next up previous
Next: Property of Up: Magnetohydrostatic Equilibria Previous: Potential Fields

Force-Free Fields

As in Section 3.3, we assume that $L \ll \Lambda $ and $\beta \ll 1$ and we again have the force-free field equation (3.8). If the magnetic field is not potential then the general solution is that the current must be parallel to the magnetic field. Thus,
\mu {\bf j} = \alpha {\bf B}, \qquad \Rightarrow \nabla \times {\bf B} = \alpha {\bf B},
\end{displaymath} (3.17)

for some scalar function $\alpha $ which may be a function of position and time.


Prof. Alan Hood