Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.
In order to register for 22.615, you should have previously completed 22.611J/8.613J/6.651J, with a grade of C or higher. Exceptions to this policy will require the permission of the instructor, and will be granted on a case-by-case basis.
Freidberg, J. P. Ideal Magnetohydrodynamics. This is out of print but Xerox copies will be available to registered students shortly after the start of classes.
Goedbloed, Hans, and Stefaan Poedts. Principles of Magnetohydrodynamics. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521626071.
Wesson, John. Tokamaks. 3rd ed. Oxford, UK: Oxford University Press, 1987. ISBN: 9780198563280.
The weekly problem sets are an essential part of the course. Working through these problems is crucial to understanding the material.
Problem sets will generally be assigned at Tuesday’s lecture and will be due at start of class on the following Thursday.
There will be a take home midterm and a take home final.
The final grade for the course will be based on the following:
|LEC #||TOPICS||KEY DATES|
|1||Derivation of the Boltzmann equation|
The moment equations
Derivation of ideal MHD equation
Validity of MHD
|4||Toroidal equilibrium and radial pressure balance|
|5||The screw pinch and the Grad-Shafranov equation||Homework 1 handed out|
|6||The safety factor and the ohmic tokamak|
|7||The first order Grad-Shafranov equation||Homework 2 handed out|
|8||Effect of a vertical field on tokamak equilibrium||Homework 1 handed in|
|9||The high beta tokamak|
|10||The high beta tokamak (cont.) and the high flux conserving tokamak||
Homework 2 handed in
Homework 3 handed out
|11||Flux conserving tokamak (cont.)|
|12||PF design I - the plasma|
|13||PF design II - the coil solver||Homework 3 handed in|
Formulation of the stability problem
Real tokamaks (with Bob Granetz)
Alternate concepts (with Darren Sarmer)
|17||Stability of simple function||Homework 4 handed out|
Homework 4 handed in
Homework 5 handed out
|21||Lecture 21||Homework 5 handed in|