On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < U_c, where U_c is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, U_c is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U^* > U_c is introduced due to the finiteness of the system. When U_c < U < U^*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U^*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.