Computation of multi-region relaxed magnetohydrodynamic equilibria

We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.The authors gratefully acknowledge support of the U.S. Department of Energy and the Australian Research Council, through Grants DP0452728, FT0991899, and DP110102881

Predictive simulations of NBI ion power load to the ICRH antenna in Wendelstein 7-X

In Wendelstein 7-X (W7-X), a new ion cyclotron resonance heating (ICRH) antenna will be commissioned during the operational campaign OP2.1. The antenna will have to sustain power loads not only from thermal plasma and radiation but also fast ions. Predictive simulations of fast-ion power loads to the antenna components are therefore important to establish safe operational limits. In this work, the fast-ion power loads from the W7-X neutral beam injection (NBI) system to the ICRH antenna was simulated using the ASCOT suite of codes. Five reference magnetic configurations and five antenna positions were considered to provide an overview of power load behavior under various operating conditions. The NBI power load was found to have an exponential dependence on the antenna insertion depth. Differences between magnetic configurations were significant, with the antenna limiter power load varying between 380 W and 100 kW depending on the configuration. Qualitative differences in power load patterns between configurations were also observed, with the low mirror and low iota configurations exhibiting higher loads to the sensitive antenna straps. The local fast-ion power flux to the antenna limiter was also considered and found to exceed the 2.0 MW m−2 steady-state safety limit only in specific cases. The NBI system might thus pose a safety concern to the ICRH antenna during concurrent NBI-ICRH operation, but additional heat propagation simulations of antenna components are needed to establish more realistic operational time limits

Fast forward modeling of neutral beam injection and halo formation including full Balmer-α emission prediction at W7-X

A full collisional-radiative (CR) neutral beam injection model based on Gaussian pencil (Gausscil) beams and a diffusive CR neutral halo model are presented. The halo is a neutral cloud around the neutral beam forming due to multiple charge exchange (CX) reactions. Both models do not rely on Monte-Carlo techniques and are thereby orders of magnitude faster than commonly used models. To model the neutral halo a system of coupled diffusion equations is solved numerically, enforcing mixed boundary conditions. From the equilibrium hydrogen neutral densities in the second excited energy state (n = 3), the Balmer-α emission intensity is calculated and the full spectrum is predicted, including effects as Doppler shifts and broadening due to the complex neutral beam geometry and the motional Stark effect (MSE) from the magnetic field. All forward models are implemented in the Minerva [1] Bayesian analysis framework to enable detailed multivariant inference from Balmer-α spectroscopy data. The modeled neutral beam and halo densities are successfully verified against calculations with a validated Monte-Carlo code for the W7-X beam and plasma geometry, especially proving the validity of the halo diffusion ansatz. A comparison of the predicted emission spectra with the experimental data proves the accuracy of the implemented model. All important parameters defining the neutral beams are inferred and compared to available reference values