Combined Taylor and Helmholtz instability in hydromagnetics including Hall effect

The problem of combined Rayleigh—Taylor and Kelvin—Helmholtz instability for incompressible plasmas carrying a uniform magnetic field is investigated taking account of the Hall current. The resistivity and the finite ion Larmor radius effects are left out. It is found that the finite Larmor frequency is destabilizing in nature. The growth rate of an otherwise (without the Hall current) unstable configuration is increased, and unstable modes may be produced in otherwise stable situations for reasonably large values of the Hall current. The Hall effect also results in overstable modes.