MHD equilibrium: Difference between revisions
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:<math>\vec \nabla p = \vec j \times \vec B</math> | :<math>\vec \nabla p = \vec j \times \vec B</math> | ||
where | where ''B'' is the magnetic field (divergence-free) and | ||
:<math>\mu_0 \vec j = \vec \nabla \times \vec B</math> | :<math>\mu_0 \vec j = \vec \nabla \times \vec B</math> | ||
is the plasma current, subject to appropriate boundary conditions. | is the plasma current, subject to appropriate boundary conditions. | ||
The word "static" refers to the assumption of zero flow, while | The word "static" refers to the assumption of zero flow, while "ideal" refers to the absence of resistivity. | ||
Here, the pressure ''p'' is assumed to be isotropic, but a generalization | Here, the pressure ''p'' is assumed to be isotropic, but a generalization | ||
for non-isotropic pressure is possible. | for non-isotropic pressure is possible. | ||
Revision as of 08:19, 19 August 2009
The static, ideal Magneto-HydroDynamic (MHD) equilibrium of a near-Maxwellian magnetically confined plasma is obtained by solving the force balance equation
where B is the magnetic field (divergence-free) and
is the plasma current, subject to appropriate boundary conditions. The word "static" refers to the assumption of zero flow, while "ideal" refers to the absence of resistivity. Here, the pressure p is assumed to be isotropic, but a generalization for non-isotropic pressure is possible. [1]
In two dimensions (assuming axisymmetry), the force balance equation reduces to the Grad-Shafranov equation.
In three dimensions, the existence of flux surfaces (nested or not) is not guaranteed. [2]
A large number of codes is available to evaluate MHD equilibria.
2-D codes
3-D codes
- VMEC (nested flux surfaces)
- NEAR (nested flux surfaces)
- IPEC (nested flux surfaces)
- HINT (islands)
- PIES (islands)
- SIESTA (islands, fixed boundary)
- BETA (finite difference)
References
- ↑ R.D. Hazeltine, J.D. Meiss, Plasma Confinement, Courier Dover Publications (2003) ISBN 0486432424
- ↑ H. Grad, Toroidal Containment of a Plasma, Phys. Fluids 10 (1967) 137