The DCON3D Code for Fast, Accurate Determination of the Ideal MHD Stability of a Stellarator

The DCON3D code is based on a generalization of the Newcomb crossing criterion for application to stellarators with nested flux surfaces, using equilibria computed by the DESC equilibrium code. The ideal MHD energy principle delta-W is expanded in a set of poloidal and toroidal Fourier harmonics (m,n) as a function of flux coordinate rho in (0,1). The Euler-Lagrange equation for minimizing delta-W is derived and found to have Hamiltonian symmetry. Integrating the solutions that are regular at the magnetic axis, the resulting solution matrix has symplectic symmetry. This is used to prove that a change of sign of a determinant of the solution matrix is the generalization of the Newcomb criterion for instability. Singular surfaces occur wherever m = nq for one or more harmonics, where q is the inverse rotational transform. Unlike in tokamaks, a singular surface can have multiple resonant harmonics. A generalized Mercier stability criterion has been derived, and a procedure for computing asymptotic series about that surface has been developed. A procedure is used to cross a singular surface, based on the criterion that dW < infinity. Large resonant solutions are removed on the left, non-resonant solutions are integrated across the surface, and new small resonant solutions are launched on the right, while maintaining the symplectic symmetry of the solution matrix. Examples will be presented for realistic stellarators. Cpu time for a typical case is of order 1 minute on a laptop computer.