 Lectures]
4. Collisions
[3 Lectures]
- Coulomb collisions; mean-free-path and collision time (single & cumulative collisions)
- Resistivity, particle diffusion, bremsstrahlung
5. Magnetohydrodynamics (MHD)
[4 Lectures]
- MHD equations; mass continuity, momentum, energy, Ohm’s law
- The convective derivative, MHD validity & assumptions
- B-field dynamics; flux freezing, resistive diffusion, magnetic Reynolds number
- Magnetic pressure & tension
6. Waves
- Electromagnetic, Langmuir, MHD (Alfvén, magnetosonic)
[2 Lectures]
7. Magnetic confinement
- MHD equilibria; flux surfaces, Z-pinches
- MHD instabilities & the safety factor, energy confinement in tokamaks
- Tokamak requirements – summary
[3 Lectures]
8. Kinetic theory
[2 Lectures]
- Vlasov & Boltzmann equations, obtaining fluid/MHD equations from Boltzmann
- Langmuir waves, resonant particles & trapping, Landau damping
- Laser-Plasma particle accelerators
*
All numbers of lectures are approximate.
Learning Outcomes – will be made available on the course website, close to the start
of the course. This will detail what you are expected to know and be able to do for each
of the syllabus items above.
S. Lebedev
Spring Term 2015–16
2
Plasma Physics
Course Outline & Arrangements
3 Arrangements
Lecture Notes & Handouts
Comprehensive lecture notes will be supplied for the course. During lectures
powerpoint presentations will be used to carefully go over the main concepts and key
derivations, plus sometimes provide material to complement that in the handed-out
notes (e.g. alternative calculations and examples). Copies of powerpoint
presentations will be made available before corresponding lectures. Lecture
notes, presentations and other handouts will be posted on the course website. Material
in presentations and handouts may appear in exams unless otherwise indicated.
Problem Sheets
5 or 6 problem sheets will be released over the duration of the course. The solutions
will be made available about 1 week later. Not graded, but it goes without saying that
attempting them is essential preparation for the exam. Some questions will help you
consolidate material seen in lectures. Others will supplement the lecture material by, e.g.,
guiding you through alternative derivations of important phenomena or further exploring
aspects of concepts seen in lectures.
Trip to see JET & MAST
Trip to the ‘Culham Centre for Fusion Energy’ near Oxford, to see the largest Magnetic
Confinement Fusion project in the World (Joint European Torus) and the UK’s MegaAmpère Spherical Tokamak. Places limited to ∼30.
Date: Wednesday afternoon, exact date to be confirmed
Exam
Worth 100% of the course mark.
Date: TBD (likely very end of May 2016)
Format: 2 hours duration; Section A (worth 40%) → compulsory, Section B (worth
60%) → answer 2 from 4 questions.
Units
The course will use SI with the exception of temperatures which are often expressed in
“eV”, really a measure of energy. An electron accelerated through a potential difference
of 1 Volt gains 1 eV of kinetic energy.
Energy of a particle (Joules) = kB T (T in K) = e T (T in eV)
where kB is the Boltzmann constant and e = 1.602 × 10 -19 C. So, given a temperature in
eV, you plug e T in place of kB T in the relevant SI equation. Note: 1 eV = kB /e Kelvin
= 11604 Kelvin.
Also some “cgs” units are still used in older texts:
B-fields in “Gauss” (1 Gauss = 10­4 Tesla),
Number densities n in per cm3 (n in per cm3 = 10­6 n in per m3).
S. Lebedev
Spring Term 2015–16
3
Plasma Physics
Course Outline & Arrangements
Text Books
You don’t need to buy a plasma physics text book. All the material required for the
exam will be covered in lectures, handouts or problem sheets. However, below is a list of
introductory texts that cover the ‘bread and butter’ fundamental concepts (e.g. waves,
particle drifts, MHD, collisions, ...). They provide an alternative view of the course
material, which is valuable, and often go into more depth than the lectures.
“Introduction to Plasma Physics and Controlled Fusion, Volume 1: Plasma Physics” ,
F. F. Chen, 2nd Ed. (Springer, 1984)
- Excellent introductory text. Very accessible with good explanations. Covers
most of the course.
“The Physics of Plasmas”, Boyd & Sanderson, (Cambridge University Press, 2003)
- Available as eBook via library. Quite advanced & formal treatment with much
more material than in this course.
“Plasma Physics: An Introductory Course”, R.O. Dendy
(Ed.), (Cambridge University Press, 1993)
- From the “Culham Summer School”. Good, if concise treatment of sections 3,
5, 8. Lots of interesting material on MCF and some ICF.
“Introduction to Plasma Physics”, Goldston & Rutherford (IoP Press, 1995)
Specialist books –The fields of MCF and especially ICF & laser-plasma interactions/applications
are rapidly evolving. The more applied material on these areas in the above books is likely to be
outdated. The lectures will be up to date. The web links below & the books are for further
reading;
“Tokamaks”, J. Wesson, (Oxford University Press, 2004)
“The Physics of Inertial Confinement Fusion: beam plasma interaction, hydrodynamics,
hot dense matter”, S. Atzeni, (Oxford University Press, 2004)
- The definitive text books on MCF (via tokamaks) & ICF, respectively!
Advanced; intended as a resource for researchers. However the basic concepts
are covered at suitable level for this course.
Links
http://wwwppd.nrl.navy.mil/nrlformulary
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
http://www.plasmacoalition.org
http://www3.imperial.ac.uk/plasmaphysics
http://www.ccfe.ac.uk
http://www.jet.efda.org
(PDF plasma physics formula book)
(physics encyclopedia)
(useful PDF resources)
(IC - Plasma Physics Group)
(MCF - ‘Culham’ website)
http://ippex.pppl.gov
http://fusedweb.pppl.gov
(ICF - National Ignition Facility)
https://lasers.llnl.gov/
http://www.plasmas.org
Check out the course website for more links.
S. Lebedev
Spring Term 2015–16
4