Exact Solution of the Direct and Inverse Dynamo Problem in the Expanding Plasma Ball
arXiv:2607.12194
The paper derives exact analytical solutions for both the forward and inverse dynamo problems in a uniformly expanding plasma ball with anisotropic conductivity, using a universal eigenvalue spectrum and generalized spherical functions.
Abstract
It was found that the differential equation of 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.
LaTeX2e, revtex4-1 documentclass, 6 pages, 3 PDF figures; v2: text extended, 1 figure added