View source for VMEC

The three-dimensional Variational Moments Equilibrium Code (VMEC) minimizes the energy functional

:<math>W = \int_{\omega_p}{ \left ( \frac{1}{2 \mu_0} B^2 + p \right ) dV}</math>

over the toroidal domain &omega;<sub>p</sub>. The solution is obtained in 
[[Flux coordinates|flux coordinates]] 
(''s'', ''&theta;'', ''&zeta;''), related to the [[Toroidal coordinates|cylindrical coordinates]] 
(''R'', ''&phi;'', ''Z'') by

:<math>R = \sum{R_{mn}(s) \cos( m\theta - n\zeta)}</math> 

:<math>Z = \sum{Z_{mn}(s) \sin( m\theta - n\zeta)}</math> 

The code assumes nested flux surfaces.
<ref>[http://dx.doi.org/10.1063/1.864116 S.P. Hirschmann et al, ''Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria'',  Phys. Fluids '''26''' (1983) 3553]</ref>
<ref>[http://dx.doi.org/10.1016/0010-4655(86)90058-5 S.P. Hirschmann et al, ''Three-dimensional free boundary calculations using a spectral Green's function method'', Computer Physics Communications '''43''', 1 (1986) 143-155]</ref>

== Implementations of the code ==

The code is being used at:
* ORNL, Oak Ridge, TN, USA ([http://www.ornl.gov/sci/fed/Theory/stci/code_library.html code origin])
* PPPL, Princeton, NJ, USA
* IPP, Garching, Germany
* CRPP, Lausanne, Switzerland
* NIFS, Japan
* [[Laboratorio Nacional de Fusión|LNF]], Spain

== Enhancements / extensions of the code ==

* DIAGNO, <ref>H.J. Gardner, Nucl. Fusion '''30''' (1990) 1417</ref> to calculate the response of magnetic diagnostics
* MFBE <ref>[http://dx.doi.org/10.1088/0029-5515/37/1/I03 E. Strumberger, ''Finite-&beta; magnetic field line tracing for Helias configurations'', Nucl. Fusion '''37''' (1997) 19]</ref>
* STELLOPT <ref>[http://dx.doi.org/10.1088/0029-5515/41/6/305 D.A. Spong et al., ''Physics issues of compact drift optimized stellarators'', Nucl. Fusion '''41''' (2001) 711]</ref>

== References ==
<references />