By Karl Schindler
Publisher: Cambridge University Press
Print Publication Year: 2006
Online Publication Date:January 2010
Online ISBN:9780511618321
Hardback ISBN:9780521858977
Paperback ISBN:9780521142366
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511618321.008
Subjects: Plasma Physics and Fusion Physics, Astrophysics
Image View Extract Fullview: Text View | Enlarge Image ‹ Previous Chapter ›Next Chapter
Earlier in this part we have encountered several different forms of equations describing steady states. The simplest case is magnetohydrostatics, physically richer versions include an anisotropic pressure tensor, directed flow or gravity.
In this chapter we consider a generalized formulation for a class of steady states that includes such generalizations. The method reduces the original fluid equations to two field equations, which can be understood as generalizations of the MHS equations (5.21) and (5.22).
In the first part the effect of an external gravity force is ignored; however, it will be incorporated in the second part. In all cases we assume that the magnetic field possesses Euler potentials. Again, it should be kept in mind that in space physics environments Euler potentials have considerable applicability (Section 5.1.2).
Remarkably, it turns out that in each of the cases that we consider the steady state problem can be reduced to solving the field equations for the Euler potentials. The form of these equations is uniquely determined by a single scalar function, which also serves as a Lagrangian generating the field equations.
However, it should be kept in mind that this is not a general theory of steady states. Besides the existence of Euler potentials this procedure excludes bulk flow perpendicular to the magnetic field. Is is only for a particular symmetric configuration that we show how a perpendicular flow component can be included (Section 7.3.2).
pp. i-vi
pp. vii-x
pp. xi-xiv
pp. 1-4
Part I - Setting the scene: Read PDF
pp. 5-6
2 - Sites of activity: Read PDF
pp. 7-24
pp. 25-54
Part II - Quiescence: Read PDF
pp. 55-56
pp. 57-60
5 - Magnetohydrostatic states: Read PDF
pp. 61-106
6 - Particle picture of steady states: Read PDF
pp. 107-122
7 - A unified theory of steady states: Read PDF
pp. 123-132
8 - Quasi-static evolution and the formation of thin current sheets: Read PDF
pp. 133-180
pp. 181-184
9 - Nonideal effects: Read PDF
pp. 185-202
10 - Selected macroinstabilities: Read PDF
pp. 203-268
11 - Magnetic reconnection: Read PDF
pp. 269-342
12 - Aspects of bifurcation and nonlinear dynamics: Read PDF
pp. 343-366
Part IV - Applications: Read PDF
pp. 367-370
13 - Magnetospheric activity: Read PDF
pp. 371-406
14 - Models of solar activity: Read PDF
pp. 407-432
pp. 433-440
Appendix 1 - Unified theory: details and derivations: Read PDF
pp. 441-450
Appendix 2 - Variational principle for collisionless plasmas: Read PDF
pp. 451-464
Appendix 3 - Symbols and fundamental constants: Read PDF
pp. 465-468
pp. 469-502
pp. 503-508