具有第一积分的无散度场的整体对称性的存在性

IF 0.5 4区 数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-03-06 DOI:10.1063/5.0152213
D. Perrella, Nathan Duignan, David Pfefferl'e
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引用次数: 0

摘要

从等离子体物理和磁约束聚变的角度出发,探讨了对称场与无散度矢量场第一积分之间的三维关系。已知一个诺ether型定理:对于每一个这样的对称,都有对应的第一个积分。在何种程度上,反过来是正确的调查。在这样做的过程中,我们发现了这个诺ether型定理的一个重新表述,它的逆命题在所谓的环面区域中成立。所提出的方法的一些结果是在高普遍性下快速证明磁场的通量坐标的存在性,而不需要像在磁流体静力学或准对称的情况下那样假设对称性。
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Existence of global symmetries of divergence-free fields with first integrals
The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type theorem is known: for each such symmetry, there corresponds a first integral. The extent to which the converse is true is investigated. In doing so, a reformulation of this Noether-type theorem is found for which the converse holds on what is called the toroidal region. Some consequences of the methods presented are quick proofs of the existence of flux coordinates for magnetic fields in high generality, without needing to assume a symmetry such as in the cases of magneto-hydrostatics or quasi-symmetry.
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来源期刊
CiteScore
0.70
自引率
20.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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