Magnetohydrodynamic (MHD) equilibria in toroidally-confined plasmas are computed with various levels of approximation. In the simplest case, a geometrical symmetry of the plasma (such as toroidal symmetry in a tokamak) reduces the problem to a single equation (the Grad-Shafranov equation) for the 2-D magnetic flux function which nevertheless requires numerical solution. In 3-D geometry (rippled tokamaks, stellarators), the assumption of toroidally-nested magnetic flux surfaces is sufficient to

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... llow efficient numerical solution methods based on coordinate inverse methods [1]. However, the presence of magnetic islands can often lower the energy of 3-D configurations and can not be described using inverse methods. The SIESTA code described here builds upon the works of Chodura and Schlüter [2] and Harafuji [3] to develop an iterative method for minimizing the total (magnetic and plasma) energy in 3D plasmas: The ideal MHD equations are used to obtain finite constrained independent variations of the magnetic field (B) and pressure (p), corresponding to discrete versions of Faraday's Law and particle conservation, combined with ideal Ohm's Law ( 0 B v E ) and adiabaticity (2) The perturbed MHD displacement =v t is treated as an independent 3D variational parameter and can be used to find a stationary (local) minimum energy state corresponding to the ideal MHD force balance: where B J 0 is the plasma current.