The DCON3D Code for the Ideal MHD Stability of Stepped-Pressure Stellarators

In a recent publication, [Phys. Plasmas 27, 042509 (2020); https://doi.org/10.1063/1.5143455], a procedure was presented to determine the ideal MHD stability of stepped-pressure stellarators by the generalized Newcomb method. The Euler-Lagrange equation (ELE) for making the energy functional $\delta W $stationary is derived as a high-order ordinary differential equation for the complex Fourier components \textbf{U} of the perturbed vector potential $\alpha $ and its derivatives. The related Hermitian Riccati matrix \textbf{P} $=$ \textbf{U}$_{\mathrm{22}}$ \textbf{U}$_{\mathrm{11}}^{\mathrm{-1\thinspace }}$is derived. The vanishing of the real scalar $D_{C} \quad =$ det \textbf{P}$^{\mathrm{-1}}$ is the condition for the existence of a fixed-boundary instability. This procedure has been implemented in a new Fortran 95 code DCON3D. Data are read from a SPEC stellarator equilibrium file. [Phys. Plasmas 19, 112502 (2012); \underline {https://doi.org/10.1063/1.4765691}] In each volume and each interface, components of the Euler-Lagrange coefficients are computed and the equation is numerically integrated. There are two departures from the paper: native SPEC coordinate (s,$\theta $,$\zeta )$ are used throughout rather than straight-fieldline coordinates; and the Riccati equation for \textbf{P}$^{\mathrm{-1}}$ rather than the ELE for \textbf{U} is integrated for improved numerical stability. Examples will be presented for an equilibrium with periodicity l $=$ 5, 8 volumes, and finite $\beta $, in which a Newcomb crossing is found in the second interface. The code runs in two minutes of cpu time on a MacBook Pro.