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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Osherovich, Vladimir Fainberg, Joseph and Webb, Alla 2013. Observational Evidence for a Double-Helix Structure in CMEs and Magnetic Clouds. Solar Physics, Vol. 284, Issue. 1, p. 261.

    Osherovich, Vladimir A. Fainberg, J. and Stone, R. G. 1999. Multi-tube model for interplanetary magnetic clouds. Geophysical Research Letters, Vol. 26, Issue. 3, p. 401.

    Woolley, M L 1990. On the mathematical structure of the equations of magnetohydrodynamic equilibrium. Journal of Physics A: Mathematical and General, Vol. 23, Issue. 12, p. 2379.

    Woolley, M. L. 1976. Three dimensional equilibria in the magnetohydrodynamic approximation. Journal of Plasma Physics, Vol. 15, Issue. 03, p. 423.


On the analytic solution of the helical equilibrium equation in the MHD approximation

  • M. L. Woolley (a1)
  • DOI:
  • Published online: 01 March 2009

The second-order elliptic partial differential equation, which describes a class of static ideally conducting magnetohydrodynamic equilibria with helical symmetry, is solved analytically. When the equilibrium is contained within an infinitely long conducting cylinder, the appropriate Dirichiet boundary-value problem may be solved in general in terms of hypergeometric functions. For a countably infinite set of particular cases, these functions are polynomials in the radial co-ordinate; and a solution may be obtained in a closed form. Necessary conditions are given for the existence of the equilibrium, which is described by the simplest of these functions. It is found that the Dirichlet boundary-value problem is not well-posed for these equiilbria; and additional information (equivalent to locating a stationary value of the hydrodynamic pressure) must be provided, in order that the solution be unique.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
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