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Magnetic Islands

< PlasmaWiki(Link to this page as [[PlasmaWiki/Magnetic Islands]])

(2007 P1 Q3),(2006 P1 Q1)

Regions of closed field lines.

From (2006 P1 Q1):

If $B=\nabla \psi \times \hat{z} + B_z \hat{z}$ then $B \cdot \nabla \psi = 0$ , so B lines lie on the surfaces of constant $ψ$

This gives the vector potential $A = (0, x B z,ψ)$

Given $ψ = ψ 0'' x 2 / 2 - ψ 1 c o s (k y)$ , the equipotnetial contours will be given by $ψ = c o n s t = K$

Solving for x,
$x = \pm \sqrt{2/\psi_0''}\sqrt{K+\psi_1 cos(ky)}$

The contour $K = ψ 1$ forms the separatrix with X points at $x = 0, y = (2 n + 1)π / k$ and O points at $x = 0, y = 2 n π / k$