2003 I 3
From QED
We have:
The equilibrium equation is:
The first term is:
Simplifying:
Then:
Plugging in:
Since the system is axisymmetric:
So that p is only a function of ψ. Then:
Giving:
Since :
So that F is a function of ψ.
If we taylor expand ψ:
The first order terms are just the magnetic field on axis (, ). If the flux surfaces are up-down symmetric, then the terms odd in z must be zero. This gives:
So that the flux surfaces will be circular around the axis if .
The curvature of the field lines is just:
This term describes the interaction of the pressure gradient and field line curvature. In cylindrical geometry, it will be:
This term will contribute to instability if is negative, since δW will be negative.
This page was recovered in October 2009 from the Plasmagicians page on Generals_2003_I_3 dated 00:53, 7 May 2007.