TY - JOUR

T1 - Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

AU - Sengupta, Wrick

AU - Paul, Elizabeth J.

AU - Weitzner, Harold

AU - Bhattacharjee, Amitava

N1 - Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.

PY - 2021

Y1 - 2021

N2 - While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805-2821; 2822-2834; Plunk & Helander, J. Plasma Phys., vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function such the field strength satisfies. Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

AB - While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805-2821; 2822-2834; Plunk & Helander, J. Plasma Phys., vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function such the field strength satisfies. Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

KW - fusion plasma

KW - plasma confinement

KW - plasma devices

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U2 - 10.1017/S0022377821000039

DO - 10.1017/S0022377821000039

M3 - Article

AN - SCOPUS:85102365489

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

M1 - 905870205

ER -