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On the boundary conditions at an insulating wall for hydromagnetic waves in a cylindrical plasma

Published online by Cambridge University Press:  28 March 2006

L. C. Woods
Affiliation:
Engineering Laboratory, Oxford University

Abstract

The order of the dispersion relation for the propagation of hydromagnetic waves along a magnetized cylindrical plasma falls by unity when the plasma resistivity, σ−1, tends to zero. A consequence of this is that the two boundary conditions necessary on an insulating wall are reduced to a single condition, a reduction brought about by the development of a current sheet. If the ratio, $\Omega \equiv \omega|\omega_{ci}$ of the wave frequency to the ion cyclotron frequency is also assumed to be vanishingly small, then the nature of the single boundary condition to be adopted in the limit σ−1 → 0 depends, for the slow hydromagnetic wave, on the limiting value of ρ½Ω2 . Similarly, if Ω [Gt ] 1, and the fast hydromagnetic wave is being considered, then the relevant boundary condition is found to depend on the limiting value of Ωσ−½.

The ‘resistive’ waves that are found to accompany the fast and slow waves, in order to satisfy the boundary conditions for small but finite values of σ−1, are studied in some detail and their contribution to the wave damping is determined.

Type
Research Article
Copyright
© 1964 Cambridge University Press

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References

Jephcott, D. F. & Stocker, P. M. 1962 J. Fluid Mech. 13, 587.
Klozenberg, McNammara & Thonemann 1963 Culham Lab. Mem. CLM M25.
Woods, L. C. 1962 J. Fluid Mech. 13, 570.