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Unified theory of damping of linear surface Alfvén waves in inhomogeneous incompressible plasmas

  • M. S. Ruderman (a1) and M. Goossens (a1)

The viscous damping of surface Alfvén waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ2Re, where Δ is the relative variation of the local Alfvén velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ ≪ 1), and to Reynolds numbers that are sufficiently large that the waves are only slightly damped during one wave period. The dispersion relation is obtained and first investigated analytically for the limiting cases of very small (Rg ≪ 1) and very large (Rg ≫ 1) values of Rg, For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but nonmonotonic variation of the damping rate with respect to Rg.

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G. Einaudi & J. Mok 1987 Alfvén wave dissipation in the solar atmosphere. Astrophys. J. 319, 520530.

M. Goossens , M. S. Ruderman & J. V. Hollweg 1995 Dissipative MHD solutions for resonant Alfvén waves in 1-dimensional magnetic flux tubes. Solar Phys. 157, 75102.

M. S. Ruderman & M. Goossens 1993 Nonlinearity effect on resonant absorption of surface Alfvén waves in incompressible plasmas. Solar Phys. 143, 6988.

C. Uberoi 1972 Alfvén waves in inhomogeneous magnetic fields. Phys. Fluids 15, 16731675.

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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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