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Decay of MHD waves by phase mixing

I. The sheet-pinch in plane geometry

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Zeitschrift für Physik A Hadrons and nuclei

Abstract

It is well known, [1–6], that the linearized equations of motion of ideal MHD possess a continuous spectrum which leads to damping of propagating waves through phase mixing. We show how this arises by examining the dispersion relation for plasmas with non-uniform profiles and comparing the results with those of a sharp boundary model. In this paper the special case of the non-uniform sheet-pinch is examined in order to present the mathematical details as clearly as possible. It is shown that as a result of the non-uniformity the frequency of the waves is a complex quantity having a real and imaginary part. The corresponding eigenfunctions and their mathematical pathology are discussed.

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Author notes

  1. J. Tataronis

    Present address: Courant Institute of Mathematical Sciences, New York University, New York, N.Y., USA

Authors and Affiliations

  1. Max-Planck-Institut für Plasmaphysik, Euratom Association, Garching bei München, Deutschland

    J. Tataronis & W. Grossmann

Authors
  1. J. Tataronis
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  2. W. Grossmann
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Additional information

This work was performed as part of the joint research program between the Institut für Plasmaphysik, Garching, and Euratom.

The authors would like to thank the following colleagues for constructive discussions during the course of the investigation; Profs. H. Grad, H. Weitzner, D. Pfirsch, Drs. E. Rebhahn, H. Derfler, and H. Tasso.

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Tataronis, J., Grossmann, W. Decay of MHD waves by phase mixing. Z. Physik 261, 203–216 (1973). https://doi.org/10.1007/BF01391913

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  • DOI: https://doi.org/10.1007/BF01391913

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