Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Description
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.
Course Prerequisites
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 casebycase basis.
Textbooks
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.
Problem Sets
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.
Exams
There will be a take home midterm and a take home final.
Grading
The final grade for the course will be based on the following:
ACTIVITIES  PERCENTAGES 

Homework  20% 
Midterm exam  40% 
Final exam  40% 
Calendar
LEC #  TOPICS  KEY DATES 

1  Derivation of the Boltzmann equation  
2 
The moment equations Derivation of ideal MHD equation 

3 
MHD equilibrium Validity of MHD 

4  Toroidal equilibrium and radial pressure balance  
5  The screw pinch and the GradShafranov equation  Homework 1 handed out 
6  The safety factor and the ohmic tokamak  
7  The first order GradShafranov 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 
14 
Formulation of the stability problem Real tokamaks (with Bob Granetz) 

15 
Variational techniques Alternate concepts (with Darren Sarmer) 

16  Variational principle  
17  Stability of simple function  Homework 4 handed out 
Midterm exam  
18  Lecture 18  
19  Lecture 19 
Homework 4 handed in Homework 5 handed out 
20  Lecture 20  
21  Lecture 21  Homework 5 handed in 
22  Lecture 22  
Final exam 