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The three-dimensional Variational Moments Equilibrium Code (VMEC) minimizes the energy functional | The three-dimensional Variational Moments Equilibrium Code (VMEC) minimizes the energy functional | ||
:<math>W = \int_{\ | :<math>W = \int_{\Omega_p}{ \left ( \frac{1}{2 \mu_0} B^2 + p \right ) dV}</math> | ||
over the toroidal domain & | over the toroidal domain Ω<sub>p</sub>. The solution is obtained in | ||
flux | [[Flux coordinates|flux coordinates]] | ||
(''s'', ''θ'', ''ζ''), related to the cylindrical | (''s'', ''θ'', ''ζ''), related to the [[Toroidal coordinates|cylindrical coordinates]] | ||
(''R'', ''φ'', ''Z'') by | (''R'', ''φ'', ''Z'') by | ||
:<math>R = \sum{R_{mn} \cos( m\theta - n\zeta)}</math> | :<math>R = \sum{R_{mn}(s) \cos( m\theta - n\zeta)}</math> | ||
:<math>Z = \sum{Z_{mn} \sin( m\theta - n\zeta)}</math> | :<math>Z = \sum{Z_{mn}(s) \sin( m\theta - n\zeta)}</math> | ||
The code assumes nested flux surfaces. | The code assumes nested flux surfaces. | ||
<ref>[ | <ref>S.P. Hirschman et al, ''Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria'', [[doi:10.1063/1.864116|Phys. Fluids '''26''' (1983) 3553]]</ref> | ||
<ref>S.P. Hirschman et al, ''Three-dimensional free boundary calculations using a spectral Green's function method'', [[doi:10.1016/0010-4655(86)90058-5|Computer Physics Communications '''43''', 1 (1986) 143-155]]</ref> | |||
== | == Uses of the code == | ||
The code is being used at: | Due to its speed in computing the MHD equilibrium problem in 3-D it has become the "de facto" standard code for calculating 3-D equilibria. This means that practically all the laboratories | ||
* IPP | with stellerator devices routinely use it. It has also been used to model tokamak equilibria and lately (2010) it has been applied to reverse field pinches, in particular helical equilibria (non-axisymmetric) in the RFX-Mod. | ||
* [[Laboratorio Nacional de Fusión|LNF]], Spain | <ref>D. Terranova et al., ''Self-Organized Helical Equilibria in the RFX-Mod Reversed Field Pinch'', [[doi:10.1002/ctpp.200900010|Contributions to Plasma Physics '''50''' (2010) 775–779]]</ref> | ||
The code is being used at fusion laboratories all over the world: | |||
* ORNL, Oak Ridge, TN, USA ([http://www.ornl.gov/sci/fed/Theory/stci/code_library.html code origin]) | |||
* PPPL, Princeton, NJ, USA | |||
* IPP, at Garching and Greifswald, Germany | |||
* CRPP, Lausanne, Switzerland | |||
* NIFS, Toki, Japan | |||
* RFX, Padova. Italy | |||
* [http://www.hsx.wisc.edu/ HSX], Madison, WI, USA | |||
* [[Laboratorio Nacional de Fusión|LNF]], Madrid, Spain | |||
== Enhancements / extensions of the code == | == Enhancements / extensions of the code == | ||
* DIAGNO, <ref>H.J. Gardner, ''Modelling the behaviour of the magnetic field diagnostic coils on the W VII-AS stellarator using a three-dimensional equilibrium code'', [[doi:10.1088/0029-5515/30/8/002|Nucl. Fusion '''30''' (1990) 1417]]</ref> to calculate the response of magnetic diagnostics | |||
* DIAGNO | * MFBE <ref>E. Strumberger, ''Finite-β magnetic field line tracing for Helias configurations'', [[doi:10.1088/0029-5515/37/1/I03|Nucl. Fusion '''37''' (1997) 19]]</ref> | ||
* STELLOPT <ref>D.A. Spong et al., ''Physics issues of compact drift optimized stellarators'', [[doi:10.1088/0029-5515/41/6/305|Nucl. Fusion '''41''' (2001) 711]]</ref> | |||
* STELLOPT <ref> | |||
== See also == | |||
* [https://princetonuniversity.github.io/STELLOPT/ VMECwiki] | |||
== References == | == References == | ||
<references /> | <references /> | ||
[[Category:Software]] | |||