MHD equilibrium: Difference between revisions

Revision as of 10:15, 14 August 2009

The ideal Magneto-HydroDynamic (MHD) equilibrium of a near-Maxwellian magnetically confined plasma is obtained by solving the force balance equation

\vec{\nabla} p = \vec{j} \times \vec{B}

where

μ_{0} \vec{j} = \vec{\nabla} \times \vec{B}

is the plasma current, subject to appropriate boundary conditions. The word "ideal" refers to the absence of resistivity.

In two dimensions (assuming axisymmetry), the force balance equation reduces to the Grad-Shafranov equation.

A large number of codes is available to evaluate MHD equilibria.

@@ Line 3: / Line 3: @@
 :<math>\vec \nabla p = \vec j \times \vec B</math>
-subject to appropriate boundary conditions.
+where
+:<math>\mu_0 \vec j = \vec \nabla \times \vec B</math>
+is the plasma current, subject to appropriate boundary conditions.
 The word "ideal" refers to the absence of resistivity.