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MHD Theory of Fusion Systems >> Content Detail



Syllabus



Syllabus

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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 case-by-case 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.

Amazon logo Goedbloed, Hans, and Stefaan Poedts. Principles of Magnetohydrodynamics. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521626071.

Amazon logo 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:


ACTIVITIESPERCENTAGES
Homework20%
Midterm exam40%
Final exam40%



Calendar



LEC #TOPICSKEY DATES
1Derivation of the Boltzmann equation
2

The moment equations

Derivation of ideal MHD equation

3

MHD equilibrium

Validity of MHD

4Toroidal equilibrium and radial pressure balance
5The screw pinch and the Grad-Shafranov equationHomework 1 handed out
6The safety factor and the ohmic tokamak
7The first order Grad-Shafranov equationHomework 2 handed out
8Effect of a vertical field on tokamak equilibriumHomework 1 handed in
9The high beta tokamak
10The high beta tokamak (cont.) and the high flux conserving tokamak

Homework 2 handed in

Homework 3 handed out

11Flux conserving tokamak (cont.)
12PF design I - the plasma
13PF design II - the coil solverHomework 3 handed in
14

Formulation of the stability problem

Real tokamaks (with Bob Granetz)

15

Variational techniques

Alternate concepts (with Darren Sarmer)

16Variational principle
17Stability of simple functionHomework 4 handed out
Midterm exam
18Lecture 18
19Lecture 19

Homework 4 handed in

Homework 5 handed out

20Lecture 20
21Lecture 21Homework 5 handed in
22Lecture 22
Final exam

 








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