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Uspekhi Mat. Nauk, 2000, Volume 55, Issue 3(333), Pages 63–102 (Mi umn291)  

This article is cited in 3 scientific papers (total in 3 papers)

Exact global plasma equilibria

O. I. Bogoyavlenskiiab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Queen's University

Abstract: Exact global axisymmetric and helically symmetric plasma equilibria are derived. These two families of exact solutions of the plasma equilibrium equations are not translation-invariant, depend on arbitrarily many parameters, and contain special $z$-invariant equilibria. All plasma equilibria constructed are smooth and localized in the sense that they have finite magnetic energy in each layer $c_1<z<c_2$. Furthermore, these exact solutions provide counterexamples to Parker's well-known theorem.

DOI: https://doi.org/10.4213/rm291

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English version:
Russian Mathematical Surveys, 2000, 55:3, 463–500

Bibliographic databases:

UDC: 533.95+517.95
MSC: Primary 76X05, 35Q99; Secondary 82D10, 37C55, 76W05, 76E20
Received: 25.01.2000

Citation: O. I. Bogoyavlenskii, “Exact global plasma equilibria”, Uspekhi Mat. Nauk, 55:3(333) (2000), 63–102; Russian Math. Surveys, 55:3 (2000), 463–500

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Ilgisonis V.I., Pozdnyakov Yu.I., “Bifurcation of the equilibrium of a current-carrying plasma column”, Plasma Physics Reports, 30:12 (2004), 988–994  crossref  adsnasa  isi  elib  scopus  scopus
    2. A. S. Demidov, “Functional geometric method for solving free boundary problems for harmonic functions”, Russian Math. Surveys, 65:1 (2010), 1–94  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Golovin S.V., Sesma L.T., “Exact Solutions of Stationary Equations of Ideal Magnetohydrodynamics in the Natural Coordinate System”, J. Appl. Mech. Tech. Phys., 60:2 (2019), 234–247  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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