Magnetohydrodynamics

Class Time

Tuesdays & Thursdays 2:00 - 4:00 pm, Wednesday 4:15-5:30 pm (X-hour)

Classroom

Cummings 200

Instructor

William Lotko

Grade Basis

Weekly homework (55%); Midterm Exam (20%); Final Exam (25%)

Textbook

Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas
J. P. Hans Goedbloed and Stefaan Poedts, Cambridge University Press, 2004

Preliminary

Week 1

Plasma Physics and Magnetohydrodynamics

Motivation: The MHD description

Review: Essential plasma physics

1,2, Notes

MHD model: Postulates, derivation of two-fluid/one-fluid MHD from kinetic theory; scale independence

3

Week 2

MHD Conservation Properties

Magnetic flux tubes; flux conservation; conservative form of MHD equations; conservation laws  

4.1 - 4.3

Dissipative MHD; jump conditions; MHD discontinuities

4.4 - 4.6

Week 3

MHD Waves and Characteristics

MHD waves; phase velocity, group velocity; dispersion diagrams

5.1 - 5.2

Friedrichs diagrams; characteristics

5.3 - 5.4

Week 4

MHD Equilibria 

MHD equilibria; magnetohydrostatics; Grad-Shafranov equation

Notes

Cylindrical plasmas

9

Week 5

Spectral Theory

Stability concepts; force operator formalism; initial value problem

6.1 - 6.3

Quadratic forms; variational principles; energy principle; extension to interface plasmas

6.4 - 6.6

Week 6

Waves and Instabilities in Inhomogeneous Plasmas

Gravitating magnetofluids; interchange and Rayleigh-Taylor instability

7

Kelvin-Helmholtz instability; rotational instability

Notes

Week 7

Channel Flows and Boundary Layers

Channel flows; boundary layers

Notes

MHD generators and propulsion

Notes

Week 8

Resistive Plasmas

Force-free magnetic fields; resistive equilibria

Notes

Magnetic reconnection; tearing instability

Notes

Week 9

Transonic Flows and Shocks

Stellar and planetary outflows

 Notes

Transonic equilibria

Notes

Week 10

Resonant Absorption

Alfvén continuum, phase mixing; resonant absorption

10,11