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

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, 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.