Hydromagnetic surface waves

Abstract

The ASW propagates as a dispersive wave along the boundaries of a bounded plasma column. At the interface of a plasma slab surrounded by two identical plasma media, two modes-symmetric and asymmetric-propagate with a phase velocity lying between the bulk Alf wave velocities of the two media. The phase velocities of both modes increase with increasing values of a, showing that the higher the magnetic field outside than inside the column, the higher will be the phase velocity of ASW. When a < ?, the group velocity of the symmetric modes is less than the phase velocity and vice versa for asymmetric modes, i.e., the symmetric modes have normal dispersion while the asymmetric modes have anomalous dispersion (Pain, 1968). When the plasma slab is surrounded by two different media, then also two modes of ASW exist. The two modes do not separate into symmetric or asymmetric modes but are coupled. The change in magnetic field strength or density in any one of the three media alters the characteristics of both modes. A cylindrical plasma column supports ASW, dispersive in nature. At the plasma杤acuum interface, the phase velocity of the surface wave is always greater than the bulk Alfv閚 wave velocity. However, when the plasma cylinder is surrounded by another plasma, the phase velocity of the ASW lies in between the bulk Alfv閚 wave velocities of the two media. In this case, the symmetric mode propagates in the frequency range (?g), which can be made very narrow by taking a very small, resulting in very little dispersion. The most important result is that there exists a critical wavenumber kc=1.59/ak_c = 1.59/akc=1.59/a for the asymmetric mode at which the phase and group velocities become equal, i.e., the ASW becomes nondispersive. This feature appears even when the plasma is surrounded by vacuum. For a < ?, the symmetric modes have normal dispersion, but the asymmetric mode for k < k_c has anomalous dispersion, whereas for k > k_c it has normal dispersion, and vice versa for a > ?. At a� = ?, only the bulk modes exist. It will be of interest to observe the ASW properties discussed here in the laboratory. We point out that the presence of the thin magnetospheric boundary layer plays an important role in affecting the propagation characteristics and decay lengths of the magnetospheric hydromagnetic surface waves. Depending on the change in the magnitude of Alfv閚 velocities across the boundary layer on either side, there exists a possibility of excitation of a long-range surface mode, the range being more than one order of magnitude greater than that in the absence of the boundary layer for large wave propagation angles. A cylindrical plasma column supports ASW, dispersive in nature. At the plasma杤acuum interface, the phase velocity of the surface wave is always greater than the bulk Alfv閚 wave velocity. However, when the plasma cylinder is surrounded by another plasma, the phase velocity of the ASW lies in between the bulk Alfv閚 wave velocities of the two media. In this case, the symmetric mode propagates in the frequency range (?g), which can be made very narrow by taking a very small, resulting in very little dispersion. The most important result is that there exists a critical wavenumber kc=1.59/ak_c = 1.59/akc=1.59/a for the asymmetric mode at which the phase and group velocities become equal, i.e., the ASW becomes nondispersive. This feature appears even when the plasma is surrounded by vacuum. For a < ?, the symmetric modes have normal dispersion, but the asymmetric mode for k < k_c has anomalous dispersion, whereas for k > k_c it has normal dispersion, and vice versa for a > ?. At a� = ?, only the bulk modes exist. It will be of interest to observe the ASW properties discussed here in the laboratory.