Abstract Details
Abstracts
Author: Nikita Nikulsin
Requested Type: Poster
Submitted: 2023-03-31 12:59:57
Co-authors: W. Sengupta, A. Bhattacharjee
Contact Info:
Princeton University/PPPL
100 Stellarator Rd
Princeton, NJ 08540
US
Abstract Text:
Various forms of the high aspect ratio expansion have been used to aid in analytical and numerical computation ever since the 1960s. Freidberg applied this expansion to the ideal MHD equilibrium to study stellarators [1]. We show that under the assumption of volumetric quasisymmetry satisfied up to the order of the inverse aspect ratio, the equations of Freidberg can be reduced to a Grad-Shafranov equation. This is a special case of the quasisymmetric Grad-Shafranov equation derived by Burby et al [2], but in this case there are no additional constraints that must be imposed. However, the assumptions made by Freidberg turn out to be so restrictive that only quasiaxisymmetric stellarators close to axisymmetry can be modelled. We compare analytical solutions in this regime to numerical results from VMEC. We also consider an s-alpha model for stellarators which can be constructed from the present equilibrium model. Finally, we discuss generalizations of the model that could admit quasihelical solutions, such as the near vacuum expansion, which is obtained by taking the steady state limit of Strauss's reduced MHD equations [3]. The end goal is to obtain a model complementary to the near axis expansion, which would allow one to take into account the effects of finite shear.
[1] J. P. Freidberg, Ideal MHD (Cambridge University Press, 2014)
[2] J. Burby, N. Kallinikos, R. MacKay, J Math Phys 61, 093503 (2020)
[3] H. Strauss, J Plasma Phys 57, 83 (1997)
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