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Explosive instabilities of reaction-diffusion equations including pinch effects

H. Wilhelmsson

  • Institute for Electromagnetic Field Theory and Centre for Fusion Science, Chalmers University of Technology, S-412 96 Göteborg, Sweden
  • Laboratoire de Physique des Milieux Ionisés, Ecole Polytechnique, F-91128 Palaiseau, France
  • Laboratoire de Physique Théorique et Mathématique, Université Paris VII, Tour centrale, 3 étage, 2 place Jussieu, Paris CEDEX 05, France

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Phys. Rev. E 47, 753 – Published 1 January, 1993

DOI: https://doi.org/10.1103/PhysRevE.47.753

Abstract

Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch, and source processes, certain ‘‘bell-shaped’’ distributions may grow explosively in time while preserving the shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or, more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma.

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References (18)

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Outline

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Phys. Rev. E 47, 753– Published 1 January, 1993
  • Received 2 July 1992

© 1993 American Physical Society

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