Abstract Details
Abstracts
Author: Nikita Nikulsin
Requested Type: Consider for Invited
Submitted: 2024-03-29 16:25:27
Co-authors: W. Sengupta, R. Jorge, A. Bhattacharjee
Contact Info:
Princeton University
112 Nassau St.
Princeton, NJ 08542
United States
Abstract Text:
The MHD equilibrium and stability for high beta quasisymmetric (QS) stellarators is of great interest for designs of stellarator experiments and fusion power plants. Attempts to solve the 3D MHD equilibrium problems have not led to tractable forms of the Grad-Shafranov equation (GSE), which are well-known to be elliptic in axisymmetric geometry. We present an asymptotic high-beta model for QS devices where beta is ordered as a small parameter epsilon, the ratio of the field due to plasma current to the coil field (arXiv:2403.08022). The first-order correction, which involves both coil and plasma current fields, is governed by a GSE and the requirement that flux surfaces exist. Further, we show that the first-order near-axis expansion (NAE) is a subset of our model. In an earlier paper (arXiv:2312.08572), we have also considered the special case of this model near axisymmetry and ballooning mode stability of its solutions.
Our analytic derivation of a high-beta GSE shows a way to incorporate fast equilibrium solvers in stellarator optimization codes. This is an improvement over the popular NAE models, which cannot account for magnetic shear easily. The NAE equations are overdetermined at all orders beyond the first, and shear appears in the third order and so depends on third-order quantities. While, in some cases, setting the third-order quantities to zero and evaluating the shear from just lower-order quantities gives a good estimate, in others this approach gives large errors. In contrast, our global model can incorporate shear by asymptotic expansion in epsilon rather than through a Taylor expansion like the NAE, which is accurate near the axis but inaccurate globally. Our model also allows more general pressure and current profiles than the NAE. We present analytical and numerical solutions outside the scope of the NAE, demonstrating our model's usefulness for QS stellarators. A further extension allows us to model compact devices.
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