Effects of an Electrically Conducting Inner Core on Planetary and Stellar Dynamos

Abstract

The influence of an electrically conducting inner core on the characteristics of kinematic spherical α2 dynamos is investigated both analytically and numerically. Emphasis is placed on the magnetic coupling between the outer turbulent fluid spherical shell where magnetic fields are generated and the electrically conducting inner core, which can control the way in which the magnetic field in the shell is produced. We illustrate the subtlety of the electromagnetic boundary conditions at the core-shell interface: continuity of the radial magnetic field, continuity of the tangential electric field, and continuity of the tangential magnetic field. In the special cases of zero and infinite core electrical conductivity, the core-shell interface conditions take different explicit forms and in the latter case depend on whether the dynamo is stationary or oscillatory. Dynamo solutions depend on η, the ratio of inner to outer shell radius; β, the ratio of core to shell magnetic diffusivity; α(r), the radially dependent α function in the outer turbulent fluid spherical shell; and Rα, the magnetic Reynolds number of the shell. For small cores, η 5.3. Time-dependent dynamo behavior can arise from the α-effect alone in the presence of a sufficiently large and electrically conducting inner core. This phenomenon could be relevant to the solar dynamo for which η = 0.8 and β = 10-3. It could also be relevant to the dynamos of planets with sufficiently large inner cores; Earth's inner core is too small, however, for the oscillatory phenomenon to be directly applicable to the geodynamo.