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, $\Omega \equiv \omega|\omega_{ci}$ 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.