Theory Weekly Highlights for April 2021

April 30, 2021

A chapter on “Magnetic-Confinement Fusion – Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability” was written by L.L. Lao, Y. Q. Liu, and A.D. Turnbull in an Encyclopedia devoted to Nuclear Fusion Research and Development. The chapter covers the MHD model, including derivation of the MHD equations, the physics principles of tokamak equilibrium and stability, and discussions of the ideal energy principle and of non-ideal effects. A detailed classification and description of the important ideal and non-ideal instabilities is also included. Also covered are sections on the plasma response to external perturbations and numerical tools to compute MHD instabilities, as well as a discussion of methods and techniques to mitigate and control plasma instabilities including disruptions. The chapter has been published by Elsevier and is available at

April 23, 2021

A collaboration between GA and MIT scientists has been awarded a Leadership Resource Allocation (LRAC) at NSF's Frontera, the world's most powerful academic supercomputer. The project will use GA's state-of-the-art kinetic and fluid turbulence codes, CGYRO and ALMA, to study negative triangularity tokamaks as an accelerated path to fusion. The study aims at predicting the core plasma performance in a negative triangularity tokamak with a compatible edge solution.

Several GA Theory scientists and collaborators gave presentations at the remote US-EU Transport Task Force Workshop this week, including Eric Bass, Tess Bernard, Chris Holland, Xiang Jian, Tom Neiser, Dmitri Orlov, Phil Snyder, and Gary Staebler.

April 16, 2021

A new integrated modeling workflow has been developed in OMFIT to predict fusion performance starting from zero dimensional parameters (Miller geometry, plasma current and magnetic field strength, and heating and current drive quantities). The workflow starts by making up plausible plasma profiles and consistently solving an MHD equilibrium (PRO-create module in OMFIT). The resulting provides an initial guess to Stability, Transport, Equilibrium, & Pedestal codes (STEP module in OMFIT see Highlight from February 12 2021 at that are iteratively coupled to find a self-consistent physics-based stationary solution. The 0-D STEP workflow has been executed on nearly 700 fusion experiments from seven different tokamaks (H98y2 database), finding a mean relative error of less than 20% between the experimental and simulated energy confinement time for cases with aspect ratio greater than 2.5. These results provide a solid foundation to identify attractive target designs for future reactor studies.

April 09, 2021

The resistive wall mode (RWM) stability is one of the critical transient issues in high-performance spherical tokamaks such as MAST-U. The n=1 RWM instability and the resonant field amplification (RFA) due to a stable RWM response are numerically investigated for a MAST high-pressure plasma scenario for the purpose of understanding the potential RWM behavior in MAST-U plasmas. Modeling finds that the unstable RWM for the target equilibrium is subject to strong damping by the plasma toroidal flow and/or the drift kinetic effects from thermal particles. As a result, the mode is found to be stable under the experimental flow conditions. Active magneto-hydrodynamic (MHD) spectroscopy modeling, using the magnetic coils designed for controlling the edge localized modes (ELMs) in MAST-U as the antenna, shows strong resonant field amplification due to a stable RWM response in the target plasma, in particular when the proper coil phasing is chosen for the ELM control coils. This study thus shows that the RWM may be stable in MAST-U but can be well detected by active MHD spectroscopy.

April 02, 2021

Fundamental mechanisms governing the prompt redeposition of tungsten impurities sputtered in tokamak divertors have been identified and analyzed to enable quantitative estimations and in-situ monitoring of the net erosion and lifetime of tungsten divertor plasma-facing components (PFCs). Using the Monte-Carlo code ERO, it was shown that tungsten prompt redeposition is mainly governed by the ratio of the characteristic ionization mean-free path of neutral tungsten to the width of the sheath, and a new scaling law for tungsten prompt redeposition in tokamak divertors was derived. This governing parameter is shown to have similar values for divertor plasma conditions in DIII-D experiments and plasma conditions expected in the far-SOL of the ITER divertor, indicating investigations of tungsten erosion in smaller devices like DIII-D are relevant for future fusion reactors like ITER. Furthermore, this governing parameter scales linearly with the magnetic field strength, such that the net erosion of tungsten in the divertor region might significantly increase in fusion devices operating at high magnetic field. It is also shown that in-situ monitoring of the prompt redeposition of tungsten impurities in divertors requires the measurement of photon emissions associated with the ionization of tungsten impurities in charge states Z>2+, typically W3+, W4+ and W5+ for divertor plasma conditions expected in the far-SOL of the ITER divertor and in the DIII-D divertor. These results have been reported in J Guterl et al., “On the prediction and monitoring of tungsten prompt redeposition in tokamak divertors”, Nuclear Materials and Energy 27 (2021) 100948, and orally presented by J. Guterl at the Joint IAEA-FZJ Technical Meeting on Collisional-Radiative Properties of W and Hydrogen in Edge Plasma of Fusion Devices, (March 29-April 1 2021

These highlights are reports of research work in progress and are accordingly subject to change or modification