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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

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

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 $\eta$ such the field strength satisfies $B = B(\eta )$ . 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.

Physics↗
DOE OSTI2023

Response to “Comment on ‘Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field’” [Phys. Plasmas 30 , 104701 (2023)]

Dr. Brizard's comment on my work is based on a conceived procedure that does not come from my work. The defense of his claim that the modification of the so-called standard Lie's transform theory is unnecessary is also unsupported. This response reveals in detail the inconsistency issues in the so-called standard Lie's transform theory by analyzing both its results and root causes. The problem in the so-called standard Lie's transform theory is beyond the issue to take into account the ordering difference between the guiding center motion and gyromotion. Here, the inconsistent commutation of derivative and limit causes another issue. In addition, the so-called standard Lie's transform formulation leads to an unnecessarily lengthy and tedious derivation process for a one or two page task under the singular (or renormalized) formalism described in my paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗