PHYSICS 726
MAGNETOHYDRODYNAMICS
HOMEWORK ASSIGNMENT 8
Due Dec. 6, 2007
Brief answers are solicited.
1. What is the expression for conservation of momentum if there is a source of mass in the system?
2. What is meant by the term closure in: A) the MHD equations; and, B) turbulence?
3. What is the principal characteristic of the stress tensor? Why?
4. What are the equations of ideal MHD? What is the principal characteristic of ideal MHD? How is this modified in resistive MHD?
5. What are the principal assumptions of reduced MHD?
6. What is similarity scaling?
7. State the Virial Theorem. What are its implications?
8. Define field line curvature. How does it enter MHD equilibrium? How is it related to a gravitational force?
9. What are the equations for force free fields?
10. What is the Grad-Shafranov equation? What are its principal assumptions?
11. Define the fluid displacement. What is a restoring force? Under what conditions is a displacement stable? Unstable?
12. What stable oscillations are supported in ideal MHD?
13. What are the boundary conditions to be applied to ideal MHD?
14. What is the Energy Principle? Why is it important?
15. What is the Extended Energy Principle?
16. What is the Kruskal-Shafranov condition? Why is it important?
17. What is the Rayleigh-Ritz procedure? Why is it important?
18. What is a rational, or singular, surface? What is its physical significance?
19. What is magnetic reconnection? What are the principal assumptions in analyzing magnetic reconnection?
20. What is the constant- approximation?
21. What is Sweet-Parker scaling? What is tearing mode scaling?
22. Briefly, what is the method of matched asymptotic expansions? How is it applied to resistive instabilities?
23. What is Kolmogorov scaling?
24. What is Taylor’s hypothesis? Why might it be valid? What are its consequences?
25. What is a dynamo? What is the -effect? What is the -effect?