## 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 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.

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 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 |

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 |