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Exact Solution of the Direct and Inverse Quasi-stationary Dynamo Problem in the Expanding Plasma Ball

  • Yurii V. Dumin
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Abstract

It is shown that differential equation of the quasi-stationary dynamo effect (i.e., generation of the electric fields and currents) in a uniformly-expanding plasma ball with strongly anisotropic conductivity possesses the unique mathematical property: namely, the spectrum of its eigenvalues is universal and independent of physical parameters of the medium. As a result, it becomes possible to introduce a special set of eigenfunctions - which we called the generalized spherical functions - that can be used to solve the dynamo problem in exactly the same way as ordinary spherical functions are used to solve the Laplace equation. The corresponding exact solutions should be especially valuable for treating the inverse dynamo problem, i.e., determination of the plasma parameters from the experimentally measured electric fields and currents.

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Cite

BibTeXRIS
BibTeX
@misc{dumin2026exact,
  title = {{Exact Solution of the Direct and Inverse Quasi-stationary Dynamo Problem in the Expanding Plasma Ball}},
  author = {Yurii V. Dumin},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.12194},
  eprint = {2607.12194},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12194},
}
RIS
TY  - UNPB
TI  - Exact Solution of the Direct and Inverse Quasi-stationary Dynamo Problem in the Expanding Plasma Ball
AU  - Yurii V. Dumin
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2607.12194
UR  - https://arxiv.org/abs/2607.12194
AB  - It is shown that differential equation of the quasi-stationary dynamo effect (i.e., generation of the electric fields and currents) in a uniformly-expanding plasma ball with strongly anisotropic conductivity possesses the unique mathematical property: namely, the spectrum of its eigenvalues is universal and independent of physical parameters of the medium. As a result, it becomes possible to introduce a special set of eigenfunctions - which we called the generalized spherical functions - that can be used to solve the dynamo problem in exactly the same way as ordinary spherical functions are used to solve the Laplace equation. The corresponding exact solutions should be especially valuable for treating the inverse dynamo problem, i.e., determination of the plasma parameters from the experimentally measured electric fields and currents.
ER  -