MHD equilibrium

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

$\overrightarrow{\mathrm{\nabla }}p=\overrightarrow{j}\times \overrightarrow{B}$

where

${\mu }_0\overrightarrow{j}=\overrightarrow{\mathrm{\nabla }}\times \overrightarrow{B}$

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.

2-D codes

• EFIT
• FBT
• HBT

3-D codes

• VMEC (nested flux surfaces)
• IPEC (nested flux surfaces)
• HINT
• PIES
• SIESTA (islands, fixed boundary)
• BETA